Stable Service Patterns in Scheduled

Transport Competition

Peran van Reeven and Maarten C W Janssen

Address for correspondence Peran van Reeven Department of Applied EconomicsErasmus University Rotterdam Burg Oudlaan 50 NL-3062 PA Rotterdam TheNetherlands (vanreevenfeweurnl) Maarten Janssen is also at Erasmus UniversityRotterdam

The authors thank Vladimir Karamychev and two anonymous referees for helpfulcomments and suggestions and especially one of the referees for pointing out a problemin the analysis

Abstract

In a horizontal product differentiation model it is shown that a stable service pattern inscheduled transport competition only exists if consumers are sufficiently sensitive to the

quality of non-scheduling service characteristics Since this sensitivity is related to traveldistance the modelling results can explain why competition in local public transportresults in unstable service patterns while competition in longer-distance air transport doesnot have the same problem

Date of receipt of final manuscript February 2005

135

Journal of Transport Economics and Policy Volume 40 Part 1 January 2006 pp 135ndash160

10 Introduction

In Western Europe most public and private sector companies in local andregional public transport have long-lasting exclusive rights that are increas-ingly tendered for (for example Sweden and France) Bus companies inGreat Britain are the exception In 1985 the British government removedquantity regulation from the provision of local bus services allowing busoperators to compete freely In addition services that are not producedin the market are tendered (such as late night and Sunday services) Conse-quently British operators including those in metropolitan areas (exceptLondon) have been subject to on-the-road competition since 1986 Thisexperience with on-the-road competition in British urban areas led policymakers to believe that competition eventuates in unstable service patternsand low levels of integration of services so that competitive tendering ofexclusive rights has become the leading concept for opening the marketin public transport1

This approach to competition in urban public transport is also reminis-cent of some ancient practices of bus operatorsdrivers Competitionbetween privately-operated buses had led to unsafe situations due notonly to the roadworthiness of vehicles but also to the on-the-road behav-iour of bus drivers and the scheduling strategies of operators trying to out-smart each other to get customers on board These consumers generallyboarded the first bus that arrived and bought a ticket on the bus Thesepractices led to the regulation of public transport in Western Europearound 1930 Foster (1985) and Foster and Golay (1986) have given anoverview of practices before regulation These practices can be distin-guished on the basis of whether they relate to scheduling or to behaviouron the road

A familiar practice with regard to scheduling behaviour is lsquoheadrunningrsquo when an operator schedules a bus just before a rivalrsquos Otherstrategies operators use for gaining market share andor forcing thecompetitor out of business that are closely related to lsquohead runningrsquo arelsquoschedule-matchingrsquo mdash putting a bus at the same published time as a rivalrsquoslsquonursingrsquo mdash scheduling a bus that accompanies a rivalrsquos bus and getting asmuch traffic away from it as possible and lsquoblanketingrsquo mdash nursing with twobuses (one before and one after the rival bus) These strategies clearly lead

1Proposal from the European Commission of 26 July 2000 for a Regulation of the European Parliament

and of the Council on action by Member States concerning public service requirements and the award

of public service contracts in passenger transport by rail road and inland waterway COM(2000)7

provisional pp 5 and 9

Journal of Transport Economics and Policy Volume 40 Part 1

136

to unstable service patterns In reaction to such practices by a competitoran operator can always improve its position by choosing another time ofdeparture

lsquoHead runningrsquo also creates counterpart behaviour on the roadlsquoHanging backrsquo lsquohanging the roadrsquo or lsquocrawlingrsquo means that buses goslowly so as to pick up as much traffic as possible that would otherwisego with the bus behind A variant is lsquowaitingrsquo at a bus stop until the bushas a fuller load or until the next bus comes over the horizon lsquoPassingrsquoor lsquoovertakingrsquo means that a bus that is behind tries to get in front of thecompetitor Related to this are lsquotailingrsquo namely keeping just behind anotherbus to overtake it or lsquocut inrsquo and lsquochasingrsquo with the same objective ofovertaking a bus in front or lsquocutting inrsquo These practices are likely toresult in lsquoleapfroggingrsquo or lsquojockeyingrsquo a situation in which buses continuallypass and re-pass each other Alternatively a bus driver can decide to golsquomissingrsquo at a bus stop or lsquoracingrsquo that is missing several bus stopsQuite similar is lsquoturningrsquo a bus before the end of the route and driving itback in the opposite direction These last strategies are not only relevantwith regard to scheduling competition but may also occur if demand atcertain places along the line is expected to be low

There is persistent anecdotal evidence that these practices recurred inthe early years of British deregulation However a microanalysis of thesepractices has never been carried out The effects of deregulation haveonly been studied at a sector (meso) level (for example Mackie et al1995 Tyson 1992) and it has become increasingly difficult to carry out amicroanalysis Operators learned quite fast that merger and acquisitionwere superior strategies to competition resulting in market concentrationThere are currently five bus groups dominating the UK market withterritorial monopolies throughout the country allowing locally basedsmall operators to operate some fringe services The market can be consid-ered to be settled Hence it appears that competition on the road was notsustainable Sector studies have given some indication of instability Animportant indication is the large number of changes in services thatoperators register Tyson (1992) indicates that in the seven metropolitanareas a total of 9628 registration changes were made in 1990 (and 9566in 1989)

This instability of service provision does not appear to be a problem inair transport also a scheduled transport mode Air transport in the UnitedStates was deregulated in 1978 followed by intra-European (EuropeanUnion) air transport in 1997 In both cases unstable scheduling did notsurface For interregional bus services in Great Britain there is a mixedpattern The initial positive experience with the deregulation of inter-regional bus services in 1980 gave rise to the deregulation of local and

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

137

regional bus services The British government argued that fares had beenreduced new services had been provided bus usage had increased andbetter quality services had been introduced and as a consequence proposedto extend deregulation to all bus services (Banister 1985) However analy-sis of the results over a longer period of time showed that competition didnot always lead to stable service patterns particularly for shorter distances(Douglas 1987) Comparison of these experiences with competition indifferent scheduled transport modes gives the impression that schedulingstability depends on the length of the journey

Consumers can be assumed to select an operator on the basis of threefactors scheduling price and quality It is not yet clear how operatorstrade-off these factors in competition whether they copy each othersrsquostrategies or whether they successfully attempt to differentiate on thebasis of one or more factors There are a number of intuitions withregard to scheduling pricing and quality strategies that need to beexplained in relation to each other

Scheduling seems to provide little opportunity for operators to distin-guish themselves An operator can easily copy departure times frequencyand originndashdestination pairs from another operator Operating the sametypes of vehicles between the same nodes and on the same routes do notallow for many elements of sustainable differentiation between operatorsThese outputs only become distinctive if the size of operations differs Pro-viding a larger network increases the chance that a service is available thatcorresponds to the specific basic transport needs of a consumer Cancianet al (1995) showed that competition between television news programmeson the basis of choosing broadcasting times alone is insufficient to createa stable equilibrium (Nash in pure strategies) Their model assumes acircular market with a uniform distribution of consumers along thecircle consumers who can only view news programmes at times that arelater than their preferred time (that is after coming home from workstudy and so on) and two stations that both have to choose a broadcastingtime This model shows that each station wants to broadcast just before itscompetitorrsquos in order to catch the largest audience possible for their newsprogramme A simple parallel can be made with scheduled transportThe model would then result in operators who want to schedule theirdepartures just in front of their competitors

In scheduled transport it has been argued that operators do not com-pete in prices Mackie et al (1995 p 241) state for local bus transportthat lsquo fares are not a particularly potent marketing weapon On a typical2 mile journey with a full cash fare of 50 pence a ride time of 15 minutesand walk and wait time of 15 minutes and a value of time of 2 pence perminute of in-vehicle time fare is less than one third of generalized costs

Journal of Transport Economics and Policy Volume 40 Part 1

138

The impulse to board the first bus is strong correspondingly the firstmarketing imperative is on service rather than on farersquo This hypothesis isbased on the observation that fares did not decrease after deregulationas was expected

Another hypothesis given for the same observation is that (ibid)lsquo operators recognize that fare competition is mutually destructiveReaction periods are short the serious entrant knows that price initiativeswill be instantly matched by the incumbentrsquo indicating that fare competi-tion is too strong a marketing weapon in the sense that even a few penceprice difference would become a highly visible and tangible sales advantagethat no operator can concede to its competitor This hypothesis has alsobeen expressed as an argument against the deregulation of US domesticair transport Although price competition was one of the main argumentsfor deregulation Brenner (1975) argued that an operator usually finds itless costly to follow a fare reduction and remain competitive rather thanto lose market share

Intuitively the first intuition seems to be relevant for short-distancetravel in which a few per cent difference in fares is insignificant in absoluteterms while waiting time at the bus stop is a significant component of totaltravel time and considered rather unpleasant The second intuition seems tobe relevant for long-distance travel in which a few per cent difference infares is a significant amount in absolute terms while waiting time con-stitutes only a small share of the total travel time

With regard to quality elements one of the greatest challenges for anyoperator is to establish such product differentiation in a meaningful fashionand by doing so to create consumer loyalty that determines consumersrsquotravel behaviour Many of the elements in which differences exist are bytheir nature subjective Examples are friendliness and courtesy ofpersonnel vehicle type interior design seats mealssnacks loungesadvertising image and so on Differentiation gives consumers differentpreferences for the services of one operator over others Long-distancetrips differ from short-distance trips in this respect Consumers are moresensitive to quality aspects in long-distance trips than in short-distancetrips so operators in long-distance passenger transport are better able todifferentiate themselves

These intuitions will be clarified by putting them in their context It willbe demonstrated that the sensitivity to quality without excluding otherfactors that may also play a role can explain the difference in schedulingstability between long-distance and short-distance scheduled transportThis will be done by analysing a circular horizontal differentiation modelin which two scheduled transport operators compete for consumers In con-trast to a similar circular horizontal differentiation model used by Cancian

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

139

et al (1995) operators are not only able to choose times of departure butalso fares and quality of service offered Horizontal product differentiationimplies that there is no univocal ranking of products among consumersFor example different consumers have different preferences for thecolour design of vehicles By contrast in the case of vertical differentiationall consumers have the same preference ranking over alternatives Forexample one can safely assume that all consumers prefer more seatingspace Basically the differentiation in quality that is considered in thispaper has both horizontal and vertical aspects In order not to complicatethe analysis too much we focus on horizontal differentiation only Prob-ably the most dominant factor differentiating operators are consumerloyalty programmes and they create horizontal differentiation betweenoperators On the basis of Neven and Thisse (1990) Ansari et al (1998)and Irmen and Thisse (1998) it can be expected that focusing on verticaldifferentiation does not qualitatively affect the results we obtain concerningscheduling decisions

The rest of this paper proceeds as follows Section 2 outlines thespecification of the model Section 3 analyses operatorsrsquo scheduling behav-iour Section 4 gives an interpretation of the modelling results FinallySection 5 draws some conclusions Technical extensions of the model anddetails of the proofs can be found in Appendices A and B respectively

20 The Model

Stability in competition is analysed through a horizontal product differen-tiation model This model describes a situation in which two operatorscompete for consumers on a fixed originndashdestination pair Both operatorsare assumed to use similar production technology Consumersrsquo preferencesfor these services are uniformly distributed over a two-dimensional locationspace Their preferences are indicated by ethxi yiTHORN The x-axis takes the formof a circumference and indicates a consumerrsquos specific preferred time ofdeparture This circumference realistically presents any repetitive timesegment (such as an hour or a day) of the combined schedule of both opera-tors The circumference is x 2 frac120 1 For simplicity both operators operateonly one service or departure per time period x 2 frac120 1 The y-axis thewidth of the circumference indicates specific consumer tastes with regardto other aspects of product differentiation The width of the circumferenceis assumed to be y 2 frac120 1 This gives an upper limit to the differentiationthat is considered Both operators determine their products by choosingdeparture time x and their y

Journal of Transport Economics and Policy Volume 40 Part 1

140

Consumers incur costs for a deviation from their preferred departuretime (x-axis) The non-availability of a departure at the preferred timecreates a disutility This waiting of a consumer for a departure is subjectto a directional constraint in both short-distance and long-distance trans-port In local public transport consumers often do not know the timetablebut they have a notion with regard to the level of frequency Given a highfrequency of departures they simply go to a stop at their preferred traveltime and wait for a vehicle to arrive Upon arrival at the stop a consumerwaits for subsequent vehicles to arrive those that have already passed thestop are gone Consumers take departures following their arrival at theplace of departure which is a backward constraint on consumersrsquo waitingThis travel behaviour is often implicitly or explicitly assumed in publictransport models (Evans 1987) In long-distance transport (such as airtravel) when frequency is not that high consumers know the timetableand plan their trip on the basis of the required time of arrival at the desti-nation This situation has also a directional constraint on consumersrsquo travelbehaviour A consumer can only leave home or work earlier in order to takedepartures before the one that arrives at the preferred time (for example tomake an appointment) Later departures are too late A consumer can onlytake departures that arrive before the consumerrsquos required arrival time (seeCancian et al 1995) which implies a forward constraint to consumersrsquowaiting Our model analyses the case of a backward constraint Using aforward constraint would give rise to mirror image results for the locationstrategies of operators on the circumference

Consumers also incur costs for a deviation from their preferred quality(y-axis) Deviations from preferred quality are assumed to imply quadraticcosts Perceived discomfortirritation can be considered to increase non-linearly (that is convex) as the deviation from preferred quality increasesIn Appendix A it is shown that there is no subgame perfect Nashequilibrium in pure strategies if these costs are taken to be linear creatingan unstable service pattern

By contrast linear waiting costs are assumed for the non-availabilityof a departure at the time desired The value of waiting time is basedon the value of alternative uses of time (opportunity costs) The value ofalternative uses of time can often be related to salary or in the case ofgoods transport the interest cost of capital These costs are linear intime

The prices charged the deviation from the preferred departure time (x-axis) and the deviation from preferred quality can be traded off againsteach other If the departure time of a service deviates from a consumerrsquospreferred time the consumer incurs costs of t per time period x Similarlyif the service deviates from a consumerrsquos preferred variety the consumer

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

141

incurs costs of j per unit y Consequently the utility U for a consumer ilocated at ethxi yiTHORN and travelling with operator 1 or 2 respectively are

Uieth1THORN frac14 V p1 teth1 xiTHORN jethy1 yiTHORN2

Uieth2THORN frac14V p2 tethx2 xiTHORN jethy2 yiTHORN2 if 0 lt xi 4x2

V p2 teth1thorn x2 xiTHORN jethy2 yiTHORN2 if x2 lt xi 4 1

(

where V is the maximum willingness to pay p1 and p2 are the prices ofoperators 1 and 2 respectively x2 is the time difference between both opera-torsrsquo departures and y1 and y2 are the respective locations of operator 1and 2 with respect to the quality they offer The maximum willingness topay reflects the existence of competition from other modes and competitionbetween alternative ways of spending time (not all requiring transport) Forsimplicity it is assumed that V is sufficiently large The x-axis locations ofboth operatorsrsquo departures are normalised around the location of departureof operator 1 This implies that the location of operator 1 x1 is 0 byassumption and that the location of operator 2 x2 is reinterpreted as thetime between both operatorsrsquo departures This time is measured as theclockwise distance of operator 2rsquos location of departure from operator1rsquos location of departure With regard to the y-axis locations it is assumedthat y25 y1 This assumption does not influence the results in a qualitativeway because quality differentiation is horizontal

Since both operators provide a single departure and share identical pro-duction technologies the production costs of both operators are assumedto be C These production costs can be left out of consideration becausethey do not qualitatively affect the strategies of operators Consequentlyprofits are given by p1 frac14 p1D1 and p2 frac14 p2D2 where D1 and D2 are thedemands of operator 1 and operator 2 respectively The decisions ofoperators are modelled in a dynamic two-stage game In the first stageboth operators simultaneously determine their products by choosinglocations x2 y1 and y2 In the second stage operators choose prices Thisorder reflects the fact that prices are easily changed at very short noticeScheduling decisions and quality are more difficult and require more timeto implement

The two stages of the game are subgames of the overall game Servicepatterns will only be stable if in the overall game there exists a subgameperfect Nash equilibrium in pure strategies Dynamic games are solvedby backward induction At stage 1 operators anticipate their optimalstrategies at stage 2 and establish their optimal strategies for stage 1accordingly Consequently the two stages of the overall game need to beanalysed in reverse order This generates two questions First at stage 2given any chosen locations of departures and qualities what are the

Journal of Transport Economics and Policy Volume 40 Part 1

142

equilibrium prices p1 and p2 Second at stage 1 what is the optimal choiceof locations of departures and qualities for both operators taking the effecton prices into account

Operatorsrsquo demands can be established by equating the utility functionsfor consumers with a preferred departure time of 0 lt xi 4x2 andx2 lt xi 4 1 respectively This generates the indifferent consumers whoget the same utility from using either the service of operator 1 or that ofoperator 2 that is

y frac14 p2 p1 teth1 x2THORN thorn jethy22 y21THORN2jethy2 y1THORN

for 0 lt xi 4x2

and

yy frac14 p2 p1 thorn tx2 thorn jethy22 y21THORN2jethy2 y1THORN

for x2 lt xi 4 1

It is noted that y lt yyA graphical representation in case the indifferent consumers y yy belong

to the interval [01] is given in Figure 1 where the area above the linesegments that position the indifferent consumer represents the demandfor operator 2 and the area under these line segments represent thedemand for operator 1

This figure shows that of the consumers with a preferred departure timeof 0 lt xi 4x2 a total of x2eth1 yTHORN will choose operator 2 because it offersthe closest departure The other consumers with a preferred departuretime 0 lt xi 4x2 a total of x2 y prefer to pass operator 2rsquos departureand wait for the departure of operator 1 For these consumers the bettermatch of the service of operator 1 with their quality preferences com-pensates for the longer waiting time Similarly of the consumers whohave a preferred departure time of x2 lt xi 4 1 a total of eth1 x2THORNyy prefer

Figure 1Representation of indifferent consumer if y yy 2 frac120 1

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

143

operator 1 which offers the closest departures and a total ofeth1 x2THORNeth1 yyTHORN prefer to pass the departure of operator 1 and wait forthe departure of operator 2

30 Analysis

The main question is whether there exists a stable service pattern and if sounder what conditions This boils down to looking for a subgame perfectNash equilibrium in pure strategies

Proposition 1 If consumers are sufficiently sensitive to quality that is j5 t asubgame perfect Nash equilibrium in pure strategies exists where for anylocation x2 that is the distance between the departure times of operator 1and 2 equilibrium locations in quality and fares are given by y1 frac14 0 y2 frac14 1and p1 frac14 p2 frac14 j In such an equilibrium the location x2 is undetermined Incontrast if consumers are insufficiently sensitive to quality there is nosubgame perfect Nash equilibrium in pure strategies

Proof As shown above the respective demands if y yy 2 frac120 1 will be

D1 frac14 x2

p2 p1 teth1 x2THORN thorn jethy22 y21THORN

2jethy2 y1THORN

thorn eth1 x2THORNp2 p1 thorn tx2 thorn jethy22 y21THORN

2jethy2 y1THORN

and

D2 frac14 x2

1 p2 p1 teth1 x2THORN thorn jethy22 y21THORN

2jethy2 y1THORN

thorn eth1 x2THORN1 p2 p1 thorn tx2 thorn jethy22 y21THORN

2jethy2 y1THORN

These demands for operator 1 and operator 2 can be rewritten as

D1 frac14p2 p1 thorn jethy22 y21THORN

2jethy2 y1THORNand D2 frac14 1thorn p1 p2 jethy22 y21THORN

2jethy2 y1THORN

It should be noted that these demands do not depend on x2 Con-sequently both operators are indifferent with regard to the distancebetween their departures This implies that an operator has no incentiveto change a location in reaction to the location of its competitor

Journal of Transport Economics and Policy Volume 40 Part 1

144

On the basis of these demands profits for operator 1 and operator 2 willbe

p1 frac14 p1

p2 p1 thorn jethy22 y21THORN

2jethy2 y1THORN

and p2 frac14 p2

1thorn p1 p2 jethy22 y21THORN

2jethy2 y1THORN

Maximising these profits with respect to fares gives the followingreaction curves

p1 frac14p2 thorn jethy22 y21THORN

2and p2 frac14

p1 thorn 2jethy2 y1THORN jethy22 y21THORN2

Substituting these reaction curves into each other gives the subgameperfect prices

p1 frac142jethy2 y1THORN thorn jethy22 y21THORN

3and p2 frac14

4jethy2 y1THORN jethy22 y21THORN3

Substituting the subgame perfect prices into the expression for demandand multiplying these by their own prices generates the following equili-brium profits

p1 frac14eth2jethy2 y1THORN thorn jethy22 y21THORNTHORN2

18jethy2 y1THORNand p2 frac14

eth4jethy2 y1THORN jethy22 y21THORNTHORN2

18jethy2 y1THORN

Maximising the profits with respect to the location of quality gives

p1y1

frac14 frac122jethy2 y1THORN thorn jethy22 y21THORNfrac12jethy22 y21THORN 4y1jethy2 y1THORN 2jethy2 y1THORN18jethy2 y1THORN2

and

p2y2

frac14 frac124jethy2 y1THORN jethy22 y21THORNfrac12jethy22 y21THORN 4y2jethy2 y1THORN thorn 4jethy2 y1THORN18jethy2 y1THORN2

The expressions show that p1=y1 lt 0 and p2=y2 gt 0 Henceoperator 1 will choose to offer quality y1 frac14 0 and operator 2 will offery2 frac14 1 Substituting these locations into the subgame perfect prices andequilibrium profits gives p1 frac14 p2 frac14 j and p1 frac14 p2 frac14 j=2 respectively Anoperator cannot generate higher profits by deviating from this differentia-tion in quality and associated fares if the conditions for this division ofdemand between both operators are satisfied that is y yy 2 frac120 1 Substitut-ing the equilibrium qualities y1 frac14 0 y2 frac14 1 and prices p1 frac14 p2 frac14 j into

y frac14 p2 p1 teth1 x2THORN thorn jethy22 y21THORN2jethy2 y1THORN

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

145

shows that y 2 frac120 1 if j5 teth1 x2THORN Doing the same for

yy frac14 p2 p1 thorn tx2 thorn jethy22 y21THORN2jethy2 y1THORN

shows that yy 2 frac120 1 if j5 tx2 Consequently

p1p2 frac14 j=2 if

j5 teth1 x2THORN for 04x2 lt 1=2

j5 tx2 for 1=24 x2 4 1

These conditions will be fulfilled for any x2 2 frac120 1 if j5 t so that anecessary condition for equilibrium is that the sensitivity to quality issufficiently large in relation to the perceived inconvenience of lsquowaitingrsquo

It has to be checked whether the operators cannot realise a higherprofit than p1 p

2 by choosing qualities and prices so that the indifferent

consumers y andor the indifferent consumers yy have a preferred qualityoutside the area defined by y yy 2 frac120 1 Figure 2 shows the situation inwhich one of the operators deviates from his equilibrium strategy bychoosing quality or price so that y lt 0 and yy 2 frac120 1

In Appendix A it has been shown that both operators cannot realisehigher profits by deviating from their equilibrium strategy by choosinglocations and prices so that either ethy lt 0 yy 2 frac120 1THORN or ethy 2 frac120 1 yy gt 1THORN

If the sensitivity to quality is sufficiently small in relation to theperceived inconvenience of waiting that is if

j ltt

2ethy2 y1THORN

then yy y gt 1 and it must be that ethy lt 0 yy 2 frac120 1THORN ethy 2 frac120 1 yy gt 1THORN orethy lt 0 yy gt 1THORN In Appendix A it has also been shown that no Nash

Figure 2Representation of indifferent consumer if ethy lt 0 yy 2 frac120 1THORN

Journal of Transport Economics and Policy Volume 40 Part 1

146

equilibrium in pure strategies exists if ethy lt 0 yy 2 frac120 1THORN orethy 2 frac120 1 yy gt 1THORN The division of demand if ethy lt 0 yy gt 1THORN is shown inFigure 3

In this division of demand the respective demands for operator 1and operator 2 are D1 frac14 1 x2 and D2 frac14 x2 so that the profits will bep1 frac14 p1eth1 x2THORN and p2 frac14 p2x2 It can be easily seen from these profitsthat there are no subgame perfect equilibrium prices And even if therewere then operators would not prefer the same distance x2 between depar-tures Operator 1 would like to have a zero distance that is x2 frac14 0 betweenboth operatorsrsquo locations and operator 2 would prefer maximum distancethat is x2 frac14 1 between departures Consequently no Nash equilibrium inpure strategies exists in the division of demand if ethy lt 0 yy gt 1THORN

Consequently there is a subgame perfect Nash equilibrium in purestrategies if the sensitivity to quality is sufficiently large that is if j5 tbut no Nash equilibrium in pure strategies exists if this sensitivity to qualityis sufficiently small

40 Interpretation of Results

The difference in consumersrsquo sensitivity to quality could explain whycompetition in local bus transport results in unstable service patternswhile air transport does not seem to have the same problem

41 Short-distance transport

Given the short-distances travelled operators in local bus transport havevery limited scope for meaningful product differentiation that could

Figure 3Representation of indifferent consumer if ethy lt 0 yy gt 1THORN

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

147

make consumers loyal A consumer will generally take the first bus thatarrives at the stop This occurs in the division of demand of Figure 3 Inthat case each operator prefers a different distance between departuretimes and will continuously try to attain his preferred distance The pre-ferred distance between departures for both operators is conflicting andno subgame perfect equilibrium in pure strategies with regard to thetiming of departures exists

This result corresponds to the generally-shared view on competition inurban public transport in continental Europe The European Commissionin its proposal for new regulation of the award of public service contractsin public transport by Member States articulates this view stating thatwithout exclusive rights lsquoservice patterns are unstablersquo2 This perceptionis based on the experiences in Great Britain of the deregulation of localpublic transport

Evans (1990) and Mackie et al (1995) observed that after deregulationof local public transport the number of travellers did not increase despitethe doubling of service levels (frequencies) and consequent reductions inwaiting times This lsquopuzzling resultrsquo could not be explained by the declinein bus usage due to higher real incomes and lower real motoring costsOne explanation that has been put forward was that frequency increasesare compensated by offsetting effects for example uncertainty caused topassengers by route instability such as irregular intervals frequently chan-ging timetables and so on (Evans 1990 Mackie et al 1995)

The model for low consumer sensitivity to quality predicts this instabil-ity of service patterns In the division of demand of Figure 3 the preferredlocation of operator 1 is just before the departure of operator 2 (x2 frac14 0)while operator 2 prefers a larger distance between departures (x2 gt 0)Given x2 frac14 0 operator 2 will choose a later departure but in reactionoperator 1 will follow in order to reduce the distance to x2 frac14 0 againand so on Basically every operator would like to be at a bus stop justbefore its competitor in order to take the whole market This implies thatoperators are lsquohead-runningrsquo each other

With regard to pricing Mackie et al (1995) stated that pricing is not aparticularly potent marketing weapon The first priority is on service ratherthan fares as travellers tend to board the first bus This behaviour of con-sumers is confirmed by the model for the situation in which an operatorrsquos

2Proposal from the European Commission of 26 July 2000 for a Regulation of the European Parliament

and of the Council on action by Member States concerning public service requirements and the award

of public service contracts in passenger transport by rail road and inland waterway COM(2000)7

provisional p 5

Journal of Transport Economics and Policy Volume 40 Part 1

148

demand is independent of prices and D1 frac14 1 x2 and D2 frac14 x2 In this casethe model shows that p1=p1 5 0 and p2=p25 0 Hence operators arecompeting over the timing of departures rather than pricing Evans statesthat (1990 p 266) lsquoThe operators match fares and tacitly collude to main-tain the pre-existing fare structure The operators also tacitly collude toincrease fares simultaneously at a rate at least as fast as inflation Faresremain the same on high-demand as on low-demand routes and on activelycompetitive as on non-competitive routesrsquo The model shows that theupward pressure on prices will only be limited by the maximum willingnessto pay Consequently the pricing discipline comes from external factorsfor example the existence of competition from another mode (such asprivate car cycling walking and so on) or competition between activitiesthat consumers can undertake (and that may or may not require transport)This clarifies why fares move at a similar rate to inflation and are notrelated to the level of demand on a route or the level of competition on aroute

42 Long-distance transport

In long-distance transport such as air transport consumers are moresensitive to quality Travel times are much longer and consequently con-sumers are more appreciative of comfort This allows for much greaterquality differentiation than in short-distance travel Hence consumerswill more easily take an alternative flight Non-price and non-schedulingfactors increase in importance for longer distances as can be seen for airtransport in the Table 1

The factors as distinguished in the Avmark Aviation Economist arelsquoschedulersquo lsquofarersquo lsquoairlinersquo lsquoairplanersquo and lsquootherrsquo lsquoSchedulersquo and lsquofarersquo areequivalent to the endogenous variables lsquoschedulersquo and lsquopricersquo lsquoAirlinersquo

Table 1

Most Influential Factors in Choosing a Flight

Factors asdistinguishedby the model

Factors asdistinguishedby Source

Length of flight

Under 2 hours () 2ndash5 hours () Over 5 hours ()

Schedule Schedule 701 430 193

Price Fare 114 137 165

Quality Airline 155 362 530Airplane 25 66 102Other 05 06 10

Source Avmark Aviation EconomistIAPA in Gialloreto 1988

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

149

lsquoairplanersquo and lsquootherrsquo can be clustered into the variable lsquoqualityrsquo Pressuredby competition airlines have become increasingly creative and effective indifferentiating their services in terms of quality including the creation ofconsumer loyalty

This situation is described by a sufficient sensitivity to quality that isj5 t as depicted in Figure 1 Given this division of demand operatorsmaximally differentiate in quality that is y1 frac14 0 and y2 frac14 1 This qualitydifferentiation relaxes competition over scheduling The model showsthat an operator cannot improve his position by choosing another timeof departure given the time of departure of his competitor Stronger consu-mer loyalty eliminates operatorsrsquo incentive to lsquohead-runrsquo each other whichcreates a subgame perfect equilibrium in timing departures Intuitively onewould say that an operator who moves to a later point of time increases hismarket but sufficiently strong consumersrsquo sensitivity to quality balancesthis tendency Consumers tend to wait for the departure of their preferredoperator

With regard to price the intuition cannot be confirmed that operatorsdo not seem to compete on price because pricing is too strong a marketingweapon According to the model operators do compete in price Furtheranalysis is needed in order to ascertain whether (and if so why) operatorsdo not seem to compete in price in long-distance transport One obser-vation (Brenner 1975) has been that scheduled transport operators tendto rival each other on frequency instead of price Such competitionincreases costs putting upward pressure on prices which could offset anyreduction in price that is normally associated with the introduction ofcompetition

43 Short-distance vs long-distanceThe impact of travel distance on stability can also be seen in the deregula-tion of lsquolong-distancersquo bus services in Great Britain In 1980 the Britishgovernment abolished a system of quantity control in the express coachmarket The deregulation allowed for free entry and competition onroutes served by nationalised carriers Douglas (1987) made a thoroughassessment of the effects of this deregulation on market structure faresservice quality and costs using data provided by express coach operatorsHe showed that on short-distance connections independent operatorsentering the market were unable to develop a significant market sharesince the two national carriers simply matched or undercut their faresand increased or manipulated departure times (Douglas 1997) Only 39per cent of such services to and from London survived during the firstfew years of deregulation The national carriers maintained some competi-tive advantages after deregulation such as sole access to major and centrally

Journal of Transport Economics and Policy Volume 40 Part 1

150

located bus stations a considerable network of services and an extensivesales network This made them better able to survive than the newindependent operators on the market

On long-distance connections however several independents captureda permanent place in the market Specialisation by offering a premierquality service allowed the independents to build up immunity to thepurely fare and scheduling responses of nationalised carriers and thuscapture a share of the market (Douglas 1997) In this way the indepen-dents were especially successful on the Anglo-Scottish routes The longertravel distance offered operators greater scope for product differentiationConsequently more operators were able to provide services even if theydeparted at the same time In the first few years of deregulation 67 percent of new long-distance services to or from London survived Henceproduct differentiation on long-distance connections made entrants resis-tant to the pricing and scheduling responses of incumbent operators bycreating consumer loyalty stabilising scheduling competition

50 Conclusion

For operators in scheduled passenger transport it is a great marketingchallenge to create an image that is distinct from their competitorsOperating the same or similar types of vehicles on the same routes doesnot have many elements of visible tangible differentiation vis-a-viscompetitors Many of the elements in which differences do exist are bytheir nature subjective and difficult to prove to the sceptical consumerExamples are friendliness and courtesy of personnel interior designseats mealssnacks lounges advertising image and so on Long-distanceoperators are better able than short-distance operators to realise suchproduct differentiation in a meaningful fashion Over longer distancesconsumers are generally more flexible with regard to departure times andare more appreciative of their preferred quality of service

In a two-dimensional horizontal product differentiation model withlinear waiting costs for departures and non-linear sensitivity to deviationsfrom preferred quality of service it is shown that a stable service patternrequires consumers to be sufficiently sensitive to differences in qualitybetween operators In reaction operators will differentiate their productsin terms of quality This differentiation prevents consumers from simplytaking the vehicle that is closest to their preferred departure time Consu-mers will be inclined to take an earlier or later departure if they feel morecomfortable with that operator or if there are additional benefits provided

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

151

by this operator In contrast if consumers are not sensitive to qualitydifferences operators would prefer to schedule their vehicles just beforetheir competitor in order to lsquostealrsquo its customers

On the basis of Neven and Thisse (1990) Ansari et al (1998) andIrmen and Thisse (1998) it can be expected that this result will notchange if the dimension of quality differentiation is modelled as verticaldifferentiation rather than horizontal differentiation It is clear that thequality differentiation considered has not only horizontal but also verticalaspects One example is seat width and pitch For the same price everyconsumer would appreciate more space The most dominant factordifferentiating operators is probably an operatorrsquos consumer loyaltyprogramme and that creates horizontal differentiation A formalanalysis for the case of vertical differentiation is beyond the scope of thispaper

The sensitivity to quality differences is a plausible factor that couldclarify the difference in existence of a stable equilibrium between differentmodes of scheduled transport A modal spectrum can be created on thebasis of the relevance of quality differentiation for the selection of an opera-tor The low-relevance end of this spectrum includes examples as containerfreight operations (such as liner shipping) and local public transport Thehigh-relevance end would probably include inter-continental passengerair transport For the low-relevance modes experience shows that com-petition results in unstable service patterns For the high-relevance modestability has never appeared to be a problem

References

Ansari A N Economides and J Steckel (1998) lsquoThe Max-min-min Principle of ProductDifferentiationrsquo Journal of Regional Science 38 207ndash30

Banister B (1985) lsquoDeregulating the Bus Industry in Britain (A) the ProposalsrsquoTransport Reviews 5 99ndash103

Brenner M A (1975) lsquoNeed for Continued Economic Regulation of Air TransportrsquoJournal of Air Law and Commerce 41 793ndash813

Cancian M A Bills and T Bergstrom (1995) lsquoHotelling Location Problems withDirectional Constraints an Application to Television News Schedulingrsquo Journal ofIndustrial Economics 43 121ndash4

DrsquoAspremont C J Jaskold Gabszewicz and J-F Thisse (1979) lsquoOn HotellingrsquoslsquolsquoStability in competitionrsquorsquorsquo Econometrica 47 1145ndash50

Douglas N J (1987) A Welfare Assessment of Transport Deregulation The Case of theExpress Coach Market in 1980 Aldershot Gower

Evans A (1987) lsquoA Theoretical Comparison of Competition with Other EconomicRegimes for Bus Servicesrsquo Journal of Transport Economics and Policy 21 7ndash36

Journal of Transport Economics and Policy Volume 40 Part 1

152

10 Introduction

In Western Europe most public and private sector companies in local andregional public transport have long-lasting exclusive rights that are increas-ingly tendered for (for example Sweden and France) Bus companies inGreat Britain are the exception In 1985 the British government removedquantity regulation from the provision of local bus services allowing busoperators to compete freely In addition services that are not producedin the market are tendered (such as late night and Sunday services) Conse-quently British operators including those in metropolitan areas (exceptLondon) have been subject to on-the-road competition since 1986 Thisexperience with on-the-road competition in British urban areas led policymakers to believe that competition eventuates in unstable service patternsand low levels of integration of services so that competitive tendering ofexclusive rights has become the leading concept for opening the marketin public transport1

This approach to competition in urban public transport is also reminis-cent of some ancient practices of bus operatorsdrivers Competitionbetween privately-operated buses had led to unsafe situations due notonly to the roadworthiness of vehicles but also to the on-the-road behav-iour of bus drivers and the scheduling strategies of operators trying to out-smart each other to get customers on board These consumers generallyboarded the first bus that arrived and bought a ticket on the bus Thesepractices led to the regulation of public transport in Western Europearound 1930 Foster (1985) and Foster and Golay (1986) have given anoverview of practices before regulation These practices can be distin-guished on the basis of whether they relate to scheduling or to behaviouron the road

A familiar practice with regard to scheduling behaviour is lsquoheadrunningrsquo when an operator schedules a bus just before a rivalrsquos Otherstrategies operators use for gaining market share andor forcing thecompetitor out of business that are closely related to lsquohead runningrsquo arelsquoschedule-matchingrsquo mdash putting a bus at the same published time as a rivalrsquoslsquonursingrsquo mdash scheduling a bus that accompanies a rivalrsquos bus and getting asmuch traffic away from it as possible and lsquoblanketingrsquo mdash nursing with twobuses (one before and one after the rival bus) These strategies clearly lead

1Proposal from the European Commission of 26 July 2000 for a Regulation of the European Parliament

and of the Council on action by Member States concerning public service requirements and the award

of public service contracts in passenger transport by rail road and inland waterway COM(2000)7

provisional pp 5 and 9

Journal of Transport Economics and Policy Volume 40 Part 1

136

to unstable service patterns In reaction to such practices by a competitoran operator can always improve its position by choosing another time ofdeparture

lsquoHead runningrsquo also creates counterpart behaviour on the roadlsquoHanging backrsquo lsquohanging the roadrsquo or lsquocrawlingrsquo means that buses goslowly so as to pick up as much traffic as possible that would otherwisego with the bus behind A variant is lsquowaitingrsquo at a bus stop until the bushas a fuller load or until the next bus comes over the horizon lsquoPassingrsquoor lsquoovertakingrsquo means that a bus that is behind tries to get in front of thecompetitor Related to this are lsquotailingrsquo namely keeping just behind anotherbus to overtake it or lsquocut inrsquo and lsquochasingrsquo with the same objective ofovertaking a bus in front or lsquocutting inrsquo These practices are likely toresult in lsquoleapfroggingrsquo or lsquojockeyingrsquo a situation in which buses continuallypass and re-pass each other Alternatively a bus driver can decide to golsquomissingrsquo at a bus stop or lsquoracingrsquo that is missing several bus stopsQuite similar is lsquoturningrsquo a bus before the end of the route and driving itback in the opposite direction These last strategies are not only relevantwith regard to scheduling competition but may also occur if demand atcertain places along the line is expected to be low

There is persistent anecdotal evidence that these practices recurred inthe early years of British deregulation However a microanalysis of thesepractices has never been carried out The effects of deregulation haveonly been studied at a sector (meso) level (for example Mackie et al1995 Tyson 1992) and it has become increasingly difficult to carry out amicroanalysis Operators learned quite fast that merger and acquisitionwere superior strategies to competition resulting in market concentrationThere are currently five bus groups dominating the UK market withterritorial monopolies throughout the country allowing locally basedsmall operators to operate some fringe services The market can be consid-ered to be settled Hence it appears that competition on the road was notsustainable Sector studies have given some indication of instability Animportant indication is the large number of changes in services thatoperators register Tyson (1992) indicates that in the seven metropolitanareas a total of 9628 registration changes were made in 1990 (and 9566in 1989)

This instability of service provision does not appear to be a problem inair transport also a scheduled transport mode Air transport in the UnitedStates was deregulated in 1978 followed by intra-European (EuropeanUnion) air transport in 1997 In both cases unstable scheduling did notsurface For interregional bus services in Great Britain there is a mixedpattern The initial positive experience with the deregulation of inter-regional bus services in 1980 gave rise to the deregulation of local and

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

137

regional bus services The British government argued that fares had beenreduced new services had been provided bus usage had increased andbetter quality services had been introduced and as a consequence proposedto extend deregulation to all bus services (Banister 1985) However analy-sis of the results over a longer period of time showed that competition didnot always lead to stable service patterns particularly for shorter distances(Douglas 1987) Comparison of these experiences with competition indifferent scheduled transport modes gives the impression that schedulingstability depends on the length of the journey

Consumers can be assumed to select an operator on the basis of threefactors scheduling price and quality It is not yet clear how operatorstrade-off these factors in competition whether they copy each othersrsquostrategies or whether they successfully attempt to differentiate on thebasis of one or more factors There are a number of intuitions withregard to scheduling pricing and quality strategies that need to beexplained in relation to each other

Scheduling seems to provide little opportunity for operators to distin-guish themselves An operator can easily copy departure times frequencyand originndashdestination pairs from another operator Operating the sametypes of vehicles between the same nodes and on the same routes do notallow for many elements of sustainable differentiation between operatorsThese outputs only become distinctive if the size of operations differs Pro-viding a larger network increases the chance that a service is available thatcorresponds to the specific basic transport needs of a consumer Cancianet al (1995) showed that competition between television news programmeson the basis of choosing broadcasting times alone is insufficient to createa stable equilibrium (Nash in pure strategies) Their model assumes acircular market with a uniform distribution of consumers along thecircle consumers who can only view news programmes at times that arelater than their preferred time (that is after coming home from workstudy and so on) and two stations that both have to choose a broadcastingtime This model shows that each station wants to broadcast just before itscompetitorrsquos in order to catch the largest audience possible for their newsprogramme A simple parallel can be made with scheduled transportThe model would then result in operators who want to schedule theirdepartures just in front of their competitors

In scheduled transport it has been argued that operators do not com-pete in prices Mackie et al (1995 p 241) state for local bus transportthat lsquo fares are not a particularly potent marketing weapon On a typical2 mile journey with a full cash fare of 50 pence a ride time of 15 minutesand walk and wait time of 15 minutes and a value of time of 2 pence perminute of in-vehicle time fare is less than one third of generalized costs

Journal of Transport Economics and Policy Volume 40 Part 1

138

The impulse to board the first bus is strong correspondingly the firstmarketing imperative is on service rather than on farersquo This hypothesis isbased on the observation that fares did not decrease after deregulationas was expected

Another hypothesis given for the same observation is that (ibid)lsquo operators recognize that fare competition is mutually destructiveReaction periods are short the serious entrant knows that price initiativeswill be instantly matched by the incumbentrsquo indicating that fare competi-tion is too strong a marketing weapon in the sense that even a few penceprice difference would become a highly visible and tangible sales advantagethat no operator can concede to its competitor This hypothesis has alsobeen expressed as an argument against the deregulation of US domesticair transport Although price competition was one of the main argumentsfor deregulation Brenner (1975) argued that an operator usually finds itless costly to follow a fare reduction and remain competitive rather thanto lose market share

Intuitively the first intuition seems to be relevant for short-distancetravel in which a few per cent difference in fares is insignificant in absoluteterms while waiting time at the bus stop is a significant component of totaltravel time and considered rather unpleasant The second intuition seems tobe relevant for long-distance travel in which a few per cent difference infares is a significant amount in absolute terms while waiting time con-stitutes only a small share of the total travel time

With regard to quality elements one of the greatest challenges for anyoperator is to establish such product differentiation in a meaningful fashionand by doing so to create consumer loyalty that determines consumersrsquotravel behaviour Many of the elements in which differences exist are bytheir nature subjective Examples are friendliness and courtesy ofpersonnel vehicle type interior design seats mealssnacks loungesadvertising image and so on Differentiation gives consumers differentpreferences for the services of one operator over others Long-distancetrips differ from short-distance trips in this respect Consumers are moresensitive to quality aspects in long-distance trips than in short-distancetrips so operators in long-distance passenger transport are better able todifferentiate themselves

These intuitions will be clarified by putting them in their context It willbe demonstrated that the sensitivity to quality without excluding otherfactors that may also play a role can explain the difference in schedulingstability between long-distance and short-distance scheduled transportThis will be done by analysing a circular horizontal differentiation modelin which two scheduled transport operators compete for consumers In con-trast to a similar circular horizontal differentiation model used by Cancian

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

139

et al (1995) operators are not only able to choose times of departure butalso fares and quality of service offered Horizontal product differentiationimplies that there is no univocal ranking of products among consumersFor example different consumers have different preferences for thecolour design of vehicles By contrast in the case of vertical differentiationall consumers have the same preference ranking over alternatives Forexample one can safely assume that all consumers prefer more seatingspace Basically the differentiation in quality that is considered in thispaper has both horizontal and vertical aspects In order not to complicatethe analysis too much we focus on horizontal differentiation only Prob-ably the most dominant factor differentiating operators are consumerloyalty programmes and they create horizontal differentiation betweenoperators On the basis of Neven and Thisse (1990) Ansari et al (1998)and Irmen and Thisse (1998) it can be expected that focusing on verticaldifferentiation does not qualitatively affect the results we obtain concerningscheduling decisions

The rest of this paper proceeds as follows Section 2 outlines thespecification of the model Section 3 analyses operatorsrsquo scheduling behav-iour Section 4 gives an interpretation of the modelling results FinallySection 5 draws some conclusions Technical extensions of the model anddetails of the proofs can be found in Appendices A and B respectively

20 The Model

Stability in competition is analysed through a horizontal product differen-tiation model This model describes a situation in which two operatorscompete for consumers on a fixed originndashdestination pair Both operatorsare assumed to use similar production technology Consumersrsquo preferencesfor these services are uniformly distributed over a two-dimensional locationspace Their preferences are indicated by ethxi yiTHORN The x-axis takes the formof a circumference and indicates a consumerrsquos specific preferred time ofdeparture This circumference realistically presents any repetitive timesegment (such as an hour or a day) of the combined schedule of both opera-tors The circumference is x 2 frac120 1 For simplicity both operators operateonly one service or departure per time period x 2 frac120 1 The y-axis thewidth of the circumference indicates specific consumer tastes with regardto other aspects of product differentiation The width of the circumferenceis assumed to be y 2 frac120 1 This gives an upper limit to the differentiationthat is considered Both operators determine their products by choosingdeparture time x and their y

Journal of Transport Economics and Policy Volume 40 Part 1

140

Consumers incur costs for a deviation from their preferred departuretime (x-axis) The non-availability of a departure at the preferred timecreates a disutility This waiting of a consumer for a departure is subjectto a directional constraint in both short-distance and long-distance trans-port In local public transport consumers often do not know the timetablebut they have a notion with regard to the level of frequency Given a highfrequency of departures they simply go to a stop at their preferred traveltime and wait for a vehicle to arrive Upon arrival at the stop a consumerwaits for subsequent vehicles to arrive those that have already passed thestop are gone Consumers take departures following their arrival at theplace of departure which is a backward constraint on consumersrsquo waitingThis travel behaviour is often implicitly or explicitly assumed in publictransport models (Evans 1987) In long-distance transport (such as airtravel) when frequency is not that high consumers know the timetableand plan their trip on the basis of the required time of arrival at the desti-nation This situation has also a directional constraint on consumersrsquo travelbehaviour A consumer can only leave home or work earlier in order to takedepartures before the one that arrives at the preferred time (for example tomake an appointment) Later departures are too late A consumer can onlytake departures that arrive before the consumerrsquos required arrival time (seeCancian et al 1995) which implies a forward constraint to consumersrsquowaiting Our model analyses the case of a backward constraint Using aforward constraint would give rise to mirror image results for the locationstrategies of operators on the circumference

Consumers also incur costs for a deviation from their preferred quality(y-axis) Deviations from preferred quality are assumed to imply quadraticcosts Perceived discomfortirritation can be considered to increase non-linearly (that is convex) as the deviation from preferred quality increasesIn Appendix A it is shown that there is no subgame perfect Nashequilibrium in pure strategies if these costs are taken to be linear creatingan unstable service pattern

By contrast linear waiting costs are assumed for the non-availabilityof a departure at the time desired The value of waiting time is basedon the value of alternative uses of time (opportunity costs) The value ofalternative uses of time can often be related to salary or in the case ofgoods transport the interest cost of capital These costs are linear intime

The prices charged the deviation from the preferred departure time (x-axis) and the deviation from preferred quality can be traded off againsteach other If the departure time of a service deviates from a consumerrsquospreferred time the consumer incurs costs of t per time period x Similarlyif the service deviates from a consumerrsquos preferred variety the consumer

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

141

incurs costs of j per unit y Consequently the utility U for a consumer ilocated at ethxi yiTHORN and travelling with operator 1 or 2 respectively are

Uieth1THORN frac14 V p1 teth1 xiTHORN jethy1 yiTHORN2

Uieth2THORN frac14V p2 tethx2 xiTHORN jethy2 yiTHORN2 if 0 lt xi 4x2

V p2 teth1thorn x2 xiTHORN jethy2 yiTHORN2 if x2 lt xi 4 1

(

where V is the maximum willingness to pay p1 and p2 are the prices ofoperators 1 and 2 respectively x2 is the time difference between both opera-torsrsquo departures and y1 and y2 are the respective locations of operator 1and 2 with respect to the quality they offer The maximum willingness topay reflects the existence of competition from other modes and competitionbetween alternative ways of spending time (not all requiring transport) Forsimplicity it is assumed that V is sufficiently large The x-axis locations ofboth operatorsrsquo departures are normalised around the location of departureof operator 1 This implies that the location of operator 1 x1 is 0 byassumption and that the location of operator 2 x2 is reinterpreted as thetime between both operatorsrsquo departures This time is measured as theclockwise distance of operator 2rsquos location of departure from operator1rsquos location of departure With regard to the y-axis locations it is assumedthat y25 y1 This assumption does not influence the results in a qualitativeway because quality differentiation is horizontal

Since both operators provide a single departure and share identical pro-duction technologies the production costs of both operators are assumedto be C These production costs can be left out of consideration becausethey do not qualitatively affect the strategies of operators Consequentlyprofits are given by p1 frac14 p1D1 and p2 frac14 p2D2 where D1 and D2 are thedemands of operator 1 and operator 2 respectively The decisions ofoperators are modelled in a dynamic two-stage game In the first stageboth operators simultaneously determine their products by choosinglocations x2 y1 and y2 In the second stage operators choose prices Thisorder reflects the fact that prices are easily changed at very short noticeScheduling decisions and quality are more difficult and require more timeto implement

The two stages of the game are subgames of the overall game Servicepatterns will only be stable if in the overall game there exists a subgameperfect Nash equilibrium in pure strategies Dynamic games are solvedby backward induction At stage 1 operators anticipate their optimalstrategies at stage 2 and establish their optimal strategies for stage 1accordingly Consequently the two stages of the overall game need to beanalysed in reverse order This generates two questions First at stage 2given any chosen locations of departures and qualities what are the

Journal of Transport Economics and Policy Volume 40 Part 1

142

equilibrium prices p1 and p2 Second at stage 1 what is the optimal choiceof locations of departures and qualities for both operators taking the effecton prices into account

Operatorsrsquo demands can be established by equating the utility functionsfor consumers with a preferred departure time of 0 lt xi 4x2 andx2 lt xi 4 1 respectively This generates the indifferent consumers whoget the same utility from using either the service of operator 1 or that ofoperator 2 that is

y frac14 p2 p1 teth1 x2THORN thorn jethy22 y21THORN2jethy2 y1THORN

for 0 lt xi 4x2

and

yy frac14 p2 p1 thorn tx2 thorn jethy22 y21THORN2jethy2 y1THORN

for x2 lt xi 4 1

It is noted that y lt yyA graphical representation in case the indifferent consumers y yy belong

to the interval [01] is given in Figure 1 where the area above the linesegments that position the indifferent consumer represents the demandfor operator 2 and the area under these line segments represent thedemand for operator 1

This figure shows that of the consumers with a preferred departure timeof 0 lt xi 4x2 a total of x2eth1 yTHORN will choose operator 2 because it offersthe closest departure The other consumers with a preferred departuretime 0 lt xi 4x2 a total of x2 y prefer to pass operator 2rsquos departureand wait for the departure of operator 1 For these consumers the bettermatch of the service of operator 1 with their quality preferences com-pensates for the longer waiting time Similarly of the consumers whohave a preferred departure time of x2 lt xi 4 1 a total of eth1 x2THORNyy prefer

Figure 1Representation of indifferent consumer if y yy 2 frac120 1

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

143

operator 1 which offers the closest departures and a total ofeth1 x2THORNeth1 yyTHORN prefer to pass the departure of operator 1 and wait forthe departure of operator 2

30 Analysis

The main question is whether there exists a stable service pattern and if sounder what conditions This boils down to looking for a subgame perfectNash equilibrium in pure strategies

Proposition 1 If consumers are sufficiently sensitive to quality that is j5 t asubgame perfect Nash equilibrium in pure strategies exists where for anylocation x2 that is the distance between the departure times of operator 1and 2 equilibrium locations in quality and fares are given by y1 frac14 0 y2 frac14 1and p1 frac14 p2 frac14 j In such an equilibrium the location x2 is undetermined Incontrast if consumers are insufficiently sensitive to quality there is nosubgame perfect Nash equilibrium in pure strategies

Proof As shown above the respective demands if y yy 2 frac120 1 will be

D1 frac14 x2

p2 p1 teth1 x2THORN thorn jethy22 y21THORN

2jethy2 y1THORN

thorn eth1 x2THORNp2 p1 thorn tx2 thorn jethy22 y21THORN

2jethy2 y1THORN

and

D2 frac14 x2

1 p2 p1 teth1 x2THORN thorn jethy22 y21THORN

2jethy2 y1THORN

thorn eth1 x2THORN1 p2 p1 thorn tx2 thorn jethy22 y21THORN

2jethy2 y1THORN

These demands for operator 1 and operator 2 can be rewritten as

D1 frac14p2 p1 thorn jethy22 y21THORN

2jethy2 y1THORNand D2 frac14 1thorn p1 p2 jethy22 y21THORN

2jethy2 y1THORN

It should be noted that these demands do not depend on x2 Con-sequently both operators are indifferent with regard to the distancebetween their departures This implies that an operator has no incentiveto change a location in reaction to the location of its competitor

Journal of Transport Economics and Policy Volume 40 Part 1

144

On the basis of these demands profits for operator 1 and operator 2 willbe

p1 frac14 p1

p2 p1 thorn jethy22 y21THORN

2jethy2 y1THORN

and p2 frac14 p2

1thorn p1 p2 jethy22 y21THORN

2jethy2 y1THORN

Maximising these profits with respect to fares gives the followingreaction curves

p1 frac14p2 thorn jethy22 y21THORN

2and p2 frac14

p1 thorn 2jethy2 y1THORN jethy22 y21THORN2

Substituting these reaction curves into each other gives the subgameperfect prices

p1 frac142jethy2 y1THORN thorn jethy22 y21THORN

3and p2 frac14

4jethy2 y1THORN jethy22 y21THORN3

Substituting the subgame perfect prices into the expression for demandand multiplying these by their own prices generates the following equili-brium profits

p1 frac14eth2jethy2 y1THORN thorn jethy22 y21THORNTHORN2

18jethy2 y1THORNand p2 frac14

eth4jethy2 y1THORN jethy22 y21THORNTHORN2

18jethy2 y1THORN

Maximising the profits with respect to the location of quality gives

p1y1

frac14 frac122jethy2 y1THORN thorn jethy22 y21THORNfrac12jethy22 y21THORN 4y1jethy2 y1THORN 2jethy2 y1THORN18jethy2 y1THORN2

and

p2y2

frac14 frac124jethy2 y1THORN jethy22 y21THORNfrac12jethy22 y21THORN 4y2jethy2 y1THORN thorn 4jethy2 y1THORN18jethy2 y1THORN2

The expressions show that p1=y1 lt 0 and p2=y2 gt 0 Henceoperator 1 will choose to offer quality y1 frac14 0 and operator 2 will offery2 frac14 1 Substituting these locations into the subgame perfect prices andequilibrium profits gives p1 frac14 p2 frac14 j and p1 frac14 p2 frac14 j=2 respectively Anoperator cannot generate higher profits by deviating from this differentia-tion in quality and associated fares if the conditions for this division ofdemand between both operators are satisfied that is y yy 2 frac120 1 Substitut-ing the equilibrium qualities y1 frac14 0 y2 frac14 1 and prices p1 frac14 p2 frac14 j into

y frac14 p2 p1 teth1 x2THORN thorn jethy22 y21THORN2jethy2 y1THORN

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

145

shows that y 2 frac120 1 if j5 teth1 x2THORN Doing the same for

yy frac14 p2 p1 thorn tx2 thorn jethy22 y21THORN2jethy2 y1THORN

shows that yy 2 frac120 1 if j5 tx2 Consequently

p1p2 frac14 j=2 if

j5 teth1 x2THORN for 04x2 lt 1=2

j5 tx2 for 1=24 x2 4 1

These conditions will be fulfilled for any x2 2 frac120 1 if j5 t so that anecessary condition for equilibrium is that the sensitivity to quality issufficiently large in relation to the perceived inconvenience of lsquowaitingrsquo

It has to be checked whether the operators cannot realise a higherprofit than p1 p

2 by choosing qualities and prices so that the indifferent

consumers y andor the indifferent consumers yy have a preferred qualityoutside the area defined by y yy 2 frac120 1 Figure 2 shows the situation inwhich one of the operators deviates from his equilibrium strategy bychoosing quality or price so that y lt 0 and yy 2 frac120 1

In Appendix A it has been shown that both operators cannot realisehigher profits by deviating from their equilibrium strategy by choosinglocations and prices so that either ethy lt 0 yy 2 frac120 1THORN or ethy 2 frac120 1 yy gt 1THORN

If the sensitivity to quality is sufficiently small in relation to theperceived inconvenience of waiting that is if

j ltt

2ethy2 y1THORN

then yy y gt 1 and it must be that ethy lt 0 yy 2 frac120 1THORN ethy 2 frac120 1 yy gt 1THORN orethy lt 0 yy gt 1THORN In Appendix A it has also been shown that no Nash

Figure 2Representation of indifferent consumer if ethy lt 0 yy 2 frac120 1THORN

Journal of Transport Economics and Policy Volume 40 Part 1

146

equilibrium in pure strategies exists if ethy lt 0 yy 2 frac120 1THORN orethy 2 frac120 1 yy gt 1THORN The division of demand if ethy lt 0 yy gt 1THORN is shown inFigure 3

In this division of demand the respective demands for operator 1and operator 2 are D1 frac14 1 x2 and D2 frac14 x2 so that the profits will bep1 frac14 p1eth1 x2THORN and p2 frac14 p2x2 It can be easily seen from these profitsthat there are no subgame perfect equilibrium prices And even if therewere then operators would not prefer the same distance x2 between depar-tures Operator 1 would like to have a zero distance that is x2 frac14 0 betweenboth operatorsrsquo locations and operator 2 would prefer maximum distancethat is x2 frac14 1 between departures Consequently no Nash equilibrium inpure strategies exists in the division of demand if ethy lt 0 yy gt 1THORN

Consequently there is a subgame perfect Nash equilibrium in purestrategies if the sensitivity to quality is sufficiently large that is if j5 tbut no Nash equilibrium in pure strategies exists if this sensitivity to qualityis sufficiently small

40 Interpretation of Results

The difference in consumersrsquo sensitivity to quality could explain whycompetition in local bus transport results in unstable service patternswhile air transport does not seem to have the same problem

41 Short-distance transport

Given the short-distances travelled operators in local bus transport havevery limited scope for meaningful product differentiation that could

Figure 3Representation of indifferent consumer if ethy lt 0 yy gt 1THORN

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

147

make consumers loyal A consumer will generally take the first bus thatarrives at the stop This occurs in the division of demand of Figure 3 Inthat case each operator prefers a different distance between departuretimes and will continuously try to attain his preferred distance The pre-ferred distance between departures for both operators is conflicting andno subgame perfect equilibrium in pure strategies with regard to thetiming of departures exists

This result corresponds to the generally-shared view on competition inurban public transport in continental Europe The European Commissionin its proposal for new regulation of the award of public service contractsin public transport by Member States articulates this view stating thatwithout exclusive rights lsquoservice patterns are unstablersquo2 This perceptionis based on the experiences in Great Britain of the deregulation of localpublic transport

Evans (1990) and Mackie et al (1995) observed that after deregulationof local public transport the number of travellers did not increase despitethe doubling of service levels (frequencies) and consequent reductions inwaiting times This lsquopuzzling resultrsquo could not be explained by the declinein bus usage due to higher real incomes and lower real motoring costsOne explanation that has been put forward was that frequency increasesare compensated by offsetting effects for example uncertainty caused topassengers by route instability such as irregular intervals frequently chan-ging timetables and so on (Evans 1990 Mackie et al 1995)

The model for low consumer sensitivity to quality predicts this instabil-ity of service patterns In the division of demand of Figure 3 the preferredlocation of operator 1 is just before the departure of operator 2 (x2 frac14 0)while operator 2 prefers a larger distance between departures (x2 gt 0)Given x2 frac14 0 operator 2 will choose a later departure but in reactionoperator 1 will follow in order to reduce the distance to x2 frac14 0 againand so on Basically every operator would like to be at a bus stop justbefore its competitor in order to take the whole market This implies thatoperators are lsquohead-runningrsquo each other

With regard to pricing Mackie et al (1995) stated that pricing is not aparticularly potent marketing weapon The first priority is on service ratherthan fares as travellers tend to board the first bus This behaviour of con-sumers is confirmed by the model for the situation in which an operatorrsquos

2Proposal from the European Commission of 26 July 2000 for a Regulation of the European Parliament

and of the Council on action by Member States concerning public service requirements and the award

of public service contracts in passenger transport by rail road and inland waterway COM(2000)7

provisional p 5

Journal of Transport Economics and Policy Volume 40 Part 1

148

demand is independent of prices and D1 frac14 1 x2 and D2 frac14 x2 In this casethe model shows that p1=p1 5 0 and p2=p25 0 Hence operators arecompeting over the timing of departures rather than pricing Evans statesthat (1990 p 266) lsquoThe operators match fares and tacitly collude to main-tain the pre-existing fare structure The operators also tacitly collude toincrease fares simultaneously at a rate at least as fast as inflation Faresremain the same on high-demand as on low-demand routes and on activelycompetitive as on non-competitive routesrsquo The model shows that theupward pressure on prices will only be limited by the maximum willingnessto pay Consequently the pricing discipline comes from external factorsfor example the existence of competition from another mode (such asprivate car cycling walking and so on) or competition between activitiesthat consumers can undertake (and that may or may not require transport)This clarifies why fares move at a similar rate to inflation and are notrelated to the level of demand on a route or the level of competition on aroute

42 Long-distance transport

In long-distance transport such as air transport consumers are moresensitive to quality Travel times are much longer and consequently con-sumers are more appreciative of comfort This allows for much greaterquality differentiation than in short-distance travel Hence consumerswill more easily take an alternative flight Non-price and non-schedulingfactors increase in importance for longer distances as can be seen for airtransport in the Table 1

The factors as distinguished in the Avmark Aviation Economist arelsquoschedulersquo lsquofarersquo lsquoairlinersquo lsquoairplanersquo and lsquootherrsquo lsquoSchedulersquo and lsquofarersquo areequivalent to the endogenous variables lsquoschedulersquo and lsquopricersquo lsquoAirlinersquo

Table 1

Most Influential Factors in Choosing a Flight

Factors asdistinguishedby the model

Factors asdistinguishedby Source

Length of flight

Under 2 hours () 2ndash5 hours () Over 5 hours ()

Schedule Schedule 701 430 193

Price Fare 114 137 165

Quality Airline 155 362 530Airplane 25 66 102Other 05 06 10

Source Avmark Aviation EconomistIAPA in Gialloreto 1988

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

149

lsquoairplanersquo and lsquootherrsquo can be clustered into the variable lsquoqualityrsquo Pressuredby competition airlines have become increasingly creative and effective indifferentiating their services in terms of quality including the creation ofconsumer loyalty

This situation is described by a sufficient sensitivity to quality that isj5 t as depicted in Figure 1 Given this division of demand operatorsmaximally differentiate in quality that is y1 frac14 0 and y2 frac14 1 This qualitydifferentiation relaxes competition over scheduling The model showsthat an operator cannot improve his position by choosing another timeof departure given the time of departure of his competitor Stronger consu-mer loyalty eliminates operatorsrsquo incentive to lsquohead-runrsquo each other whichcreates a subgame perfect equilibrium in timing departures Intuitively onewould say that an operator who moves to a later point of time increases hismarket but sufficiently strong consumersrsquo sensitivity to quality balancesthis tendency Consumers tend to wait for the departure of their preferredoperator

With regard to price the intuition cannot be confirmed that operatorsdo not seem to compete on price because pricing is too strong a marketingweapon According to the model operators do compete in price Furtheranalysis is needed in order to ascertain whether (and if so why) operatorsdo not seem to compete in price in long-distance transport One obser-vation (Brenner 1975) has been that scheduled transport operators tendto rival each other on frequency instead of price Such competitionincreases costs putting upward pressure on prices which could offset anyreduction in price that is normally associated with the introduction ofcompetition

43 Short-distance vs long-distanceThe impact of travel distance on stability can also be seen in the deregula-tion of lsquolong-distancersquo bus services in Great Britain In 1980 the Britishgovernment abolished a system of quantity control in the express coachmarket The deregulation allowed for free entry and competition onroutes served by nationalised carriers Douglas (1987) made a thoroughassessment of the effects of this deregulation on market structure faresservice quality and costs using data provided by express coach operatorsHe showed that on short-distance connections independent operatorsentering the market were unable to develop a significant market sharesince the two national carriers simply matched or undercut their faresand increased or manipulated departure times (Douglas 1997) Only 39per cent of such services to and from London survived during the firstfew years of deregulation The national carriers maintained some competi-tive advantages after deregulation such as sole access to major and centrally

Journal of Transport Economics and Policy Volume 40 Part 1

150

located bus stations a considerable network of services and an extensivesales network This made them better able to survive than the newindependent operators on the market

On long-distance connections however several independents captureda permanent place in the market Specialisation by offering a premierquality service allowed the independents to build up immunity to thepurely fare and scheduling responses of nationalised carriers and thuscapture a share of the market (Douglas 1997) In this way the indepen-dents were especially successful on the Anglo-Scottish routes The longertravel distance offered operators greater scope for product differentiationConsequently more operators were able to provide services even if theydeparted at the same time In the first few years of deregulation 67 percent of new long-distance services to or from London survived Henceproduct differentiation on long-distance connections made entrants resis-tant to the pricing and scheduling responses of incumbent operators bycreating consumer loyalty stabilising scheduling competition

50 Conclusion

For operators in scheduled passenger transport it is a great marketingchallenge to create an image that is distinct from their competitorsOperating the same or similar types of vehicles on the same routes doesnot have many elements of visible tangible differentiation vis-a-viscompetitors Many of the elements in which differences do exist are bytheir nature subjective and difficult to prove to the sceptical consumerExamples are friendliness and courtesy of personnel interior designseats mealssnacks lounges advertising image and so on Long-distanceoperators are better able than short-distance operators to realise suchproduct differentiation in a meaningful fashion Over longer distancesconsumers are generally more flexible with regard to departure times andare more appreciative of their preferred quality of service

In a two-dimensional horizontal product differentiation model withlinear waiting costs for departures and non-linear sensitivity to deviationsfrom preferred quality of service it is shown that a stable service patternrequires consumers to be sufficiently sensitive to differences in qualitybetween operators In reaction operators will differentiate their productsin terms of quality This differentiation prevents consumers from simplytaking the vehicle that is closest to their preferred departure time Consu-mers will be inclined to take an earlier or later departure if they feel morecomfortable with that operator or if there are additional benefits provided

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

151

by this operator In contrast if consumers are not sensitive to qualitydifferences operators would prefer to schedule their vehicles just beforetheir competitor in order to lsquostealrsquo its customers

On the basis of Neven and Thisse (1990) Ansari et al (1998) andIrmen and Thisse (1998) it can be expected that this result will notchange if the dimension of quality differentiation is modelled as verticaldifferentiation rather than horizontal differentiation It is clear that thequality differentiation considered has not only horizontal but also verticalaspects One example is seat width and pitch For the same price everyconsumer would appreciate more space The most dominant factordifferentiating operators is probably an operatorrsquos consumer loyaltyprogramme and that creates horizontal differentiation A formalanalysis for the case of vertical differentiation is beyond the scope of thispaper

The sensitivity to quality differences is a plausible factor that couldclarify the difference in existence of a stable equilibrium between differentmodes of scheduled transport A modal spectrum can be created on thebasis of the relevance of quality differentiation for the selection of an opera-tor The low-relevance end of this spectrum includes examples as containerfreight operations (such as liner shipping) and local public transport Thehigh-relevance end would probably include inter-continental passengerair transport For the low-relevance modes experience shows that com-petition results in unstable service patterns For the high-relevance modestability has never appeared to be a problem

References

Ansari A N Economides and J Steckel (1998) lsquoThe Max-min-min Principle of ProductDifferentiationrsquo Journal of Regional Science 38 207ndash30

Banister B (1985) lsquoDeregulating the Bus Industry in Britain (A) the ProposalsrsquoTransport Reviews 5 99ndash103

Brenner M A (1975) lsquoNeed for Continued Economic Regulation of Air TransportrsquoJournal of Air Law and Commerce 41 793ndash813

Cancian M A Bills and T Bergstrom (1995) lsquoHotelling Location Problems withDirectional Constraints an Application to Television News Schedulingrsquo Journal ofIndustrial Economics 43 121ndash4

DrsquoAspremont C J Jaskold Gabszewicz and J-F Thisse (1979) lsquoOn HotellingrsquoslsquolsquoStability in competitionrsquorsquorsquo Econometrica 47 1145ndash50

Douglas N J (1987) A Welfare Assessment of Transport Deregulation The Case of theExpress Coach Market in 1980 Aldershot Gower

Evans A (1987) lsquoA Theoretical Comparison of Competition with Other EconomicRegimes for Bus Servicesrsquo Journal of Transport Economics and Policy 21 7ndash36

Journal of Transport Economics and Policy Volume 40 Part 1

152

to unstable service patterns In reaction to such practices by a competitoran operator can always improve its position by choosing another time ofdeparture

lsquoHead runningrsquo also creates counterpart behaviour on the roadlsquoHanging backrsquo lsquohanging the roadrsquo or lsquocrawlingrsquo means that buses goslowly so as to pick up as much traffic as possible that would otherwisego with the bus behind A variant is lsquowaitingrsquo at a bus stop until the bushas a fuller load or until the next bus comes over the horizon lsquoPassingrsquoor lsquoovertakingrsquo means that a bus that is behind tries to get in front of thecompetitor Related to this are lsquotailingrsquo namely keeping just behind anotherbus to overtake it or lsquocut inrsquo and lsquochasingrsquo with the same objective ofovertaking a bus in front or lsquocutting inrsquo These practices are likely toresult in lsquoleapfroggingrsquo or lsquojockeyingrsquo a situation in which buses continuallypass and re-pass each other Alternatively a bus driver can decide to golsquomissingrsquo at a bus stop or lsquoracingrsquo that is missing several bus stopsQuite similar is lsquoturningrsquo a bus before the end of the route and driving itback in the opposite direction These last strategies are not only relevantwith regard to scheduling competition but may also occur if demand atcertain places along the line is expected to be low

There is persistent anecdotal evidence that these practices recurred inthe early years of British deregulation However a microanalysis of thesepractices has never been carried out The effects of deregulation haveonly been studied at a sector (meso) level (for example Mackie et al1995 Tyson 1992) and it has become increasingly difficult to carry out amicroanalysis Operators learned quite fast that merger and acquisitionwere superior strategies to competition resulting in market concentrationThere are currently five bus groups dominating the UK market withterritorial monopolies throughout the country allowing locally basedsmall operators to operate some fringe services The market can be consid-ered to be settled Hence it appears that competition on the road was notsustainable Sector studies have given some indication of instability Animportant indication is the large number of changes in services thatoperators register Tyson (1992) indicates that in the seven metropolitanareas a total of 9628 registration changes were made in 1990 (and 9566in 1989)

This instability of service provision does not appear to be a problem inair transport also a scheduled transport mode Air transport in the UnitedStates was deregulated in 1978 followed by intra-European (EuropeanUnion) air transport in 1997 In both cases unstable scheduling did notsurface For interregional bus services in Great Britain there is a mixedpattern The initial positive experience with the deregulation of inter-regional bus services in 1980 gave rise to the deregulation of local and

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

137

regional bus services The British government argued that fares had beenreduced new services had been provided bus usage had increased andbetter quality services had been introduced and as a consequence proposedto extend deregulation to all bus services (Banister 1985) However analy-sis of the results over a longer period of time showed that competition didnot always lead to stable service patterns particularly for shorter distances(Douglas 1987) Comparison of these experiences with competition indifferent scheduled transport modes gives the impression that schedulingstability depends on the length of the journey

Consumers can be assumed to select an operator on the basis of threefactors scheduling price and quality It is not yet clear how operatorstrade-off these factors in competition whether they copy each othersrsquostrategies or whether they successfully attempt to differentiate on thebasis of one or more factors There are a number of intuitions withregard to scheduling pricing and quality strategies that need to beexplained in relation to each other

Scheduling seems to provide little opportunity for operators to distin-guish themselves An operator can easily copy departure times frequencyand originndashdestination pairs from another operator Operating the sametypes of vehicles between the same nodes and on the same routes do notallow for many elements of sustainable differentiation between operatorsThese outputs only become distinctive if the size of operations differs Pro-viding a larger network increases the chance that a service is available thatcorresponds to the specific basic transport needs of a consumer Cancianet al (1995) showed that competition between television news programmeson the basis of choosing broadcasting times alone is insufficient to createa stable equilibrium (Nash in pure strategies) Their model assumes acircular market with a uniform distribution of consumers along thecircle consumers who can only view news programmes at times that arelater than their preferred time (that is after coming home from workstudy and so on) and two stations that both have to choose a broadcastingtime This model shows that each station wants to broadcast just before itscompetitorrsquos in order to catch the largest audience possible for their newsprogramme A simple parallel can be made with scheduled transportThe model would then result in operators who want to schedule theirdepartures just in front of their competitors

In scheduled transport it has been argued that operators do not com-pete in prices Mackie et al (1995 p 241) state for local bus transportthat lsquo fares are not a particularly potent marketing weapon On a typical2 mile journey with a full cash fare of 50 pence a ride time of 15 minutesand walk and wait time of 15 minutes and a value of time of 2 pence perminute of in-vehicle time fare is less than one third of generalized costs

Journal of Transport Economics and Policy Volume 40 Part 1

138

The impulse to board the first bus is strong correspondingly the firstmarketing imperative is on service rather than on farersquo This hypothesis isbased on the observation that fares did not decrease after deregulationas was expected

Another hypothesis given for the same observation is that (ibid)lsquo operators recognize that fare competition is mutually destructiveReaction periods are short the serious entrant knows that price initiativeswill be instantly matched by the incumbentrsquo indicating that fare competi-tion is too strong a marketing weapon in the sense that even a few penceprice difference would become a highly visible and tangible sales advantagethat no operator can concede to its competitor This hypothesis has alsobeen expressed as an argument against the deregulation of US domesticair transport Although price competition was one of the main argumentsfor deregulation Brenner (1975) argued that an operator usually finds itless costly to follow a fare reduction and remain competitive rather thanto lose market share

Intuitively the first intuition seems to be relevant for short-distancetravel in which a few per cent difference in fares is insignificant in absoluteterms while waiting time at the bus stop is a significant component of totaltravel time and considered rather unpleasant The second intuition seems tobe relevant for long-distance travel in which a few per cent difference infares is a significant amount in absolute terms while waiting time con-stitutes only a small share of the total travel time

With regard to quality elements one of the greatest challenges for anyoperator is to establish such product differentiation in a meaningful fashionand by doing so to create consumer loyalty that determines consumersrsquotravel behaviour Many of the elements in which differences exist are bytheir nature subjective Examples are friendliness and courtesy ofpersonnel vehicle type interior design seats mealssnacks loungesadvertising image and so on Differentiation gives consumers differentpreferences for the services of one operator over others Long-distancetrips differ from short-distance trips in this respect Consumers are moresensitive to quality aspects in long-distance trips than in short-distancetrips so operators in long-distance passenger transport are better able todifferentiate themselves

These intuitions will be clarified by putting them in their context It willbe demonstrated that the sensitivity to quality without excluding otherfactors that may also play a role can explain the difference in schedulingstability between long-distance and short-distance scheduled transportThis will be done by analysing a circular horizontal differentiation modelin which two scheduled transport operators compete for consumers In con-trast to a similar circular horizontal differentiation model used by Cancian

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

139

et al (1995) operators are not only able to choose times of departure butalso fares and quality of service offered Horizontal product differentiationimplies that there is no univocal ranking of products among consumersFor example different consumers have different preferences for thecolour design of vehicles By contrast in the case of vertical differentiationall consumers have the same preference ranking over alternatives Forexample one can safely assume that all consumers prefer more seatingspace Basically the differentiation in quality that is considered in thispaper has both horizontal and vertical aspects In order not to complicatethe analysis too much we focus on horizontal differentiation only Prob-ably the most dominant factor differentiating operators are consumerloyalty programmes and they create horizontal differentiation betweenoperators On the basis of Neven and Thisse (1990) Ansari et al (1998)and Irmen and Thisse (1998) it can be expected that focusing on verticaldifferentiation does not qualitatively affect the results we obtain concerningscheduling decisions

The rest of this paper proceeds as follows Section 2 outlines thespecification of the model Section 3 analyses operatorsrsquo scheduling behav-iour Section 4 gives an interpretation of the modelling results FinallySection 5 draws some conclusions Technical extensions of the model anddetails of the proofs can be found in Appendices A and B respectively

20 The Model

Stability in competition is analysed through a horizontal product differen-tiation model This model describes a situation in which two operatorscompete for consumers on a fixed originndashdestination pair Both operatorsare assumed to use similar production technology Consumersrsquo preferencesfor these services are uniformly distributed over a two-dimensional locationspace Their preferences are indicated by ethxi yiTHORN The x-axis takes the formof a circumference and indicates a consumerrsquos specific preferred time ofdeparture This circumference realistically presents any repetitive timesegment (such as an hour or a day) of the combined schedule of both opera-tors The circumference is x 2 frac120 1 For simplicity both operators operateonly one service or departure per time period x 2 frac120 1 The y-axis thewidth of the circumference indicates specific consumer tastes with regardto other aspects of product differentiation The width of the circumferenceis assumed to be y 2 frac120 1 This gives an upper limit to the differentiationthat is considered Both operators determine their products by choosingdeparture time x and their y

Journal of Transport Economics and Policy Volume 40 Part 1

140

Consumers incur costs for a deviation from their preferred departuretime (x-axis) The non-availability of a departure at the preferred timecreates a disutility This waiting of a consumer for a departure is subjectto a directional constraint in both short-distance and long-distance trans-port In local public transport consumers often do not know the timetablebut they have a notion with regard to the level of frequency Given a highfrequency of departures they simply go to a stop at their preferred traveltime and wait for a vehicle to arrive Upon arrival at the stop a consumerwaits for subsequent vehicles to arrive those that have already passed thestop are gone Consumers take departures following their arrival at theplace of departure which is a backward constraint on consumersrsquo waitingThis travel behaviour is often implicitly or explicitly assumed in publictransport models (Evans 1987) In long-distance transport (such as airtravel) when frequency is not that high consumers know the timetableand plan their trip on the basis of the required time of arrival at the desti-nation This situation has also a directional constraint on consumersrsquo travelbehaviour A consumer can only leave home or work earlier in order to takedepartures before the one that arrives at the preferred time (for example tomake an appointment) Later departures are too late A consumer can onlytake departures that arrive before the consumerrsquos required arrival time (seeCancian et al 1995) which implies a forward constraint to consumersrsquowaiting Our model analyses the case of a backward constraint Using aforward constraint would give rise to mirror image results for the locationstrategies of operators on the circumference

Consumers also incur costs for a deviation from their preferred quality(y-axis) Deviations from preferred quality are assumed to imply quadraticcosts Perceived discomfortirritation can be considered to increase non-linearly (that is convex) as the deviation from preferred quality increasesIn Appendix A it is shown that there is no subgame perfect Nashequilibrium in pure strategies if these costs are taken to be linear creatingan unstable service pattern

By contrast linear waiting costs are assumed for the non-availabilityof a departure at the time desired The value of waiting time is basedon the value of alternative uses of time (opportunity costs) The value ofalternative uses of time can often be related to salary or in the case ofgoods transport the interest cost of capital These costs are linear intime

The prices charged the deviation from the preferred departure time (x-axis) and the deviation from preferred quality can be traded off againsteach other If the departure time of a service deviates from a consumerrsquospreferred time the consumer incurs costs of t per time period x Similarlyif the service deviates from a consumerrsquos preferred variety the consumer

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

141

incurs costs of j per unit y Consequently the utility U for a consumer ilocated at ethxi yiTHORN and travelling with operator 1 or 2 respectively are

Uieth1THORN frac14 V p1 teth1 xiTHORN jethy1 yiTHORN2

Uieth2THORN frac14V p2 tethx2 xiTHORN jethy2 yiTHORN2 if 0 lt xi 4x2

V p2 teth1thorn x2 xiTHORN jethy2 yiTHORN2 if x2 lt xi 4 1

(

where V is the maximum willingness to pay p1 and p2 are the prices ofoperators 1 and 2 respectively x2 is the time difference between both opera-torsrsquo departures and y1 and y2 are the respective locations of operator 1and 2 with respect to the quality they offer The maximum willingness topay reflects the existence of competition from other modes and competitionbetween alternative ways of spending time (not all requiring transport) Forsimplicity it is assumed that V is sufficiently large The x-axis locations ofboth operatorsrsquo departures are normalised around the location of departureof operator 1 This implies that the location of operator 1 x1 is 0 byassumption and that the location of operator 2 x2 is reinterpreted as thetime between both operatorsrsquo departures This time is measured as theclockwise distance of operator 2rsquos location of departure from operator1rsquos location of departure With regard to the y-axis locations it is assumedthat y25 y1 This assumption does not influence the results in a qualitativeway because quality differentiation is horizontal

Since both operators provide a single departure and share identical pro-duction technologies the production costs of both operators are assumedto be C These production costs can be left out of consideration becausethey do not qualitatively affect the strategies of operators Consequentlyprofits are given by p1 frac14 p1D1 and p2 frac14 p2D2 where D1 and D2 are thedemands of operator 1 and operator 2 respectively The decisions ofoperators are modelled in a dynamic two-stage game In the first stageboth operators simultaneously determine their products by choosinglocations x2 y1 and y2 In the second stage operators choose prices Thisorder reflects the fact that prices are easily changed at very short noticeScheduling decisions and quality are more difficult and require more timeto implement

The two stages of the game are subgames of the overall game Servicepatterns will only be stable if in the overall game there exists a subgameperfect Nash equilibrium in pure strategies Dynamic games are solvedby backward induction At stage 1 operators anticipate their optimalstrategies at stage 2 and establish their optimal strategies for stage 1accordingly Consequently the two stages of the overall game need to beanalysed in reverse order This generates two questions First at stage 2given any chosen locations of departures and qualities what are the

Journal of Transport Economics and Policy Volume 40 Part 1

142

equilibrium prices p1 and p2 Second at stage 1 what is the optimal choiceof locations of departures and qualities for both operators taking the effecton prices into account

Operatorsrsquo demands can be established by equating the utility functionsfor consumers with a preferred departure time of 0 lt xi 4x2 andx2 lt xi 4 1 respectively This generates the indifferent consumers whoget the same utility from using either the service of operator 1 or that ofoperator 2 that is

y frac14 p2 p1 teth1 x2THORN thorn jethy22 y21THORN2jethy2 y1THORN

for 0 lt xi 4x2

and

yy frac14 p2 p1 thorn tx2 thorn jethy22 y21THORN2jethy2 y1THORN

for x2 lt xi 4 1

It is noted that y lt yyA graphical representation in case the indifferent consumers y yy belong

to the interval [01] is given in Figure 1 where the area above the linesegments that position the indifferent consumer represents the demandfor operator 2 and the area under these line segments represent thedemand for operator 1

This figure shows that of the consumers with a preferred departure timeof 0 lt xi 4x2 a total of x2eth1 yTHORN will choose operator 2 because it offersthe closest departure The other consumers with a preferred departuretime 0 lt xi 4x2 a total of x2 y prefer to pass operator 2rsquos departureand wait for the departure of operator 1 For these consumers the bettermatch of the service of operator 1 with their quality preferences com-pensates for the longer waiting time Similarly of the consumers whohave a preferred departure time of x2 lt xi 4 1 a total of eth1 x2THORNyy prefer

Figure 1Representation of indifferent consumer if y yy 2 frac120 1

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

143

operator 1 which offers the closest departures and a total ofeth1 x2THORNeth1 yyTHORN prefer to pass the departure of operator 1 and wait forthe departure of operator 2

30 Analysis

The main question is whether there exists a stable service pattern and if sounder what conditions This boils down to looking for a subgame perfectNash equilibrium in pure strategies

Proposition 1 If consumers are sufficiently sensitive to quality that is j5 t asubgame perfect Nash equilibrium in pure strategies exists where for anylocation x2 that is the distance between the departure times of operator 1and 2 equilibrium locations in quality and fares are given by y1 frac14 0 y2 frac14 1and p1 frac14 p2 frac14 j In such an equilibrium the location x2 is undetermined Incontrast if consumers are insufficiently sensitive to quality there is nosubgame perfect Nash equilibrium in pure strategies

Proof As shown above the respective demands if y yy 2 frac120 1 will be

D1 frac14 x2

p2 p1 teth1 x2THORN thorn jethy22 y21THORN

2jethy2 y1THORN

thorn eth1 x2THORNp2 p1 thorn tx2 thorn jethy22 y21THORN

2jethy2 y1THORN

and

D2 frac14 x2

1 p2 p1 teth1 x2THORN thorn jethy22 y21THORN

2jethy2 y1THORN

thorn eth1 x2THORN1 p2 p1 thorn tx2 thorn jethy22 y21THORN

2jethy2 y1THORN

These demands for operator 1 and operator 2 can be rewritten as

D1 frac14p2 p1 thorn jethy22 y21THORN

2jethy2 y1THORNand D2 frac14 1thorn p1 p2 jethy22 y21THORN

2jethy2 y1THORN

It should be noted that these demands do not depend on x2 Con-sequently both operators are indifferent with regard to the distancebetween their departures This implies that an operator has no incentiveto change a location in reaction to the location of its competitor

Journal of Transport Economics and Policy Volume 40 Part 1

144

On the basis of these demands profits for operator 1 and operator 2 willbe

p1 frac14 p1

p2 p1 thorn jethy22 y21THORN

2jethy2 y1THORN

and p2 frac14 p2

1thorn p1 p2 jethy22 y21THORN

2jethy2 y1THORN

Maximising these profits with respect to fares gives the followingreaction curves

p1 frac14p2 thorn jethy22 y21THORN

2and p2 frac14

p1 thorn 2jethy2 y1THORN jethy22 y21THORN2

Substituting these reaction curves into each other gives the subgameperfect prices

p1 frac142jethy2 y1THORN thorn jethy22 y21THORN

3and p2 frac14

4jethy2 y1THORN jethy22 y21THORN3

Substituting the subgame perfect prices into the expression for demandand multiplying these by their own prices generates the following equili-brium profits

p1 frac14eth2jethy2 y1THORN thorn jethy22 y21THORNTHORN2

18jethy2 y1THORNand p2 frac14

eth4jethy2 y1THORN jethy22 y21THORNTHORN2

18jethy2 y1THORN

Maximising the profits with respect to the location of quality gives

p1y1

frac14 frac122jethy2 y1THORN thorn jethy22 y21THORNfrac12jethy22 y21THORN 4y1jethy2 y1THORN 2jethy2 y1THORN18jethy2 y1THORN2

and

p2y2

frac14 frac124jethy2 y1THORN jethy22 y21THORNfrac12jethy22 y21THORN 4y2jethy2 y1THORN thorn 4jethy2 y1THORN18jethy2 y1THORN2

The expressions show that p1=y1 lt 0 and p2=y2 gt 0 Henceoperator 1 will choose to offer quality y1 frac14 0 and operator 2 will offery2 frac14 1 Substituting these locations into the subgame perfect prices andequilibrium profits gives p1 frac14 p2 frac14 j and p1 frac14 p2 frac14 j=2 respectively Anoperator cannot generate higher profits by deviating from this differentia-tion in quality and associated fares if the conditions for this division ofdemand between both operators are satisfied that is y yy 2 frac120 1 Substitut-ing the equilibrium qualities y1 frac14 0 y2 frac14 1 and prices p1 frac14 p2 frac14 j into

y frac14 p2 p1 teth1 x2THORN thorn jethy22 y21THORN2jethy2 y1THORN

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

145

shows that y 2 frac120 1 if j5 teth1 x2THORN Doing the same for

yy frac14 p2 p1 thorn tx2 thorn jethy22 y21THORN2jethy2 y1THORN

shows that yy 2 frac120 1 if j5 tx2 Consequently

p1p2 frac14 j=2 if

j5 teth1 x2THORN for 04x2 lt 1=2

j5 tx2 for 1=24 x2 4 1

These conditions will be fulfilled for any x2 2 frac120 1 if j5 t so that anecessary condition for equilibrium is that the sensitivity to quality issufficiently large in relation to the perceived inconvenience of lsquowaitingrsquo

It has to be checked whether the operators cannot realise a higherprofit than p1 p

2 by choosing qualities and prices so that the indifferent

consumers y andor the indifferent consumers yy have a preferred qualityoutside the area defined by y yy 2 frac120 1 Figure 2 shows the situation inwhich one of the operators deviates from his equilibrium strategy bychoosing quality or price so that y lt 0 and yy 2 frac120 1

In Appendix A it has been shown that both operators cannot realisehigher profits by deviating from their equilibrium strategy by choosinglocations and prices so that either ethy lt 0 yy 2 frac120 1THORN or ethy 2 frac120 1 yy gt 1THORN

If the sensitivity to quality is sufficiently small in relation to theperceived inconvenience of waiting that is if

j ltt

2ethy2 y1THORN

then yy y gt 1 and it must be that ethy lt 0 yy 2 frac120 1THORN ethy 2 frac120 1 yy gt 1THORN orethy lt 0 yy gt 1THORN In Appendix A it has also been shown that no Nash

Figure 2Representation of indifferent consumer if ethy lt 0 yy 2 frac120 1THORN

Journal of Transport Economics and Policy Volume 40 Part 1

146

equilibrium in pure strategies exists if ethy lt 0 yy 2 frac120 1THORN orethy 2 frac120 1 yy gt 1THORN The division of demand if ethy lt 0 yy gt 1THORN is shown inFigure 3

In this division of demand the respective demands for operator 1and operator 2 are D1 frac14 1 x2 and D2 frac14 x2 so that the profits will bep1 frac14 p1eth1 x2THORN and p2 frac14 p2x2 It can be easily seen from these profitsthat there are no subgame perfect equilibrium prices And even if therewere then operators would not prefer the same distance x2 between depar-tures Operator 1 would like to have a zero distance that is x2 frac14 0 betweenboth operatorsrsquo locations and operator 2 would prefer maximum distancethat is x2 frac14 1 between departures Consequently no Nash equilibrium inpure strategies exists in the division of demand if ethy lt 0 yy gt 1THORN

Consequently there is a subgame perfect Nash equilibrium in purestrategies if the sensitivity to quality is sufficiently large that is if j5 tbut no Nash equilibrium in pure strategies exists if this sensitivity to qualityis sufficiently small

40 Interpretation of Results

The difference in consumersrsquo sensitivity to quality could explain whycompetition in local bus transport results in unstable service patternswhile air transport does not seem to have the same problem

41 Short-distance transport

Given the short-distances travelled operators in local bus transport havevery limited scope for meaningful product differentiation that could

Figure 3Representation of indifferent consumer if ethy lt 0 yy gt 1THORN

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

147

make consumers loyal A consumer will generally take the first bus thatarrives at the stop This occurs in the division of demand of Figure 3 Inthat case each operator prefers a different distance between departuretimes and will continuously try to attain his preferred distance The pre-ferred distance between departures for both operators is conflicting andno subgame perfect equilibrium in pure strategies with regard to thetiming of departures exists

This result corresponds to the generally-shared view on competition inurban public transport in continental Europe The European Commissionin its proposal for new regulation of the award of public service contractsin public transport by Member States articulates this view stating thatwithout exclusive rights lsquoservice patterns are unstablersquo2 This perceptionis based on the experiences in Great Britain of the deregulation of localpublic transport

Evans (1990) and Mackie et al (1995) observed that after deregulationof local public transport the number of travellers did not increase despitethe doubling of service levels (frequencies) and consequent reductions inwaiting times This lsquopuzzling resultrsquo could not be explained by the declinein bus usage due to higher real incomes and lower real motoring costsOne explanation that has been put forward was that frequency increasesare compensated by offsetting effects for example uncertainty caused topassengers by route instability such as irregular intervals frequently chan-ging timetables and so on (Evans 1990 Mackie et al 1995)

The model for low consumer sensitivity to quality predicts this instabil-ity of service patterns In the division of demand of Figure 3 the preferredlocation of operator 1 is just before the departure of operator 2 (x2 frac14 0)while operator 2 prefers a larger distance between departures (x2 gt 0)Given x2 frac14 0 operator 2 will choose a later departure but in reactionoperator 1 will follow in order to reduce the distance to x2 frac14 0 againand so on Basically every operator would like to be at a bus stop justbefore its competitor in order to take the whole market This implies thatoperators are lsquohead-runningrsquo each other

With regard to pricing Mackie et al (1995) stated that pricing is not aparticularly potent marketing weapon The first priority is on service ratherthan fares as travellers tend to board the first bus This behaviour of con-sumers is confirmed by the model for the situation in which an operatorrsquos

2Proposal from the European Commission of 26 July 2000 for a Regulation of the European Parliament

and of the Council on action by Member States concerning public service requirements and the award

of public service contracts in passenger transport by rail road and inland waterway COM(2000)7

provisional p 5

Journal of Transport Economics and Policy Volume 40 Part 1

148

demand is independent of prices and D1 frac14 1 x2 and D2 frac14 x2 In this casethe model shows that p1=p1 5 0 and p2=p25 0 Hence operators arecompeting over the timing of departures rather than pricing Evans statesthat (1990 p 266) lsquoThe operators match fares and tacitly collude to main-tain the pre-existing fare structure The operators also tacitly collude toincrease fares simultaneously at a rate at least as fast as inflation Faresremain the same on high-demand as on low-demand routes and on activelycompetitive as on non-competitive routesrsquo The model shows that theupward pressure on prices will only be limited by the maximum willingnessto pay Consequently the pricing discipline comes from external factorsfor example the existence of competition from another mode (such asprivate car cycling walking and so on) or competition between activitiesthat consumers can undertake (and that may or may not require transport)This clarifies why fares move at a similar rate to inflation and are notrelated to the level of demand on a route or the level of competition on aroute

42 Long-distance transport

In long-distance transport such as air transport consumers are moresensitive to quality Travel times are much longer and consequently con-sumers are more appreciative of comfort This allows for much greaterquality differentiation than in short-distance travel Hence consumerswill more easily take an alternative flight Non-price and non-schedulingfactors increase in importance for longer distances as can be seen for airtransport in the Table 1

The factors as distinguished in the Avmark Aviation Economist arelsquoschedulersquo lsquofarersquo lsquoairlinersquo lsquoairplanersquo and lsquootherrsquo lsquoSchedulersquo and lsquofarersquo areequivalent to the endogenous variables lsquoschedulersquo and lsquopricersquo lsquoAirlinersquo

Table 1

Most Influential Factors in Choosing a Flight

Factors asdistinguishedby the model

Factors asdistinguishedby Source

Length of flight

Under 2 hours () 2ndash5 hours () Over 5 hours ()

Schedule Schedule 701 430 193

Price Fare 114 137 165

Quality Airline 155 362 530Airplane 25 66 102Other 05 06 10

Source Avmark Aviation EconomistIAPA in Gialloreto 1988

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

149

lsquoairplanersquo and lsquootherrsquo can be clustered into the variable lsquoqualityrsquo Pressuredby competition airlines have become increasingly creative and effective indifferentiating their services in terms of quality including the creation ofconsumer loyalty

This situation is described by a sufficient sensitivity to quality that isj5 t as depicted in Figure 1 Given this division of demand operatorsmaximally differentiate in quality that is y1 frac14 0 and y2 frac14 1 This qualitydifferentiation relaxes competition over scheduling The model showsthat an operator cannot improve his position by choosing another timeof departure given the time of departure of his competitor Stronger consu-mer loyalty eliminates operatorsrsquo incentive to lsquohead-runrsquo each other whichcreates a subgame perfect equilibrium in timing departures Intuitively onewould say that an operator who moves to a later point of time increases hismarket but sufficiently strong consumersrsquo sensitivity to quality balancesthis tendency Consumers tend to wait for the departure of their preferredoperator

With regard to price the intuition cannot be confirmed that operatorsdo not seem to compete on price because pricing is too strong a marketingweapon According to the model operators do compete in price Furtheranalysis is needed in order to ascertain whether (and if so why) operatorsdo not seem to compete in price in long-distance transport One obser-vation (Brenner 1975) has been that scheduled transport operators tendto rival each other on frequency instead of price Such competitionincreases costs putting upward pressure on prices which could offset anyreduction in price that is normally associated with the introduction ofcompetition

43 Short-distance vs long-distanceThe impact of travel distance on stability can also be seen in the deregula-tion of lsquolong-distancersquo bus services in Great Britain In 1980 the Britishgovernment abolished a system of quantity control in the express coachmarket The deregulation allowed for free entry and competition onroutes served by nationalised carriers Douglas (1987) made a thoroughassessment of the effects of this deregulation on market structure faresservice quality and costs using data provided by express coach operatorsHe showed that on short-distance connections independent operatorsentering the market were unable to develop a significant market sharesince the two national carriers simply matched or undercut their faresand increased or manipulated departure times (Douglas 1997) Only 39per cent of such services to and from London survived during the firstfew years of deregulation The national carriers maintained some competi-tive advantages after deregulation such as sole access to major and centrally

Journal of Transport Economics and Policy Volume 40 Part 1

150

located bus stations a considerable network of services and an extensivesales network This made them better able to survive than the newindependent operators on the market

On long-distance connections however several independents captureda permanent place in the market Specialisation by offering a premierquality service allowed the independents to build up immunity to thepurely fare and scheduling responses of nationalised carriers and thuscapture a share of the market (Douglas 1997) In this way the indepen-dents were especially successful on the Anglo-Scottish routes The longertravel distance offered operators greater scope for product differentiationConsequently more operators were able to provide services even if theydeparted at the same time In the first few years of deregulation 67 percent of new long-distance services to or from London survived Henceproduct differentiation on long-distance connections made entrants resis-tant to the pricing and scheduling responses of incumbent operators bycreating consumer loyalty stabilising scheduling competition

50 Conclusion

For operators in scheduled passenger transport it is a great marketingchallenge to create an image that is distinct from their competitorsOperating the same or similar types of vehicles on the same routes doesnot have many elements of visible tangible differentiation vis-a-viscompetitors Many of the elements in which differences do exist are bytheir nature subjective and difficult to prove to the sceptical consumerExamples are friendliness and courtesy of personnel interior designseats mealssnacks lounges advertising image and so on Long-distanceoperators are better able than short-distance operators to realise suchproduct differentiation in a meaningful fashion Over longer distancesconsumers are generally more flexible with regard to departure times andare more appreciative of their preferred quality of service

In a two-dimensional horizontal product differentiation model withlinear waiting costs for departures and non-linear sensitivity to deviationsfrom preferred quality of service it is shown that a stable service patternrequires consumers to be sufficiently sensitive to differences in qualitybetween operators In reaction operators will differentiate their productsin terms of quality This differentiation prevents consumers from simplytaking the vehicle that is closest to their preferred departure time Consu-mers will be inclined to take an earlier or later departure if they feel morecomfortable with that operator or if there are additional benefits provided

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

151

by this operator In contrast if consumers are not sensitive to qualitydifferences operators would prefer to schedule their vehicles just beforetheir competitor in order to lsquostealrsquo its customers

On the basis of Neven and Thisse (1990) Ansari et al (1998) andIrmen and Thisse (1998) it can be expected that this result will notchange if the dimension of quality differentiation is modelled as verticaldifferentiation rather than horizontal differentiation It is clear that thequality differentiation considered has not only horizontal but also verticalaspects One example is seat width and pitch For the same price everyconsumer would appreciate more space The most dominant factordifferentiating operators is probably an operatorrsquos consumer loyaltyprogramme and that creates horizontal differentiation A formalanalysis for the case of vertical differentiation is beyond the scope of thispaper

The sensitivity to quality differences is a plausible factor that couldclarify the difference in existence of a stable equilibrium between differentmodes of scheduled transport A modal spectrum can be created on thebasis of the relevance of quality differentiation for the selection of an opera-tor The low-relevance end of this spectrum includes examples as containerfreight operations (such as liner shipping) and local public transport Thehigh-relevance end would probably include inter-continental passengerair transport For the low-relevance modes experience shows that com-petition results in unstable service patterns For the high-relevance modestability has never appeared to be a problem

References

Ansari A N Economides and J Steckel (1998) lsquoThe Max-min-min Principle of ProductDifferentiationrsquo Journal of Regional Science 38 207ndash30

Banister B (1985) lsquoDeregulating the Bus Industry in Britain (A) the ProposalsrsquoTransport Reviews 5 99ndash103

Brenner M A (1975) lsquoNeed for Continued Economic Regulation of Air TransportrsquoJournal of Air Law and Commerce 41 793ndash813

Cancian M A Bills and T Bergstrom (1995) lsquoHotelling Location Problems withDirectional Constraints an Application to Television News Schedulingrsquo Journal ofIndustrial Economics 43 121ndash4

DrsquoAspremont C J Jaskold Gabszewicz and J-F Thisse (1979) lsquoOn HotellingrsquoslsquolsquoStability in competitionrsquorsquorsquo Econometrica 47 1145ndash50

Douglas N J (1987) A Welfare Assessment of Transport Deregulation The Case of theExpress Coach Market in 1980 Aldershot Gower

Evans A (1987) lsquoA Theoretical Comparison of Competition with Other EconomicRegimes for Bus Servicesrsquo Journal of Transport Economics and Policy 21 7ndash36

Journal of Transport Economics and Policy Volume 40 Part 1

152

regional bus services The British government argued that fares had beenreduced new services had been provided bus usage had increased andbetter quality services had been introduced and as a consequence proposedto extend deregulation to all bus services (Banister 1985) However analy-sis of the results over a longer period of time showed that competition didnot always lead to stable service patterns particularly for shorter distances(Douglas 1987) Comparison of these experiences with competition indifferent scheduled transport modes gives the impression that schedulingstability depends on the length of the journey

Consumers can be assumed to select an operator on the basis of threefactors scheduling price and quality It is not yet clear how operatorstrade-off these factors in competition whether they copy each othersrsquostrategies or whether they successfully attempt to differentiate on thebasis of one or more factors There are a number of intuitions withregard to scheduling pricing and quality strategies that need to beexplained in relation to each other

Scheduling seems to provide little opportunity for operators to distin-guish themselves An operator can easily copy departure times frequencyand originndashdestination pairs from another operator Operating the sametypes of vehicles between the same nodes and on the same routes do notallow for many elements of sustainable differentiation between operatorsThese outputs only become distinctive if the size of operations differs Pro-viding a larger network increases the chance that a service is available thatcorresponds to the specific basic transport needs of a consumer Cancianet al (1995) showed that competition between television news programmeson the basis of choosing broadcasting times alone is insufficient to createa stable equilibrium (Nash in pure strategies) Their model assumes acircular market with a uniform distribution of consumers along thecircle consumers who can only view news programmes at times that arelater than their preferred time (that is after coming home from workstudy and so on) and two stations that both have to choose a broadcastingtime This model shows that each station wants to broadcast just before itscompetitorrsquos in order to catch the largest audience possible for their newsprogramme A simple parallel can be made with scheduled transportThe model would then result in operators who want to schedule theirdepartures just in front of their competitors

In scheduled transport it has been argued that operators do not com-pete in prices Mackie et al (1995 p 241) state for local bus transportthat lsquo fares are not a particularly potent marketing weapon On a typical2 mile journey with a full cash fare of 50 pence a ride time of 15 minutesand walk and wait time of 15 minutes and a value of time of 2 pence perminute of in-vehicle time fare is less than one third of generalized costs

Journal of Transport Economics and Policy Volume 40 Part 1

138

The impulse to board the first bus is strong correspondingly the firstmarketing imperative is on service rather than on farersquo This hypothesis isbased on the observation that fares did not decrease after deregulationas was expected

Another hypothesis given for the same observation is that (ibid)lsquo operators recognize that fare competition is mutually destructiveReaction periods are short the serious entrant knows that price initiativeswill be instantly matched by the incumbentrsquo indicating that fare competi-tion is too strong a marketing weapon in the sense that even a few penceprice difference would become a highly visible and tangible sales advantagethat no operator can concede to its competitor This hypothesis has alsobeen expressed as an argument against the deregulation of US domesticair transport Although price competition was one of the main argumentsfor deregulation Brenner (1975) argued that an operator usually finds itless costly to follow a fare reduction and remain competitive rather thanto lose market share

Intuitively the first intuition seems to be relevant for short-distancetravel in which a few per cent difference in fares is insignificant in absoluteterms while waiting time at the bus stop is a significant component of totaltravel time and considered rather unpleasant The second intuition seems tobe relevant for long-distance travel in which a few per cent difference infares is a significant amount in absolute terms while waiting time con-stitutes only a small share of the total travel time

With regard to quality elements one of the greatest challenges for anyoperator is to establish such product differentiation in a meaningful fashionand by doing so to create consumer loyalty that determines consumersrsquotravel behaviour Many of the elements in which differences exist are bytheir nature subjective Examples are friendliness and courtesy ofpersonnel vehicle type interior design seats mealssnacks loungesadvertising image and so on Differentiation gives consumers differentpreferences for the services of one operator over others Long-distancetrips differ from short-distance trips in this respect Consumers are moresensitive to quality aspects in long-distance trips than in short-distancetrips so operators in long-distance passenger transport are better able todifferentiate themselves

These intuitions will be clarified by putting them in their context It willbe demonstrated that the sensitivity to quality without excluding otherfactors that may also play a role can explain the difference in schedulingstability between long-distance and short-distance scheduled transportThis will be done by analysing a circular horizontal differentiation modelin which two scheduled transport operators compete for consumers In con-trast to a similar circular horizontal differentiation model used by Cancian

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

139

et al (1995) operators are not only able to choose times of departure butalso fares and quality of service offered Horizontal product differentiationimplies that there is no univocal ranking of products among consumersFor example different consumers have different preferences for thecolour design of vehicles By contrast in the case of vertical differentiationall consumers have the same preference ranking over alternatives Forexample one can safely assume that all consumers prefer more seatingspace Basically the differentiation in quality that is considered in thispaper has both horizontal and vertical aspects In order not to complicatethe analysis too much we focus on horizontal differentiation only Prob-ably the most dominant factor differentiating operators are consumerloyalty programmes and they create horizontal differentiation betweenoperators On the basis of Neven and Thisse (1990) Ansari et al (1998)and Irmen and Thisse (1998) it can be expected that focusing on verticaldifferentiation does not qualitatively affect the results we obtain concerningscheduling decisions

The rest of this paper proceeds as follows Section 2 outlines thespecification of the model Section 3 analyses operatorsrsquo scheduling behav-iour Section 4 gives an interpretation of the modelling results FinallySection 5 draws some conclusions Technical extensions of the model anddetails of the proofs can be found in Appendices A and B respectively

20 The Model

Stability in competition is analysed through a horizontal product differen-tiation model This model describes a situation in which two operatorscompete for consumers on a fixed originndashdestination pair Both operatorsare assumed to use similar production technology Consumersrsquo preferencesfor these services are uniformly distributed over a two-dimensional locationspace Their preferences are indicated by ethxi yiTHORN The x-axis takes the formof a circumference and indicates a consumerrsquos specific preferred time ofdeparture This circumference realistically presents any repetitive timesegment (such as an hour or a day) of the combined schedule of both opera-tors The circumference is x 2 frac120 1 For simplicity both operators operateonly one service or departure per time period x 2 frac120 1 The y-axis thewidth of the circumference indicates specific consumer tastes with regardto other aspects of product differentiation The width of the circumferenceis assumed to be y 2 frac120 1 This gives an upper limit to the differentiationthat is considered Both operators determine their products by choosingdeparture time x and their y

Journal of Transport Economics and Policy Volume 40 Part 1

140

Consumers incur costs for a deviation from their preferred departuretime (x-axis) The non-availability of a departure at the preferred timecreates a disutility This waiting of a consumer for a departure is subjectto a directional constraint in both short-distance and long-distance trans-port In local public transport consumers often do not know the timetablebut they have a notion with regard to the level of frequency Given a highfrequency of departures they simply go to a stop at their preferred traveltime and wait for a vehicle to arrive Upon arrival at the stop a consumerwaits for subsequent vehicles to arrive those that have already passed thestop are gone Consumers take departures following their arrival at theplace of departure which is a backward constraint on consumersrsquo waitingThis travel behaviour is often implicitly or explicitly assumed in publictransport models (Evans 1987) In long-distance transport (such as airtravel) when frequency is not that high consumers know the timetableand plan their trip on the basis of the required time of arrival at the desti-nation This situation has also a directional constraint on consumersrsquo travelbehaviour A consumer can only leave home or work earlier in order to takedepartures before the one that arrives at the preferred time (for example tomake an appointment) Later departures are too late A consumer can onlytake departures that arrive before the consumerrsquos required arrival time (seeCancian et al 1995) which implies a forward constraint to consumersrsquowaiting Our model analyses the case of a backward constraint Using aforward constraint would give rise to mirror image results for the locationstrategies of operators on the circumference

Consumers also incur costs for a deviation from their preferred quality(y-axis) Deviations from preferred quality are assumed to imply quadraticcosts Perceived discomfortirritation can be considered to increase non-linearly (that is convex) as the deviation from preferred quality increasesIn Appendix A it is shown that there is no subgame perfect Nashequilibrium in pure strategies if these costs are taken to be linear creatingan unstable service pattern

By contrast linear waiting costs are assumed for the non-availabilityof a departure at the time desired The value of waiting time is basedon the value of alternative uses of time (opportunity costs) The value ofalternative uses of time can often be related to salary or in the case ofgoods transport the interest cost of capital These costs are linear intime

The prices charged the deviation from the preferred departure time (x-axis) and the deviation from preferred quality can be traded off againsteach other If the departure time of a service deviates from a consumerrsquospreferred time the consumer incurs costs of t per time period x Similarlyif the service deviates from a consumerrsquos preferred variety the consumer

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

141

incurs costs of j per unit y Consequently the utility U for a consumer ilocated at ethxi yiTHORN and travelling with operator 1 or 2 respectively are

Uieth1THORN frac14 V p1 teth1 xiTHORN jethy1 yiTHORN2

Uieth2THORN frac14V p2 tethx2 xiTHORN jethy2 yiTHORN2 if 0 lt xi 4x2

V p2 teth1thorn x2 xiTHORN jethy2 yiTHORN2 if x2 lt xi 4 1

(

where V is the maximum willingness to pay p1 and p2 are the prices ofoperators 1 and 2 respectively x2 is the time difference between both opera-torsrsquo departures and y1 and y2 are the respective locations of operator 1and 2 with respect to the quality they offer The maximum willingness topay reflects the existence of competition from other modes and competitionbetween alternative ways of spending time (not all requiring transport) Forsimplicity it is assumed that V is sufficiently large The x-axis locations ofboth operatorsrsquo departures are normalised around the location of departureof operator 1 This implies that the location of operator 1 x1 is 0 byassumption and that the location of operator 2 x2 is reinterpreted as thetime between both operatorsrsquo departures This time is measured as theclockwise distance of operator 2rsquos location of departure from operator1rsquos location of departure With regard to the y-axis locations it is assumedthat y25 y1 This assumption does not influence the results in a qualitativeway because quality differentiation is horizontal

Since both operators provide a single departure and share identical pro-duction technologies the production costs of both operators are assumedto be C These production costs can be left out of consideration becausethey do not qualitatively affect the strategies of operators Consequentlyprofits are given by p1 frac14 p1D1 and p2 frac14 p2D2 where D1 and D2 are thedemands of operator 1 and operator 2 respectively The decisions ofoperators are modelled in a dynamic two-stage game In the first stageboth operators simultaneously determine their products by choosinglocations x2 y1 and y2 In the second stage operators choose prices Thisorder reflects the fact that prices are easily changed at very short noticeScheduling decisions and quality are more difficult and require more timeto implement

The two stages of the game are subgames of the overall game Servicepatterns will only be stable if in the overall game there exists a subgameperfect Nash equilibrium in pure strategies Dynamic games are solvedby backward induction At stage 1 operators anticipate their optimalstrategies at stage 2 and establish their optimal strategies for stage 1accordingly Consequently the two stages of the overall game need to beanalysed in reverse order This generates two questions First at stage 2given any chosen locations of departures and qualities what are the

Journal of Transport Economics and Policy Volume 40 Part 1

142

equilibrium prices p1 and p2 Second at stage 1 what is the optimal choiceof locations of departures and qualities for both operators taking the effecton prices into account

Operatorsrsquo demands can be established by equating the utility functionsfor consumers with a preferred departure time of 0 lt xi 4x2 andx2 lt xi 4 1 respectively This generates the indifferent consumers whoget the same utility from using either the service of operator 1 or that ofoperator 2 that is

y frac14 p2 p1 teth1 x2THORN thorn jethy22 y21THORN2jethy2 y1THORN

for 0 lt xi 4x2

and

yy frac14 p2 p1 thorn tx2 thorn jethy22 y21THORN2jethy2 y1THORN

for x2 lt xi 4 1

It is noted that y lt yyA graphical representation in case the indifferent consumers y yy belong

to the interval [01] is given in Figure 1 where the area above the linesegments that position the indifferent consumer represents the demandfor operator 2 and the area under these line segments represent thedemand for operator 1

This figure shows that of the consumers with a preferred departure timeof 0 lt xi 4x2 a total of x2eth1 yTHORN will choose operator 2 because it offersthe closest departure The other consumers with a preferred departuretime 0 lt xi 4x2 a total of x2 y prefer to pass operator 2rsquos departureand wait for the departure of operator 1 For these consumers the bettermatch of the service of operator 1 with their quality preferences com-pensates for the longer waiting time Similarly of the consumers whohave a preferred departure time of x2 lt xi 4 1 a total of eth1 x2THORNyy prefer

Figure 1Representation of indifferent consumer if y yy 2 frac120 1

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

143

operator 1 which offers the closest departures and a total ofeth1 x2THORNeth1 yyTHORN prefer to pass the departure of operator 1 and wait forthe departure of operator 2

30 Analysis

The main question is whether there exists a stable service pattern and if sounder what conditions This boils down to looking for a subgame perfectNash equilibrium in pure strategies

Proposition 1 If consumers are sufficiently sensitive to quality that is j5 t asubgame perfect Nash equilibrium in pure strategies exists where for anylocation x2 that is the distance between the departure times of operator 1and 2 equilibrium locations in quality and fares are given by y1 frac14 0 y2 frac14 1and p1 frac14 p2 frac14 j In such an equilibrium the location x2 is undetermined Incontrast if consumers are insufficiently sensitive to quality there is nosubgame perfect Nash equilibrium in pure strategies

Proof As shown above the respective demands if y yy 2 frac120 1 will be

D1 frac14 x2

p2 p1 teth1 x2THORN thorn jethy22 y21THORN

2jethy2 y1THORN

thorn eth1 x2THORNp2 p1 thorn tx2 thorn jethy22 y21THORN

2jethy2 y1THORN

and

D2 frac14 x2

1 p2 p1 teth1 x2THORN thorn jethy22 y21THORN

2jethy2 y1THORN

thorn eth1 x2THORN1 p2 p1 thorn tx2 thorn jethy22 y21THORN

2jethy2 y1THORN

These demands for operator 1 and operator 2 can be rewritten as

D1 frac14p2 p1 thorn jethy22 y21THORN

2jethy2 y1THORNand D2 frac14 1thorn p1 p2 jethy22 y21THORN

2jethy2 y1THORN

It should be noted that these demands do not depend on x2 Con-sequently both operators are indifferent with regard to the distancebetween their departures This implies that an operator has no incentiveto change a location in reaction to the location of its competitor

Journal of Transport Economics and Policy Volume 40 Part 1

144

On the basis of these demands profits for operator 1 and operator 2 willbe

p1 frac14 p1

p2 p1 thorn jethy22 y21THORN

2jethy2 y1THORN

and p2 frac14 p2

1thorn p1 p2 jethy22 y21THORN

2jethy2 y1THORN

Maximising these profits with respect to fares gives the followingreaction curves

p1 frac14p2 thorn jethy22 y21THORN

2and p2 frac14

p1 thorn 2jethy2 y1THORN jethy22 y21THORN2

Substituting these reaction curves into each other gives the subgameperfect prices

p1 frac142jethy2 y1THORN thorn jethy22 y21THORN

3and p2 frac14

4jethy2 y1THORN jethy22 y21THORN3

Substituting the subgame perfect prices into the expression for demandand multiplying these by their own prices generates the following equili-brium profits

p1 frac14eth2jethy2 y1THORN thorn jethy22 y21THORNTHORN2

18jethy2 y1THORNand p2 frac14

eth4jethy2 y1THORN jethy22 y21THORNTHORN2

18jethy2 y1THORN

Maximising the profits with respect to the location of quality gives

p1y1

frac14 frac122jethy2 y1THORN thorn jethy22 y21THORNfrac12jethy22 y21THORN 4y1jethy2 y1THORN 2jethy2 y1THORN18jethy2 y1THORN2

and

p2y2

frac14 frac124jethy2 y1THORN jethy22 y21THORNfrac12jethy22 y21THORN 4y2jethy2 y1THORN thorn 4jethy2 y1THORN18jethy2 y1THORN2

The expressions show that p1=y1 lt 0 and p2=y2 gt 0 Henceoperator 1 will choose to offer quality y1 frac14 0 and operator 2 will offery2 frac14 1 Substituting these locations into the subgame perfect prices andequilibrium profits gives p1 frac14 p2 frac14 j and p1 frac14 p2 frac14 j=2 respectively Anoperator cannot generate higher profits by deviating from this differentia-tion in quality and associated fares if the conditions for this division ofdemand between both operators are satisfied that is y yy 2 frac120 1 Substitut-ing the equilibrium qualities y1 frac14 0 y2 frac14 1 and prices p1 frac14 p2 frac14 j into

y frac14 p2 p1 teth1 x2THORN thorn jethy22 y21THORN2jethy2 y1THORN

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

145

shows that y 2 frac120 1 if j5 teth1 x2THORN Doing the same for

yy frac14 p2 p1 thorn tx2 thorn jethy22 y21THORN2jethy2 y1THORN

shows that yy 2 frac120 1 if j5 tx2 Consequently

p1p2 frac14 j=2 if

j5 teth1 x2THORN for 04x2 lt 1=2

j5 tx2 for 1=24 x2 4 1

These conditions will be fulfilled for any x2 2 frac120 1 if j5 t so that anecessary condition for equilibrium is that the sensitivity to quality issufficiently large in relation to the perceived inconvenience of lsquowaitingrsquo

It has to be checked whether the operators cannot realise a higherprofit than p1 p

2 by choosing qualities and prices so that the indifferent

consumers y andor the indifferent consumers yy have a preferred qualityoutside the area defined by y yy 2 frac120 1 Figure 2 shows the situation inwhich one of the operators deviates from his equilibrium strategy bychoosing quality or price so that y lt 0 and yy 2 frac120 1

In Appendix A it has been shown that both operators cannot realisehigher profits by deviating from their equilibrium strategy by choosinglocations and prices so that either ethy lt 0 yy 2 frac120 1THORN or ethy 2 frac120 1 yy gt 1THORN

If the sensitivity to quality is sufficiently small in relation to theperceived inconvenience of waiting that is if

j ltt

2ethy2 y1THORN

then yy y gt 1 and it must be that ethy lt 0 yy 2 frac120 1THORN ethy 2 frac120 1 yy gt 1THORN orethy lt 0 yy gt 1THORN In Appendix A it has also been shown that no Nash

Figure 2Representation of indifferent consumer if ethy lt 0 yy 2 frac120 1THORN

Journal of Transport Economics and Policy Volume 40 Part 1

146

equilibrium in pure strategies exists if ethy lt 0 yy 2 frac120 1THORN orethy 2 frac120 1 yy gt 1THORN The division of demand if ethy lt 0 yy gt 1THORN is shown inFigure 3

In this division of demand the respective demands for operator 1and operator 2 are D1 frac14 1 x2 and D2 frac14 x2 so that the profits will bep1 frac14 p1eth1 x2THORN and p2 frac14 p2x2 It can be easily seen from these profitsthat there are no subgame perfect equilibrium prices And even if therewere then operators would not prefer the same distance x2 between depar-tures Operator 1 would like to have a zero distance that is x2 frac14 0 betweenboth operatorsrsquo locations and operator 2 would prefer maximum distancethat is x2 frac14 1 between departures Consequently no Nash equilibrium inpure strategies exists in the division of demand if ethy lt 0 yy gt 1THORN

Consequently there is a subgame perfect Nash equilibrium in purestrategies if the sensitivity to quality is sufficiently large that is if j5 tbut no Nash equilibrium in pure strategies exists if this sensitivity to qualityis sufficiently small

40 Interpretation of Results

The difference in consumersrsquo sensitivity to quality could explain whycompetition in local bus transport results in unstable service patternswhile air transport does not seem to have the same problem

41 Short-distance transport

Given the short-distances travelled operators in local bus transport havevery limited scope for meaningful product differentiation that could

Figure 3Representation of indifferent consumer if ethy lt 0 yy gt 1THORN

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

147

make consumers loyal A consumer will generally take the first bus thatarrives at the stop This occurs in the division of demand of Figure 3 Inthat case each operator prefers a different distance between departuretimes and will continuously try to attain his preferred distance The pre-ferred distance between departures for both operators is conflicting andno subgame perfect equilibrium in pure strategies with regard to thetiming of departures exists

This result corresponds to the generally-shared view on competition inurban public transport in continental Europe The European Commissionin its proposal for new regulation of the award of public service contractsin public transport by Member States articulates this view stating thatwithout exclusive rights lsquoservice patterns are unstablersquo2 This perceptionis based on the experiences in Great Britain of the deregulation of localpublic transport

Evans (1990) and Mackie et al (1995) observed that after deregulationof local public transport the number of travellers did not increase despitethe doubling of service levels (frequencies) and consequent reductions inwaiting times This lsquopuzzling resultrsquo could not be explained by the declinein bus usage due to higher real incomes and lower real motoring costsOne explanation that has been put forward was that frequency increasesare compensated by offsetting effects for example uncertainty caused topassengers by route instability such as irregular intervals frequently chan-ging timetables and so on (Evans 1990 Mackie et al 1995)

The model for low consumer sensitivity to quality predicts this instabil-ity of service patterns In the division of demand of Figure 3 the preferredlocation of operator 1 is just before the departure of operator 2 (x2 frac14 0)while operator 2 prefers a larger distance between departures (x2 gt 0)Given x2 frac14 0 operator 2 will choose a later departure but in reactionoperator 1 will follow in order to reduce the distance to x2 frac14 0 againand so on Basically every operator would like to be at a bus stop justbefore its competitor in order to take the whole market This implies thatoperators are lsquohead-runningrsquo each other

With regard to pricing Mackie et al (1995) stated that pricing is not aparticularly potent marketing weapon The first priority is on service ratherthan fares as travellers tend to board the first bus This behaviour of con-sumers is confirmed by the model for the situation in which an operatorrsquos

2Proposal from the European Commission of 26 July 2000 for a Regulation of the European Parliament

and of the Council on action by Member States concerning public service requirements and the award

of public service contracts in passenger transport by rail road and inland waterway COM(2000)7

provisional p 5

Journal of Transport Economics and Policy Volume 40 Part 1

148

demand is independent of prices and D1 frac14 1 x2 and D2 frac14 x2 In this casethe model shows that p1=p1 5 0 and p2=p25 0 Hence operators arecompeting over the timing of departures rather than pricing Evans statesthat (1990 p 266) lsquoThe operators match fares and tacitly collude to main-tain the pre-existing fare structure The operators also tacitly collude toincrease fares simultaneously at a rate at least as fast as inflation Faresremain the same on high-demand as on low-demand routes and on activelycompetitive as on non-competitive routesrsquo The model shows that theupward pressure on prices will only be limited by the maximum willingnessto pay Consequently the pricing discipline comes from external factorsfor example the existence of competition from another mode (such asprivate car cycling walking and so on) or competition between activitiesthat consumers can undertake (and that may or may not require transport)This clarifies why fares move at a similar rate to inflation and are notrelated to the level of demand on a route or the level of competition on aroute

42 Long-distance transport

In long-distance transport such as air transport consumers are moresensitive to quality Travel times are much longer and consequently con-sumers are more appreciative of comfort This allows for much greaterquality differentiation than in short-distance travel Hence consumerswill more easily take an alternative flight Non-price and non-schedulingfactors increase in importance for longer distances as can be seen for airtransport in the Table 1

The factors as distinguished in the Avmark Aviation Economist arelsquoschedulersquo lsquofarersquo lsquoairlinersquo lsquoairplanersquo and lsquootherrsquo lsquoSchedulersquo and lsquofarersquo areequivalent to the endogenous variables lsquoschedulersquo and lsquopricersquo lsquoAirlinersquo

Table 1

Most Influential Factors in Choosing a Flight

Factors asdistinguishedby the model

Factors asdistinguishedby Source

Length of flight

Under 2 hours () 2ndash5 hours () Over 5 hours ()

Schedule Schedule 701 430 193

Price Fare 114 137 165

Quality Airline 155 362 530Airplane 25 66 102Other 05 06 10

Source Avmark Aviation EconomistIAPA in Gialloreto 1988

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

149

lsquoairplanersquo and lsquootherrsquo can be clustered into the variable lsquoqualityrsquo Pressuredby competition airlines have become increasingly creative and effective indifferentiating their services in terms of quality including the creation ofconsumer loyalty

This situation is described by a sufficient sensitivity to quality that isj5 t as depicted in Figure 1 Given this division of demand operatorsmaximally differentiate in quality that is y1 frac14 0 and y2 frac14 1 This qualitydifferentiation relaxes competition over scheduling The model showsthat an operator cannot improve his position by choosing another timeof departure given the time of departure of his competitor Stronger consu-mer loyalty eliminates operatorsrsquo incentive to lsquohead-runrsquo each other whichcreates a subgame perfect equilibrium in timing departures Intuitively onewould say that an operator who moves to a later point of time increases hismarket but sufficiently strong consumersrsquo sensitivity to quality balancesthis tendency Consumers tend to wait for the departure of their preferredoperator

With regard to price the intuition cannot be confirmed that operatorsdo not seem to compete on price because pricing is too strong a marketingweapon According to the model operators do compete in price Furtheranalysis is needed in order to ascertain whether (and if so why) operatorsdo not seem to compete in price in long-distance transport One obser-vation (Brenner 1975) has been that scheduled transport operators tendto rival each other on frequency instead of price Such competitionincreases costs putting upward pressure on prices which could offset anyreduction in price that is normally associated with the introduction ofcompetition

43 Short-distance vs long-distanceThe impact of travel distance on stability can also be seen in the deregula-tion of lsquolong-distancersquo bus services in Great Britain In 1980 the Britishgovernment abolished a system of quantity control in the express coachmarket The deregulation allowed for free entry and competition onroutes served by nationalised carriers Douglas (1987) made a thoroughassessment of the effects of this deregulation on market structure faresservice quality and costs using data provided by express coach operatorsHe showed that on short-distance connections independent operatorsentering the market were unable to develop a significant market sharesince the two national carriers simply matched or undercut their faresand increased or manipulated departure times (Douglas 1997) Only 39per cent of such services to and from London survived during the firstfew years of deregulation The national carriers maintained some competi-tive advantages after deregulation such as sole access to major and centrally

Journal of Transport Economics and Policy Volume 40 Part 1

150

located bus stations a considerable network of services and an extensivesales network This made them better able to survive than the newindependent operators on the market

On long-distance connections however several independents captureda permanent place in the market Specialisation by offering a premierquality service allowed the independents to build up immunity to thepurely fare and scheduling responses of nationalised carriers and thuscapture a share of the market (Douglas 1997) In this way the indepen-dents were especially successful on the Anglo-Scottish routes The longertravel distance offered operators greater scope for product differentiationConsequently more operators were able to provide services even if theydeparted at the same time In the first few years of deregulation 67 percent of new long-distance services to or from London survived Henceproduct differentiation on long-distance connections made entrants resis-tant to the pricing and scheduling responses of incumbent operators bycreating consumer loyalty stabilising scheduling competition

50 Conclusion

For operators in scheduled passenger transport it is a great marketingchallenge to create an image that is distinct from their competitorsOperating the same or similar types of vehicles on the same routes doesnot have many elements of visible tangible differentiation vis-a-viscompetitors Many of the elements in which differences do exist are bytheir nature subjective and difficult to prove to the sceptical consumerExamples are friendliness and courtesy of personnel interior designseats mealssnacks lounges advertising image and so on Long-distanceoperators are better able than short-distance operators to realise suchproduct differentiation in a meaningful fashion Over longer distancesconsumers are generally more flexible with regard to departure times andare more appreciative of their preferred quality of service

In a two-dimensional horizontal product differentiation model withlinear waiting costs for departures and non-linear sensitivity to deviationsfrom preferred quality of service it is shown that a stable service patternrequires consumers to be sufficiently sensitive to differences in qualitybetween operators In reaction operators will differentiate their productsin terms of quality This differentiation prevents consumers from simplytaking the vehicle that is closest to their preferred departure time Consu-mers will be inclined to take an earlier or later departure if they feel morecomfortable with that operator or if there are additional benefits provided

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

151

by this operator In contrast if consumers are not sensitive to qualitydifferences operators would prefer to schedule their vehicles just beforetheir competitor in order to lsquostealrsquo its customers

On the basis of Neven and Thisse (1990) Ansari et al (1998) andIrmen and Thisse (1998) it can be expected that this result will notchange if the dimension of quality differentiation is modelled as verticaldifferentiation rather than horizontal differentiation It is clear that thequality differentiation considered has not only horizontal but also verticalaspects One example is seat width and pitch For the same price everyconsumer would appreciate more space The most dominant factordifferentiating operators is probably an operatorrsquos consumer loyaltyprogramme and that creates horizontal differentiation A formalanalysis for the case of vertical differentiation is beyond the scope of thispaper

The sensitivity to quality differences is a plausible factor that couldclarify the difference in existence of a stable equilibrium between differentmodes of scheduled transport A modal spectrum can be created on thebasis of the relevance of quality differentiation for the selection of an opera-tor The low-relevance end of this spectrum includes examples as containerfreight operations (such as liner shipping) and local public transport Thehigh-relevance end would probably include inter-continental passengerair transport For the low-relevance modes experience shows that com-petition results in unstable service patterns For the high-relevance modestability has never appeared to be a problem

References

Ansari A N Economides and J Steckel (1998) lsquoThe Max-min-min Principle of ProductDifferentiationrsquo Journal of Regional Science 38 207ndash30

Banister B (1985) lsquoDeregulating the Bus Industry in Britain (A) the ProposalsrsquoTransport Reviews 5 99ndash103

Brenner M A (1975) lsquoNeed for Continued Economic Regulation of Air TransportrsquoJournal of Air Law and Commerce 41 793ndash813

Cancian M A Bills and T Bergstrom (1995) lsquoHotelling Location Problems withDirectional Constraints an Application to Television News Schedulingrsquo Journal ofIndustrial Economics 43 121ndash4

DrsquoAspremont C J Jaskold Gabszewicz and J-F Thisse (1979) lsquoOn HotellingrsquoslsquolsquoStability in competitionrsquorsquorsquo Econometrica 47 1145ndash50

Douglas N J (1987) A Welfare Assessment of Transport Deregulation The Case of theExpress Coach Market in 1980 Aldershot Gower

Evans A (1987) lsquoA Theoretical Comparison of Competition with Other EconomicRegimes for Bus Servicesrsquo Journal of Transport Economics and Policy 21 7ndash36

Journal of Transport Economics and Policy Volume 40 Part 1

152

The impulse to board the first bus is strong correspondingly the firstmarketing imperative is on service rather than on farersquo This hypothesis isbased on the observation that fares did not decrease after deregulationas was expected

Another hypothesis given for the same observation is that (ibid)lsquo operators recognize that fare competition is mutually destructiveReaction periods are short the serious entrant knows that price initiativeswill be instantly matched by the incumbentrsquo indicating that fare competi-tion is too strong a marketing weapon in the sense that even a few penceprice difference would become a highly visible and tangible sales advantagethat no operator can concede to its competitor This hypothesis has alsobeen expressed as an argument against the deregulation of US domesticair transport Although price competition was one of the main argumentsfor deregulation Brenner (1975) argued that an operator usually finds itless costly to follow a fare reduction and remain competitive rather thanto lose market share

Intuitively the first intuition seems to be relevant for short-distancetravel in which a few per cent difference in fares is insignificant in absoluteterms while waiting time at the bus stop is a significant component of totaltravel time and considered rather unpleasant The second intuition seems tobe relevant for long-distance travel in which a few per cent difference infares is a significant amount in absolute terms while waiting time con-stitutes only a small share of the total travel time

With regard to quality elements one of the greatest challenges for anyoperator is to establish such product differentiation in a meaningful fashionand by doing so to create consumer loyalty that determines consumersrsquotravel behaviour Many of the elements in which differences exist are bytheir nature subjective Examples are friendliness and courtesy ofpersonnel vehicle type interior design seats mealssnacks loungesadvertising image and so on Differentiation gives consumers differentpreferences for the services of one operator over others Long-distancetrips differ from short-distance trips in this respect Consumers are moresensitive to quality aspects in long-distance trips than in short-distancetrips so operators in long-distance passenger transport are better able todifferentiate themselves

These intuitions will be clarified by putting them in their context It willbe demonstrated that the sensitivity to quality without excluding otherfactors that may also play a role can explain the difference in schedulingstability between long-distance and short-distance scheduled transportThis will be done by analysing a circular horizontal differentiation modelin which two scheduled transport operators compete for consumers In con-trast to a similar circular horizontal differentiation model used by Cancian

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

139

et al (1995) operators are not only able to choose times of departure butalso fares and quality of service offered Horizontal product differentiationimplies that there is no univocal ranking of products among consumersFor example different consumers have different preferences for thecolour design of vehicles By contrast in the case of vertical differentiationall consumers have the same preference ranking over alternatives Forexample one can safely assume that all consumers prefer more seatingspace Basically the differentiation in quality that is considered in thispaper has both horizontal and vertical aspects In order not to complicatethe analysis too much we focus on horizontal differentiation only Prob-ably the most dominant factor differentiating operators are consumerloyalty programmes and they create horizontal differentiation betweenoperators On the basis of Neven and Thisse (1990) Ansari et al (1998)and Irmen and Thisse (1998) it can be expected that focusing on verticaldifferentiation does not qualitatively affect the results we obtain concerningscheduling decisions

The rest of this paper proceeds as follows Section 2 outlines thespecification of the model Section 3 analyses operatorsrsquo scheduling behav-iour Section 4 gives an interpretation of the modelling results FinallySection 5 draws some conclusions Technical extensions of the model anddetails of the proofs can be found in Appendices A and B respectively

20 The Model

Stability in competition is analysed through a horizontal product differen-tiation model This model describes a situation in which two operatorscompete for consumers on a fixed originndashdestination pair Both operatorsare assumed to use similar production technology Consumersrsquo preferencesfor these services are uniformly distributed over a two-dimensional locationspace Their preferences are indicated by ethxi yiTHORN The x-axis takes the formof a circumference and indicates a consumerrsquos specific preferred time ofdeparture This circumference realistically presents any repetitive timesegment (such as an hour or a day) of the combined schedule of both opera-tors The circumference is x 2 frac120 1 For simplicity both operators operateonly one service or departure per time period x 2 frac120 1 The y-axis thewidth of the circumference indicates specific consumer tastes with regardto other aspects of product differentiation The width of the circumferenceis assumed to be y 2 frac120 1 This gives an upper limit to the differentiationthat is considered Both operators determine their products by choosingdeparture time x and their y

Journal of Transport Economics and Policy Volume 40 Part 1

140

Consumers incur costs for a deviation from their preferred departuretime (x-axis) The non-availability of a departure at the preferred timecreates a disutility This waiting of a consumer for a departure is subjectto a directional constraint in both short-distance and long-distance trans-port In local public transport consumers often do not know the timetablebut they have a notion with regard to the level of frequency Given a highfrequency of departures they simply go to a stop at their preferred traveltime and wait for a vehicle to arrive Upon arrival at the stop a consumerwaits for subsequent vehicles to arrive those that have already passed thestop are gone Consumers take departures following their arrival at theplace of departure which is a backward constraint on consumersrsquo waitingThis travel behaviour is often implicitly or explicitly assumed in publictransport models (Evans 1987) In long-distance transport (such as airtravel) when frequency is not that high consumers know the timetableand plan their trip on the basis of the required time of arrival at the desti-nation This situation has also a directional constraint on consumersrsquo travelbehaviour A consumer can only leave home or work earlier in order to takedepartures before the one that arrives at the preferred time (for example tomake an appointment) Later departures are too late A consumer can onlytake departures that arrive before the consumerrsquos required arrival time (seeCancian et al 1995) which implies a forward constraint to consumersrsquowaiting Our model analyses the case of a backward constraint Using aforward constraint would give rise to mirror image results for the locationstrategies of operators on the circumference

Consumers also incur costs for a deviation from their preferred quality(y-axis) Deviations from preferred quality are assumed to imply quadraticcosts Perceived discomfortirritation can be considered to increase non-linearly (that is convex) as the deviation from preferred quality increasesIn Appendix A it is shown that there is no subgame perfect Nashequilibrium in pure strategies if these costs are taken to be linear creatingan unstable service pattern

By contrast linear waiting costs are assumed for the non-availabilityof a departure at the time desired The value of waiting time is basedon the value of alternative uses of time (opportunity costs) The value ofalternative uses of time can often be related to salary or in the case ofgoods transport the interest cost of capital These costs are linear intime

The prices charged the deviation from the preferred departure time (x-axis) and the deviation from preferred quality can be traded off againsteach other If the departure time of a service deviates from a consumerrsquospreferred time the consumer incurs costs of t per time period x Similarlyif the service deviates from a consumerrsquos preferred variety the consumer

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

141

incurs costs of j per unit y Consequently the utility U for a consumer ilocated at ethxi yiTHORN and travelling with operator 1 or 2 respectively are

Uieth1THORN frac14 V p1 teth1 xiTHORN jethy1 yiTHORN2

Uieth2THORN frac14V p2 tethx2 xiTHORN jethy2 yiTHORN2 if 0 lt xi 4x2

V p2 teth1thorn x2 xiTHORN jethy2 yiTHORN2 if x2 lt xi 4 1

(

where V is the maximum willingness to pay p1 and p2 are the prices ofoperators 1 and 2 respectively x2 is the time difference between both opera-torsrsquo departures and y1 and y2 are the respective locations of operator 1and 2 with respect to the quality they offer The maximum willingness topay reflects the existence of competition from other modes and competitionbetween alternative ways of spending time (not all requiring transport) Forsimplicity it is assumed that V is sufficiently large The x-axis locations ofboth operatorsrsquo departures are normalised around the location of departureof operator 1 This implies that the location of operator 1 x1 is 0 byassumption and that the location of operator 2 x2 is reinterpreted as thetime between both operatorsrsquo departures This time is measured as theclockwise distance of operator 2rsquos location of departure from operator1rsquos location of departure With regard to the y-axis locations it is assumedthat y25 y1 This assumption does not influence the results in a qualitativeway because quality differentiation is horizontal

Since both operators provide a single departure and share identical pro-duction technologies the production costs of both operators are assumedto be C These production costs can be left out of consideration becausethey do not qualitatively affect the strategies of operators Consequentlyprofits are given by p1 frac14 p1D1 and p2 frac14 p2D2 where D1 and D2 are thedemands of operator 1 and operator 2 respectively The decisions ofoperators are modelled in a dynamic two-stage game In the first stageboth operators simultaneously determine their products by choosinglocations x2 y1 and y2 In the second stage operators choose prices Thisorder reflects the fact that prices are easily changed at very short noticeScheduling decisions and quality are more difficult and require more timeto implement

The two stages of the game are subgames of the overall game Servicepatterns will only be stable if in the overall game there exists a subgameperfect Nash equilibrium in pure strategies Dynamic games are solvedby backward induction At stage 1 operators anticipate their optimalstrategies at stage 2 and establish their optimal strategies for stage 1accordingly Consequently the two stages of the overall game need to beanalysed in reverse order This generates two questions First at stage 2given any chosen locations of departures and qualities what are the

Journal of Transport Economics and Policy Volume 40 Part 1

142

equilibrium prices p1 and p2 Second at stage 1 what is the optimal choiceof locations of departures and qualities for both operators taking the effecton prices into account

Operatorsrsquo demands can be established by equating the utility functionsfor consumers with a preferred departure time of 0 lt xi 4x2 andx2 lt xi 4 1 respectively This generates the indifferent consumers whoget the same utility from using either the service of operator 1 or that ofoperator 2 that is

y frac14 p2 p1 teth1 x2THORN thorn jethy22 y21THORN2jethy2 y1THORN

for 0 lt xi 4x2

and

yy frac14 p2 p1 thorn tx2 thorn jethy22 y21THORN2jethy2 y1THORN

for x2 lt xi 4 1

It is noted that y lt yyA graphical representation in case the indifferent consumers y yy belong

to the interval [01] is given in Figure 1 where the area above the linesegments that position the indifferent consumer represents the demandfor operator 2 and the area under these line segments represent thedemand for operator 1

This figure shows that of the consumers with a preferred departure timeof 0 lt xi 4x2 a total of x2eth1 yTHORN will choose operator 2 because it offersthe closest departure The other consumers with a preferred departuretime 0 lt xi 4x2 a total of x2 y prefer to pass operator 2rsquos departureand wait for the departure of operator 1 For these consumers the bettermatch of the service of operator 1 with their quality preferences com-pensates for the longer waiting time Similarly of the consumers whohave a preferred departure time of x2 lt xi 4 1 a total of eth1 x2THORNyy prefer

Figure 1Representation of indifferent consumer if y yy 2 frac120 1

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

143

operator 1 which offers the closest departures and a total ofeth1 x2THORNeth1 yyTHORN prefer to pass the departure of operator 1 and wait forthe departure of operator 2

30 Analysis

The main question is whether there exists a stable service pattern and if sounder what conditions This boils down to looking for a subgame perfectNash equilibrium in pure strategies

Proposition 1 If consumers are sufficiently sensitive to quality that is j5 t asubgame perfect Nash equilibrium in pure strategies exists where for anylocation x2 that is the distance between the departure times of operator 1and 2 equilibrium locations in quality and fares are given by y1 frac14 0 y2 frac14 1and p1 frac14 p2 frac14 j In such an equilibrium the location x2 is undetermined Incontrast if consumers are insufficiently sensitive to quality there is nosubgame perfect Nash equilibrium in pure strategies

Proof As shown above the respective demands if y yy 2 frac120 1 will be

D1 frac14 x2

p2 p1 teth1 x2THORN thorn jethy22 y21THORN

2jethy2 y1THORN

thorn eth1 x2THORNp2 p1 thorn tx2 thorn jethy22 y21THORN

2jethy2 y1THORN

and

D2 frac14 x2

1 p2 p1 teth1 x2THORN thorn jethy22 y21THORN

2jethy2 y1THORN

thorn eth1 x2THORN1 p2 p1 thorn tx2 thorn jethy22 y21THORN

2jethy2 y1THORN

These demands for operator 1 and operator 2 can be rewritten as

D1 frac14p2 p1 thorn jethy22 y21THORN

2jethy2 y1THORNand D2 frac14 1thorn p1 p2 jethy22 y21THORN

2jethy2 y1THORN

It should be noted that these demands do not depend on x2 Con-sequently both operators are indifferent with regard to the distancebetween their departures This implies that an operator has no incentiveto change a location in reaction to the location of its competitor

Journal of Transport Economics and Policy Volume 40 Part 1

144

On the basis of these demands profits for operator 1 and operator 2 willbe

p1 frac14 p1

p2 p1 thorn jethy22 y21THORN

2jethy2 y1THORN

and p2 frac14 p2

1thorn p1 p2 jethy22 y21THORN

2jethy2 y1THORN

Maximising these profits with respect to fares gives the followingreaction curves

p1 frac14p2 thorn jethy22 y21THORN

2and p2 frac14

p1 thorn 2jethy2 y1THORN jethy22 y21THORN2

Substituting these reaction curves into each other gives the subgameperfect prices

p1 frac142jethy2 y1THORN thorn jethy22 y21THORN

3and p2 frac14

4jethy2 y1THORN jethy22 y21THORN3

Substituting the subgame perfect prices into the expression for demandand multiplying these by their own prices generates the following equili-brium profits

p1 frac14eth2jethy2 y1THORN thorn jethy22 y21THORNTHORN2

18jethy2 y1THORNand p2 frac14

eth4jethy2 y1THORN jethy22 y21THORNTHORN2

18jethy2 y1THORN

Maximising the profits with respect to the location of quality gives

p1y1

frac14 frac122jethy2 y1THORN thorn jethy22 y21THORNfrac12jethy22 y21THORN 4y1jethy2 y1THORN 2jethy2 y1THORN18jethy2 y1THORN2

and

p2y2

frac14 frac124jethy2 y1THORN jethy22 y21THORNfrac12jethy22 y21THORN 4y2jethy2 y1THORN thorn 4jethy2 y1THORN18jethy2 y1THORN2

The expressions show that p1=y1 lt 0 and p2=y2 gt 0 Henceoperator 1 will choose to offer quality y1 frac14 0 and operator 2 will offery2 frac14 1 Substituting these locations into the subgame perfect prices andequilibrium profits gives p1 frac14 p2 frac14 j and p1 frac14 p2 frac14 j=2 respectively Anoperator cannot generate higher profits by deviating from this differentia-tion in quality and associated fares if the conditions for this division ofdemand between both operators are satisfied that is y yy 2 frac120 1 Substitut-ing the equilibrium qualities y1 frac14 0 y2 frac14 1 and prices p1 frac14 p2 frac14 j into

y frac14 p2 p1 teth1 x2THORN thorn jethy22 y21THORN2jethy2 y1THORN

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

145

shows that y 2 frac120 1 if j5 teth1 x2THORN Doing the same for

yy frac14 p2 p1 thorn tx2 thorn jethy22 y21THORN2jethy2 y1THORN

shows that yy 2 frac120 1 if j5 tx2 Consequently

p1p2 frac14 j=2 if

j5 teth1 x2THORN for 04x2 lt 1=2

j5 tx2 for 1=24 x2 4 1

These conditions will be fulfilled for any x2 2 frac120 1 if j5 t so that anecessary condition for equilibrium is that the sensitivity to quality issufficiently large in relation to the perceived inconvenience of lsquowaitingrsquo

It has to be checked whether the operators cannot realise a higherprofit than p1 p

2 by choosing qualities and prices so that the indifferent

consumers y andor the indifferent consumers yy have a preferred qualityoutside the area defined by y yy 2 frac120 1 Figure 2 shows the situation inwhich one of the operators deviates from his equilibrium strategy bychoosing quality or price so that y lt 0 and yy 2 frac120 1

In Appendix A it has been shown that both operators cannot realisehigher profits by deviating from their equilibrium strategy by choosinglocations and prices so that either ethy lt 0 yy 2 frac120 1THORN or ethy 2 frac120 1 yy gt 1THORN

If the sensitivity to quality is sufficiently small in relation to theperceived inconvenience of waiting that is if

j ltt

2ethy2 y1THORN

then yy y gt 1 and it must be that ethy lt 0 yy 2 frac120 1THORN ethy 2 frac120 1 yy gt 1THORN orethy lt 0 yy gt 1THORN In Appendix A it has also been shown that no Nash

Figure 2Representation of indifferent consumer if ethy lt 0 yy 2 frac120 1THORN

Journal of Transport Economics and Policy Volume 40 Part 1

146

equilibrium in pure strategies exists if ethy lt 0 yy 2 frac120 1THORN orethy 2 frac120 1 yy gt 1THORN The division of demand if ethy lt 0 yy gt 1THORN is shown inFigure 3

In this division of demand the respective demands for operator 1and operator 2 are D1 frac14 1 x2 and D2 frac14 x2 so that the profits will bep1 frac14 p1eth1 x2THORN and p2 frac14 p2x2 It can be easily seen from these profitsthat there are no subgame perfect equilibrium prices And even if therewere then operators would not prefer the same distance x2 between depar-tures Operator 1 would like to have a zero distance that is x2 frac14 0 betweenboth operatorsrsquo locations and operator 2 would prefer maximum distancethat is x2 frac14 1 between departures Consequently no Nash equilibrium inpure strategies exists in the division of demand if ethy lt 0 yy gt 1THORN

Consequently there is a subgame perfect Nash equilibrium in purestrategies if the sensitivity to quality is sufficiently large that is if j5 tbut no Nash equilibrium in pure strategies exists if this sensitivity to qualityis sufficiently small

40 Interpretation of Results

The difference in consumersrsquo sensitivity to quality could explain whycompetition in local bus transport results in unstable service patternswhile air transport does not seem to have the same problem

41 Short-distance transport

Given the short-distances travelled operators in local bus transport havevery limited scope for meaningful product differentiation that could

Figure 3Representation of indifferent consumer if ethy lt 0 yy gt 1THORN

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

147

make consumers loyal A consumer will generally take the first bus thatarrives at the stop This occurs in the division of demand of Figure 3 Inthat case each operator prefers a different distance between departuretimes and will continuously try to attain his preferred distance The pre-ferred distance between departures for both operators is conflicting andno subgame perfect equilibrium in pure strategies with regard to thetiming of departures exists

This result corresponds to the generally-shared view on competition inurban public transport in continental Europe The European Commissionin its proposal for new regulation of the award of public service contractsin public transport by Member States articulates this view stating thatwithout exclusive rights lsquoservice patterns are unstablersquo2 This perceptionis based on the experiences in Great Britain of the deregulation of localpublic transport

Evans (1990) and Mackie et al (1995) observed that after deregulationof local public transport the number of travellers did not increase despitethe doubling of service levels (frequencies) and consequent reductions inwaiting times This lsquopuzzling resultrsquo could not be explained by the declinein bus usage due to higher real incomes and lower real motoring costsOne explanation that has been put forward was that frequency increasesare compensated by offsetting effects for example uncertainty caused topassengers by route instability such as irregular intervals frequently chan-ging timetables and so on (Evans 1990 Mackie et al 1995)

The model for low consumer sensitivity to quality predicts this instabil-ity of service patterns In the division of demand of Figure 3 the preferredlocation of operator 1 is just before the departure of operator 2 (x2 frac14 0)while operator 2 prefers a larger distance between departures (x2 gt 0)Given x2 frac14 0 operator 2 will choose a later departure but in reactionoperator 1 will follow in order to reduce the distance to x2 frac14 0 againand so on Basically every operator would like to be at a bus stop justbefore its competitor in order to take the whole market This implies thatoperators are lsquohead-runningrsquo each other

With regard to pricing Mackie et al (1995) stated that pricing is not aparticularly potent marketing weapon The first priority is on service ratherthan fares as travellers tend to board the first bus This behaviour of con-sumers is confirmed by the model for the situation in which an operatorrsquos

2Proposal from the European Commission of 26 July 2000 for a Regulation of the European Parliament

and of the Council on action by Member States concerning public service requirements and the award

of public service contracts in passenger transport by rail road and inland waterway COM(2000)7

provisional p 5

Journal of Transport Economics and Policy Volume 40 Part 1

148

demand is independent of prices and D1 frac14 1 x2 and D2 frac14 x2 In this casethe model shows that p1=p1 5 0 and p2=p25 0 Hence operators arecompeting over the timing of departures rather than pricing Evans statesthat (1990 p 266) lsquoThe operators match fares and tacitly collude to main-tain the pre-existing fare structure The operators also tacitly collude toincrease fares simultaneously at a rate at least as fast as inflation Faresremain the same on high-demand as on low-demand routes and on activelycompetitive as on non-competitive routesrsquo The model shows that theupward pressure on prices will only be limited by the maximum willingnessto pay Consequently the pricing discipline comes from external factorsfor example the existence of competition from another mode (such asprivate car cycling walking and so on) or competition between activitiesthat consumers can undertake (and that may or may not require transport)This clarifies why fares move at a similar rate to inflation and are notrelated to the level of demand on a route or the level of competition on aroute

42 Long-distance transport

In long-distance transport such as air transport consumers are moresensitive to quality Travel times are much longer and consequently con-sumers are more appreciative of comfort This allows for much greaterquality differentiation than in short-distance travel Hence consumerswill more easily take an alternative flight Non-price and non-schedulingfactors increase in importance for longer distances as can be seen for airtransport in the Table 1

The factors as distinguished in the Avmark Aviation Economist arelsquoschedulersquo lsquofarersquo lsquoairlinersquo lsquoairplanersquo and lsquootherrsquo lsquoSchedulersquo and lsquofarersquo areequivalent to the endogenous variables lsquoschedulersquo and lsquopricersquo lsquoAirlinersquo

Table 1

Most Influential Factors in Choosing a Flight

Factors asdistinguishedby the model

Factors asdistinguishedby Source

Length of flight

Under 2 hours () 2ndash5 hours () Over 5 hours ()

Schedule Schedule 701 430 193

Price Fare 114 137 165

Quality Airline 155 362 530Airplane 25 66 102Other 05 06 10

Source Avmark Aviation EconomistIAPA in Gialloreto 1988

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

149

lsquoairplanersquo and lsquootherrsquo can be clustered into the variable lsquoqualityrsquo Pressuredby competition airlines have become increasingly creative and effective indifferentiating their services in terms of quality including the creation ofconsumer loyalty

This situation is described by a sufficient sensitivity to quality that isj5 t as depicted in Figure 1 Given this division of demand operatorsmaximally differentiate in quality that is y1 frac14 0 and y2 frac14 1 This qualitydifferentiation relaxes competition over scheduling The model showsthat an operator cannot improve his position by choosing another timeof departure given the time of departure of his competitor Stronger consu-mer loyalty eliminates operatorsrsquo incentive to lsquohead-runrsquo each other whichcreates a subgame perfect equilibrium in timing departures Intuitively onewould say that an operator who moves to a later point of time increases hismarket but sufficiently strong consumersrsquo sensitivity to quality balancesthis tendency Consumers tend to wait for the departure of their preferredoperator

With regard to price the intuition cannot be confirmed that operatorsdo not seem to compete on price because pricing is too strong a marketingweapon According to the model operators do compete in price Furtheranalysis is needed in order to ascertain whether (and if so why) operatorsdo not seem to compete in price in long-distance transport One obser-vation (Brenner 1975) has been that scheduled transport operators tendto rival each other on frequency instead of price Such competitionincreases costs putting upward pressure on prices which could offset anyreduction in price that is normally associated with the introduction ofcompetition

43 Short-distance vs long-distanceThe impact of travel distance on stability can also be seen in the deregula-tion of lsquolong-distancersquo bus services in Great Britain In 1980 the Britishgovernment abolished a system of quantity control in the express coachmarket The deregulation allowed for free entry and competition onroutes served by nationalised carriers Douglas (1987) made a thoroughassessment of the effects of this deregulation on market structure faresservice quality and costs using data provided by express coach operatorsHe showed that on short-distance connections independent operatorsentering the market were unable to develop a significant market sharesince the two national carriers simply matched or undercut their faresand increased or manipulated departure times (Douglas 1997) Only 39per cent of such services to and from London survived during the firstfew years of deregulation The national carriers maintained some competi-tive advantages after deregulation such as sole access to major and centrally

Journal of Transport Economics and Policy Volume 40 Part 1

150

located bus stations a considerable network of services and an extensivesales network This made them better able to survive than the newindependent operators on the market

On long-distance connections however several independents captureda permanent place in the market Specialisation by offering a premierquality service allowed the independents to build up immunity to thepurely fare and scheduling responses of nationalised carriers and thuscapture a share of the market (Douglas 1997) In this way the indepen-dents were especially successful on the Anglo-Scottish routes The longertravel distance offered operators greater scope for product differentiationConsequently more operators were able to provide services even if theydeparted at the same time In the first few years of deregulation 67 percent of new long-distance services to or from London survived Henceproduct differentiation on long-distance connections made entrants resis-tant to the pricing and scheduling responses of incumbent operators bycreating consumer loyalty stabilising scheduling competition

50 Conclusion

For operators in scheduled passenger transport it is a great marketingchallenge to create an image that is distinct from their competitorsOperating the same or similar types of vehicles on the same routes doesnot have many elements of visible tangible differentiation vis-a-viscompetitors Many of the elements in which differences do exist are bytheir nature subjective and difficult to prove to the sceptical consumerExamples are friendliness and courtesy of personnel interior designseats mealssnacks lounges advertising image and so on Long-distanceoperators are better able than short-distance operators to realise suchproduct differentiation in a meaningful fashion Over longer distancesconsumers are generally more flexible with regard to departure times andare more appreciative of their preferred quality of service

In a two-dimensional horizontal product differentiation model withlinear waiting costs for departures and non-linear sensitivity to deviationsfrom preferred quality of service it is shown that a stable service patternrequires consumers to be sufficiently sensitive to differences in qualitybetween operators In reaction operators will differentiate their productsin terms of quality This differentiation prevents consumers from simplytaking the vehicle that is closest to their preferred departure time Consu-mers will be inclined to take an earlier or later departure if they feel morecomfortable with that operator or if there are additional benefits provided

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

151

by this operator In contrast if consumers are not sensitive to qualitydifferences operators would prefer to schedule their vehicles just beforetheir competitor in order to lsquostealrsquo its customers

On the basis of Neven and Thisse (1990) Ansari et al (1998) andIrmen and Thisse (1998) it can be expected that this result will notchange if the dimension of quality differentiation is modelled as verticaldifferentiation rather than horizontal differentiation It is clear that thequality differentiation considered has not only horizontal but also verticalaspects One example is seat width and pitch For the same price everyconsumer would appreciate more space The most dominant factordifferentiating operators is probably an operatorrsquos consumer loyaltyprogramme and that creates horizontal differentiation A formalanalysis for the case of vertical differentiation is beyond the scope of thispaper

The sensitivity to quality differences is a plausible factor that couldclarify the difference in existence of a stable equilibrium between differentmodes of scheduled transport A modal spectrum can be created on thebasis of the relevance of quality differentiation for the selection of an opera-tor The low-relevance end of this spectrum includes examples as containerfreight operations (such as liner shipping) and local public transport Thehigh-relevance end would probably include inter-continental passengerair transport For the low-relevance modes experience shows that com-petition results in unstable service patterns For the high-relevance modestability has never appeared to be a problem

References

Ansari A N Economides and J Steckel (1998) lsquoThe Max-min-min Principle of ProductDifferentiationrsquo Journal of Regional Science 38 207ndash30

Banister B (1985) lsquoDeregulating the Bus Industry in Britain (A) the ProposalsrsquoTransport Reviews 5 99ndash103

Brenner M A (1975) lsquoNeed for Continued Economic Regulation of Air TransportrsquoJournal of Air Law and Commerce 41 793ndash813

Cancian M A Bills and T Bergstrom (1995) lsquoHotelling Location Problems withDirectional Constraints an Application to Television News Schedulingrsquo Journal ofIndustrial Economics 43 121ndash4

DrsquoAspremont C J Jaskold Gabszewicz and J-F Thisse (1979) lsquoOn HotellingrsquoslsquolsquoStability in competitionrsquorsquorsquo Econometrica 47 1145ndash50

Douglas N J (1987) A Welfare Assessment of Transport Deregulation The Case of theExpress Coach Market in 1980 Aldershot Gower

Evans A (1987) lsquoA Theoretical Comparison of Competition with Other EconomicRegimes for Bus Servicesrsquo Journal of Transport Economics and Policy 21 7ndash36

Journal of Transport Economics and Policy Volume 40 Part 1

152

et al (1995) operators are not only able to choose times of departure butalso fares and quality of service offered Horizontal product differentiationimplies that there is no univocal ranking of products among consumersFor example different consumers have different preferences for thecolour design of vehicles By contrast in the case of vertical differentiationall consumers have the same preference ranking over alternatives Forexample one can safely assume that all consumers prefer more seatingspace Basically the differentiation in quality that is considered in thispaper has both horizontal and vertical aspects In order not to complicatethe analysis too much we focus on horizontal differentiation only Prob-ably the most dominant factor differentiating operators are consumerloyalty programmes and they create horizontal differentiation betweenoperators On the basis of Neven and Thisse (1990) Ansari et al (1998)and Irmen and Thisse (1998) it can be expected that focusing on verticaldifferentiation does not qualitatively affect the results we obtain concerningscheduling decisions

The rest of this paper proceeds as follows Section 2 outlines thespecification of the model Section 3 analyses operatorsrsquo scheduling behav-iour Section 4 gives an interpretation of the modelling results FinallySection 5 draws some conclusions Technical extensions of the model anddetails of the proofs can be found in Appendices A and B respectively

20 The Model

Stability in competition is analysed through a horizontal product differen-tiation model This model describes a situation in which two operatorscompete for consumers on a fixed originndashdestination pair Both operatorsare assumed to use similar production technology Consumersrsquo preferencesfor these services are uniformly distributed over a two-dimensional locationspace Their preferences are indicated by ethxi yiTHORN The x-axis takes the formof a circumference and indicates a consumerrsquos specific preferred time ofdeparture This circumference realistically presents any repetitive timesegment (such as an hour or a day) of the combined schedule of both opera-tors The circumference is x 2 frac120 1 For simplicity both operators operateonly one service or departure per time period x 2 frac120 1 The y-axis thewidth of the circumference indicates specific consumer tastes with regardto other aspects of product differentiation The width of the circumferenceis assumed to be y 2 frac120 1 This gives an upper limit to the differentiationthat is considered Both operators determine their products by choosingdeparture time x and their y

Journal of Transport Economics and Policy Volume 40 Part 1

140

Consumers incur costs for a deviation from their preferred departuretime (x-axis) The non-availability of a departure at the preferred timecreates a disutility This waiting of a consumer for a departure is subjectto a directional constraint in both short-distance and long-distance trans-port In local public transport consumers often do not know the timetablebut they have a notion with regard to the level of frequency Given a highfrequency of departures they simply go to a stop at their preferred traveltime and wait for a vehicle to arrive Upon arrival at the stop a consumerwaits for subsequent vehicles to arrive those that have already passed thestop are gone Consumers take departures following their arrival at theplace of departure which is a backward constraint on consumersrsquo waitingThis travel behaviour is often implicitly or explicitly assumed in publictransport models (Evans 1987) In long-distance transport (such as airtravel) when frequency is not that high consumers know the timetableand plan their trip on the basis of the required time of arrival at the desti-nation This situation has also a directional constraint on consumersrsquo travelbehaviour A consumer can only leave home or work earlier in order to takedepartures before the one that arrives at the preferred time (for example tomake an appointment) Later departures are too late A consumer can onlytake departures that arrive before the consumerrsquos required arrival time (seeCancian et al 1995) which implies a forward constraint to consumersrsquowaiting Our model analyses the case of a backward constraint Using aforward constraint would give rise to mirror image results for the locationstrategies of operators on the circumference

Consumers also incur costs for a deviation from their preferred quality(y-axis) Deviations from preferred quality are assumed to imply quadraticcosts Perceived discomfortirritation can be considered to increase non-linearly (that is convex) as the deviation from preferred quality increasesIn Appendix A it is shown that there is no subgame perfect Nashequilibrium in pure strategies if these costs are taken to be linear creatingan unstable service pattern

By contrast linear waiting costs are assumed for the non-availabilityof a departure at the time desired The value of waiting time is basedon the value of alternative uses of time (opportunity costs) The value ofalternative uses of time can often be related to salary or in the case ofgoods transport the interest cost of capital These costs are linear intime

The prices charged the deviation from the preferred departure time (x-axis) and the deviation from preferred quality can be traded off againsteach other If the departure time of a service deviates from a consumerrsquospreferred time the consumer incurs costs of t per time period x Similarlyif the service deviates from a consumerrsquos preferred variety the consumer

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

141

incurs costs of j per unit y Consequently the utility U for a consumer ilocated at ethxi yiTHORN and travelling with operator 1 or 2 respectively are

Uieth1THORN frac14 V p1 teth1 xiTHORN jethy1 yiTHORN2

Uieth2THORN frac14V p2 tethx2 xiTHORN jethy2 yiTHORN2 if 0 lt xi 4x2

V p2 teth1thorn x2 xiTHORN jethy2 yiTHORN2 if x2 lt xi 4 1

(

where V is the maximum willingness to pay p1 and p2 are the prices ofoperators 1 and 2 respectively x2 is the time difference between both opera-torsrsquo departures and y1 and y2 are the respective locations of operator 1and 2 with respect to the quality they offer The maximum willingness topay reflects the existence of competition from other modes and competitionbetween alternative ways of spending time (not all requiring transport) Forsimplicity it is assumed that V is sufficiently large The x-axis locations ofboth operatorsrsquo departures are normalised around the location of departureof operator 1 This implies that the location of operator 1 x1 is 0 byassumption and that the location of operator 2 x2 is reinterpreted as thetime between both operatorsrsquo departures This time is measured as theclockwise distance of operator 2rsquos location of departure from operator1rsquos location of departure With regard to the y-axis locations it is assumedthat y25 y1 This assumption does not influence the results in a qualitativeway because quality differentiation is horizontal

Since both operators provide a single departure and share identical pro-duction technologies the production costs of both operators are assumedto be C These production costs can be left out of consideration becausethey do not qualitatively affect the strategies of operators Consequentlyprofits are given by p1 frac14 p1D1 and p2 frac14 p2D2 where D1 and D2 are thedemands of operator 1 and operator 2 respectively The decisions ofoperators are modelled in a dynamic two-stage game In the first stageboth operators simultaneously determine their products by choosinglocations x2 y1 and y2 In the second stage operators choose prices Thisorder reflects the fact that prices are easily changed at very short noticeScheduling decisions and quality are more difficult and require more timeto implement

The two stages of the game are subgames of the overall game Servicepatterns will only be stable if in the overall game there exists a subgameperfect Nash equilibrium in pure strategies Dynamic games are solvedby backward induction At stage 1 operators anticipate their optimalstrategies at stage 2 and establish their optimal strategies for stage 1accordingly Consequently the two stages of the overall game need to beanalysed in reverse order This generates two questions First at stage 2given any chosen locations of departures and qualities what are the

Journal of Transport Economics and Policy Volume 40 Part 1

142

equilibrium prices p1 and p2 Second at stage 1 what is the optimal choiceof locations of departures and qualities for both operators taking the effecton prices into account

Operatorsrsquo demands can be established by equating the utility functionsfor consumers with a preferred departure time of 0 lt xi 4x2 andx2 lt xi 4 1 respectively This generates the indifferent consumers whoget the same utility from using either the service of operator 1 or that ofoperator 2 that is

y frac14 p2 p1 teth1 x2THORN thorn jethy22 y21THORN2jethy2 y1THORN

for 0 lt xi 4x2

and

yy frac14 p2 p1 thorn tx2 thorn jethy22 y21THORN2jethy2 y1THORN

for x2 lt xi 4 1

It is noted that y lt yyA graphical representation in case the indifferent consumers y yy belong

to the interval [01] is given in Figure 1 where the area above the linesegments that position the indifferent consumer represents the demandfor operator 2 and the area under these line segments represent thedemand for operator 1

This figure shows that of the consumers with a preferred departure timeof 0 lt xi 4x2 a total of x2eth1 yTHORN will choose operator 2 because it offersthe closest departure The other consumers with a preferred departuretime 0 lt xi 4x2 a total of x2 y prefer to pass operator 2rsquos departureand wait for the departure of operator 1 For these consumers the bettermatch of the service of operator 1 with their quality preferences com-pensates for the longer waiting time Similarly of the consumers whohave a preferred departure time of x2 lt xi 4 1 a total of eth1 x2THORNyy prefer

Figure 1Representation of indifferent consumer if y yy 2 frac120 1

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

143

operator 1 which offers the closest departures and a total ofeth1 x2THORNeth1 yyTHORN prefer to pass the departure of operator 1 and wait forthe departure of operator 2

30 Analysis

The main question is whether there exists a stable service pattern and if sounder what conditions This boils down to looking for a subgame perfectNash equilibrium in pure strategies

Proposition 1 If consumers are sufficiently sensitive to quality that is j5 t asubgame perfect Nash equilibrium in pure strategies exists where for anylocation x2 that is the distance between the departure times of operator 1and 2 equilibrium locations in quality and fares are given by y1 frac14 0 y2 frac14 1and p1 frac14 p2 frac14 j In such an equilibrium the location x2 is undetermined Incontrast if consumers are insufficiently sensitive to quality there is nosubgame perfect Nash equilibrium in pure strategies

Proof As shown above the respective demands if y yy 2 frac120 1 will be

D1 frac14 x2

p2 p1 teth1 x2THORN thorn jethy22 y21THORN

2jethy2 y1THORN

thorn eth1 x2THORNp2 p1 thorn tx2 thorn jethy22 y21THORN

2jethy2 y1THORN

and

D2 frac14 x2

1 p2 p1 teth1 x2THORN thorn jethy22 y21THORN

2jethy2 y1THORN

thorn eth1 x2THORN1 p2 p1 thorn tx2 thorn jethy22 y21THORN

2jethy2 y1THORN

These demands for operator 1 and operator 2 can be rewritten as

D1 frac14p2 p1 thorn jethy22 y21THORN

2jethy2 y1THORNand D2 frac14 1thorn p1 p2 jethy22 y21THORN

2jethy2 y1THORN

It should be noted that these demands do not depend on x2 Con-sequently both operators are indifferent with regard to the distancebetween their departures This implies that an operator has no incentiveto change a location in reaction to the location of its competitor

Journal of Transport Economics and Policy Volume 40 Part 1

144

On the basis of these demands profits for operator 1 and operator 2 willbe

p1 frac14 p1

p2 p1 thorn jethy22 y21THORN

2jethy2 y1THORN

and p2 frac14 p2

1thorn p1 p2 jethy22 y21THORN

2jethy2 y1THORN

Maximising these profits with respect to fares gives the followingreaction curves

p1 frac14p2 thorn jethy22 y21THORN

2and p2 frac14

p1 thorn 2jethy2 y1THORN jethy22 y21THORN2

Substituting these reaction curves into each other gives the subgameperfect prices

p1 frac142jethy2 y1THORN thorn jethy22 y21THORN

3and p2 frac14

4jethy2 y1THORN jethy22 y21THORN3

Substituting the subgame perfect prices into the expression for demandand multiplying these by their own prices generates the following equili-brium profits

p1 frac14eth2jethy2 y1THORN thorn jethy22 y21THORNTHORN2

18jethy2 y1THORNand p2 frac14

eth4jethy2 y1THORN jethy22 y21THORNTHORN2

18jethy2 y1THORN

Maximising the profits with respect to the location of quality gives

p1y1

frac14 frac122jethy2 y1THORN thorn jethy22 y21THORNfrac12jethy22 y21THORN 4y1jethy2 y1THORN 2jethy2 y1THORN18jethy2 y1THORN2

and

p2y2

frac14 frac124jethy2 y1THORN jethy22 y21THORNfrac12jethy22 y21THORN 4y2jethy2 y1THORN thorn 4jethy2 y1THORN18jethy2 y1THORN2

The expressions show that p1=y1 lt 0 and p2=y2 gt 0 Henceoperator 1 will choose to offer quality y1 frac14 0 and operator 2 will offery2 frac14 1 Substituting these locations into the subgame perfect prices andequilibrium profits gives p1 frac14 p2 frac14 j and p1 frac14 p2 frac14 j=2 respectively Anoperator cannot generate higher profits by deviating from this differentia-tion in quality and associated fares if the conditions for this division ofdemand between both operators are satisfied that is y yy 2 frac120 1 Substitut-ing the equilibrium qualities y1 frac14 0 y2 frac14 1 and prices p1 frac14 p2 frac14 j into

y frac14 p2 p1 teth1 x2THORN thorn jethy22 y21THORN2jethy2 y1THORN

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

145

shows that y 2 frac120 1 if j5 teth1 x2THORN Doing the same for

yy frac14 p2 p1 thorn tx2 thorn jethy22 y21THORN2jethy2 y1THORN

shows that yy 2 frac120 1 if j5 tx2 Consequently

p1p2 frac14 j=2 if

j5 teth1 x2THORN for 04x2 lt 1=2

j5 tx2 for 1=24 x2 4 1

These conditions will be fulfilled for any x2 2 frac120 1 if j5 t so that anecessary condition for equilibrium is that the sensitivity to quality issufficiently large in relation to the perceived inconvenience of lsquowaitingrsquo

It has to be checked whether the operators cannot realise a higherprofit than p1 p

2 by choosing qualities and prices so that the indifferent

consumers y andor the indifferent consumers yy have a preferred qualityoutside the area defined by y yy 2 frac120 1 Figure 2 shows the situation inwhich one of the operators deviates from his equilibrium strategy bychoosing quality or price so that y lt 0 and yy 2 frac120 1

In Appendix A it has been shown that both operators cannot realisehigher profits by deviating from their equilibrium strategy by choosinglocations and prices so that either ethy lt 0 yy 2 frac120 1THORN or ethy 2 frac120 1 yy gt 1THORN

If the sensitivity to quality is sufficiently small in relation to theperceived inconvenience of waiting that is if

j ltt

2ethy2 y1THORN

then yy y gt 1 and it must be that ethy lt 0 yy 2 frac120 1THORN ethy 2 frac120 1 yy gt 1THORN orethy lt 0 yy gt 1THORN In Appendix A it has also been shown that no Nash

Figure 2Representation of indifferent consumer if ethy lt 0 yy 2 frac120 1THORN

Journal of Transport Economics and Policy Volume 40 Part 1

146

equilibrium in pure strategies exists if ethy lt 0 yy 2 frac120 1THORN orethy 2 frac120 1 yy gt 1THORN The division of demand if ethy lt 0 yy gt 1THORN is shown inFigure 3

In this division of demand the respective demands for operator 1and operator 2 are D1 frac14 1 x2 and D2 frac14 x2 so that the profits will bep1 frac14 p1eth1 x2THORN and p2 frac14 p2x2 It can be easily seen from these profitsthat there are no subgame perfect equilibrium prices And even if therewere then operators would not prefer the same distance x2 between depar-tures Operator 1 would like to have a zero distance that is x2 frac14 0 betweenboth operatorsrsquo locations and operator 2 would prefer maximum distancethat is x2 frac14 1 between departures Consequently no Nash equilibrium inpure strategies exists in the division of demand if ethy lt 0 yy gt 1THORN

Consequently there is a subgame perfect Nash equilibrium in purestrategies if the sensitivity to quality is sufficiently large that is if j5 tbut no Nash equilibrium in pure strategies exists if this sensitivity to qualityis sufficiently small

40 Interpretation of Results

The difference in consumersrsquo sensitivity to quality could explain whycompetition in local bus transport results in unstable service patternswhile air transport does not seem to have the same problem

41 Short-distance transport

Given the short-distances travelled operators in local bus transport havevery limited scope for meaningful product differentiation that could

Figure 3Representation of indifferent consumer if ethy lt 0 yy gt 1THORN

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

147

make consumers loyal A consumer will generally take the first bus thatarrives at the stop This occurs in the division of demand of Figure 3 Inthat case each operator prefers a different distance between departuretimes and will continuously try to attain his preferred distance The pre-ferred distance between departures for both operators is conflicting andno subgame perfect equilibrium in pure strategies with regard to thetiming of departures exists

This result corresponds to the generally-shared view on competition inurban public transport in continental Europe The European Commissionin its proposal for new regulation of the award of public service contractsin public transport by Member States articulates this view stating thatwithout exclusive rights lsquoservice patterns are unstablersquo2 This perceptionis based on the experiences in Great Britain of the deregulation of localpublic transport

Evans (1990) and Mackie et al (1995) observed that after deregulationof local public transport the number of travellers did not increase despitethe doubling of service levels (frequencies) and consequent reductions inwaiting times This lsquopuzzling resultrsquo could not be explained by the declinein bus usage due to higher real incomes and lower real motoring costsOne explanation that has been put forward was that frequency increasesare compensated by offsetting effects for example uncertainty caused topassengers by route instability such as irregular intervals frequently chan-ging timetables and so on (Evans 1990 Mackie et al 1995)

The model for low consumer sensitivity to quality predicts this instabil-ity of service patterns In the division of demand of Figure 3 the preferredlocation of operator 1 is just before the departure of operator 2 (x2 frac14 0)while operator 2 prefers a larger distance between departures (x2 gt 0)Given x2 frac14 0 operator 2 will choose a later departure but in reactionoperator 1 will follow in order to reduce the distance to x2 frac14 0 againand so on Basically every operator would like to be at a bus stop justbefore its competitor in order to take the whole market This implies thatoperators are lsquohead-runningrsquo each other

With regard to pricing Mackie et al (1995) stated that pricing is not aparticularly potent marketing weapon The first priority is on service ratherthan fares as travellers tend to board the first bus This behaviour of con-sumers is confirmed by the model for the situation in which an operatorrsquos

2Proposal from the European Commission of 26 July 2000 for a Regulation of the European Parliament

and of the Council on action by Member States concerning public service requirements and the award

of public service contracts in passenger transport by rail road and inland waterway COM(2000)7

provisional p 5

Journal of Transport Economics and Policy Volume 40 Part 1

148

demand is independent of prices and D1 frac14 1 x2 and D2 frac14 x2 In this casethe model shows that p1=p1 5 0 and p2=p25 0 Hence operators arecompeting over the timing of departures rather than pricing Evans statesthat (1990 p 266) lsquoThe operators match fares and tacitly collude to main-tain the pre-existing fare structure The operators also tacitly collude toincrease fares simultaneously at a rate at least as fast as inflation Faresremain the same on high-demand as on low-demand routes and on activelycompetitive as on non-competitive routesrsquo The model shows that theupward pressure on prices will only be limited by the maximum willingnessto pay Consequently the pricing discipline comes from external factorsfor example the existence of competition from another mode (such asprivate car cycling walking and so on) or competition between activitiesthat consumers can undertake (and that may or may not require transport)This clarifies why fares move at a similar rate to inflation and are notrelated to the level of demand on a route or the level of competition on aroute

42 Long-distance transport

In long-distance transport such as air transport consumers are moresensitive to quality Travel times are much longer and consequently con-sumers are more appreciative of comfort This allows for much greaterquality differentiation than in short-distance travel Hence consumerswill more easily take an alternative flight Non-price and non-schedulingfactors increase in importance for longer distances as can be seen for airtransport in the Table 1

The factors as distinguished in the Avmark Aviation Economist arelsquoschedulersquo lsquofarersquo lsquoairlinersquo lsquoairplanersquo and lsquootherrsquo lsquoSchedulersquo and lsquofarersquo areequivalent to the endogenous variables lsquoschedulersquo and lsquopricersquo lsquoAirlinersquo

Table 1

Most Influential Factors in Choosing a Flight

Factors asdistinguishedby the model

Factors asdistinguishedby Source

Length of flight

Under 2 hours () 2ndash5 hours () Over 5 hours ()

Schedule Schedule 701 430 193

Price Fare 114 137 165

Quality Airline 155 362 530Airplane 25 66 102Other 05 06 10

Source Avmark Aviation EconomistIAPA in Gialloreto 1988

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

149

lsquoairplanersquo and lsquootherrsquo can be clustered into the variable lsquoqualityrsquo Pressuredby competition airlines have become increasingly creative and effective indifferentiating their services in terms of quality including the creation ofconsumer loyalty

This situation is described by a sufficient sensitivity to quality that isj5 t as depicted in Figure 1 Given this division of demand operatorsmaximally differentiate in quality that is y1 frac14 0 and y2 frac14 1 This qualitydifferentiation relaxes competition over scheduling The model showsthat an operator cannot improve his position by choosing another timeof departure given the time of departure of his competitor Stronger consu-mer loyalty eliminates operatorsrsquo incentive to lsquohead-runrsquo each other whichcreates a subgame perfect equilibrium in timing departures Intuitively onewould say that an operator who moves to a later point of time increases hismarket but sufficiently strong consumersrsquo sensitivity to quality balancesthis tendency Consumers tend to wait for the departure of their preferredoperator

With regard to price the intuition cannot be confirmed that operatorsdo not seem to compete on price because pricing is too strong a marketingweapon According to the model operators do compete in price Furtheranalysis is needed in order to ascertain whether (and if so why) operatorsdo not seem to compete in price in long-distance transport One obser-vation (Brenner 1975) has been that scheduled transport operators tendto rival each other on frequency instead of price Such competitionincreases costs putting upward pressure on prices which could offset anyreduction in price that is normally associated with the introduction ofcompetition

43 Short-distance vs long-distanceThe impact of travel distance on stability can also be seen in the deregula-tion of lsquolong-distancersquo bus services in Great Britain In 1980 the Britishgovernment abolished a system of quantity control in the express coachmarket The deregulation allowed for free entry and competition onroutes served by nationalised carriers Douglas (1987) made a thoroughassessment of the effects of this deregulation on market structure faresservice quality and costs using data provided by express coach operatorsHe showed that on short-distance connections independent operatorsentering the market were unable to develop a significant market sharesince the two national carriers simply matched or undercut their faresand increased or manipulated departure times (Douglas 1997) Only 39per cent of such services to and from London survived during the firstfew years of deregulation The national carriers maintained some competi-tive advantages after deregulation such as sole access to major and centrally

Journal of Transport Economics and Policy Volume 40 Part 1

150

located bus stations a considerable network of services and an extensivesales network This made them better able to survive than the newindependent operators on the market

On long-distance connections however several independents captureda permanent place in the market Specialisation by offering a premierquality service allowed the independents to build up immunity to thepurely fare and scheduling responses of nationalised carriers and thuscapture a share of the market (Douglas 1997) In this way the indepen-dents were especially successful on the Anglo-Scottish routes The longertravel distance offered operators greater scope for product differentiationConsequently more operators were able to provide services even if theydeparted at the same time In the first few years of deregulation 67 percent of new long-distance services to or from London survived Henceproduct differentiation on long-distance connections made entrants resis-tant to the pricing and scheduling responses of incumbent operators bycreating consumer loyalty stabilising scheduling competition

50 Conclusion

For operators in scheduled passenger transport it is a great marketingchallenge to create an image that is distinct from their competitorsOperating the same or similar types of vehicles on the same routes doesnot have many elements of visible tangible differentiation vis-a-viscompetitors Many of the elements in which differences do exist are bytheir nature subjective and difficult to prove to the sceptical consumerExamples are friendliness and courtesy of personnel interior designseats mealssnacks lounges advertising image and so on Long-distanceoperators are better able than short-distance operators to realise suchproduct differentiation in a meaningful fashion Over longer distancesconsumers are generally more flexible with regard to departure times andare more appreciative of their preferred quality of service

In a two-dimensional horizontal product differentiation model withlinear waiting costs for departures and non-linear sensitivity to deviationsfrom preferred quality of service it is shown that a stable service patternrequires consumers to be sufficiently sensitive to differences in qualitybetween operators In reaction operators will differentiate their productsin terms of quality This differentiation prevents consumers from simplytaking the vehicle that is closest to their preferred departure time Consu-mers will be inclined to take an earlier or later departure if they feel morecomfortable with that operator or if there are additional benefits provided

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

151

by this operator In contrast if consumers are not sensitive to qualitydifferences operators would prefer to schedule their vehicles just beforetheir competitor in order to lsquostealrsquo its customers

On the basis of Neven and Thisse (1990) Ansari et al (1998) andIrmen and Thisse (1998) it can be expected that this result will notchange if the dimension of quality differentiation is modelled as verticaldifferentiation rather than horizontal differentiation It is clear that thequality differentiation considered has not only horizontal but also verticalaspects One example is seat width and pitch For the same price everyconsumer would appreciate more space The most dominant factordifferentiating operators is probably an operatorrsquos consumer loyaltyprogramme and that creates horizontal differentiation A formalanalysis for the case of vertical differentiation is beyond the scope of thispaper

The sensitivity to quality differences is a plausible factor that couldclarify the difference in existence of a stable equilibrium between differentmodes of scheduled transport A modal spectrum can be created on thebasis of the relevance of quality differentiation for the selection of an opera-tor The low-relevance end of this spectrum includes examples as containerfreight operations (such as liner shipping) and local public transport Thehigh-relevance end would probably include inter-continental passengerair transport For the low-relevance modes experience shows that com-petition results in unstable service patterns For the high-relevance modestability has never appeared to be a problem

References

Ansari A N Economides and J Steckel (1998) lsquoThe Max-min-min Principle of ProductDifferentiationrsquo Journal of Regional Science 38 207ndash30

Banister B (1985) lsquoDeregulating the Bus Industry in Britain (A) the ProposalsrsquoTransport Reviews 5 99ndash103

Brenner M A (1975) lsquoNeed for Continued Economic Regulation of Air TransportrsquoJournal of Air Law and Commerce 41 793ndash813

Cancian M A Bills and T Bergstrom (1995) lsquoHotelling Location Problems withDirectional Constraints an Application to Television News Schedulingrsquo Journal ofIndustrial Economics 43 121ndash4

DrsquoAspremont C J Jaskold Gabszewicz and J-F Thisse (1979) lsquoOn HotellingrsquoslsquolsquoStability in competitionrsquorsquorsquo Econometrica 47 1145ndash50

Douglas N J (1987) A Welfare Assessment of Transport Deregulation The Case of theExpress Coach Market in 1980 Aldershot Gower

Evans A (1987) lsquoA Theoretical Comparison of Competition with Other EconomicRegimes for Bus Servicesrsquo Journal of Transport Economics and Policy 21 7ndash36

Journal of Transport Economics and Policy Volume 40 Part 1

152

Consumers incur costs for a deviation from their preferred departuretime (x-axis) The non-availability of a departure at the preferred timecreates a disutility This waiting of a consumer for a departure is subjectto a directional constraint in both short-distance and long-distance trans-port In local public transport consumers often do not know the timetablebut they have a notion with regard to the level of frequency Given a highfrequency of departures they simply go to a stop at their preferred traveltime and wait for a vehicle to arrive Upon arrival at the stop a consumerwaits for subsequent vehicles to arrive those that have already passed thestop are gone Consumers take departures following their arrival at theplace of departure which is a backward constraint on consumersrsquo waitingThis travel behaviour is often implicitly or explicitly assumed in publictransport models (Evans 1987) In long-distance transport (such as airtravel) when frequency is not that high consumers know the timetableand plan their trip on the basis of the required time of arrival at the desti-nation This situation has also a directional constraint on consumersrsquo travelbehaviour A consumer can only leave home or work earlier in order to takedepartures before the one that arrives at the preferred time (for example tomake an appointment) Later departures are too late A consumer can onlytake departures that arrive before the consumerrsquos required arrival time (seeCancian et al 1995) which implies a forward constraint to consumersrsquowaiting Our model analyses the case of a backward constraint Using aforward constraint would give rise to mirror image results for the locationstrategies of operators on the circumference

Consumers also incur costs for a deviation from their preferred quality(y-axis) Deviations from preferred quality are assumed to imply quadraticcosts Perceived discomfortirritation can be considered to increase non-linearly (that is convex) as the deviation from preferred quality increasesIn Appendix A it is shown that there is no subgame perfect Nashequilibrium in pure strategies if these costs are taken to be linear creatingan unstable service pattern

By contrast linear waiting costs are assumed for the non-availabilityof a departure at the time desired The value of waiting time is basedon the value of alternative uses of time (opportunity costs) The value ofalternative uses of time can often be related to salary or in the case ofgoods transport the interest cost of capital These costs are linear intime

The prices charged the deviation from the preferred departure time (x-axis) and the deviation from preferred quality can be traded off againsteach other If the departure time of a service deviates from a consumerrsquospreferred time the consumer incurs costs of t per time period x Similarlyif the service deviates from a consumerrsquos preferred variety the consumer

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

141

incurs costs of j per unit y Consequently the utility U for a consumer ilocated at ethxi yiTHORN and travelling with operator 1 or 2 respectively are

Uieth1THORN frac14 V p1 teth1 xiTHORN jethy1 yiTHORN2

Uieth2THORN frac14V p2 tethx2 xiTHORN jethy2 yiTHORN2 if 0 lt xi 4x2

V p2 teth1thorn x2 xiTHORN jethy2 yiTHORN2 if x2 lt xi 4 1

(

where V is the maximum willingness to pay p1 and p2 are the prices ofoperators 1 and 2 respectively x2 is the time difference between both opera-torsrsquo departures and y1 and y2 are the respective locations of operator 1and 2 with respect to the quality they offer The maximum willingness topay reflects the existence of competition from other modes and competitionbetween alternative ways of spending time (not all requiring transport) Forsimplicity it is assumed that V is sufficiently large The x-axis locations ofboth operatorsrsquo departures are normalised around the location of departureof operator 1 This implies that the location of operator 1 x1 is 0 byassumption and that the location of operator 2 x2 is reinterpreted as thetime between both operatorsrsquo departures This time is measured as theclockwise distance of operator 2rsquos location of departure from operator1rsquos location of departure With regard to the y-axis locations it is assumedthat y25 y1 This assumption does not influence the results in a qualitativeway because quality differentiation is horizontal

Since both operators provide a single departure and share identical pro-duction technologies the production costs of both operators are assumedto be C These production costs can be left out of consideration becausethey do not qualitatively affect the strategies of operators Consequentlyprofits are given by p1 frac14 p1D1 and p2 frac14 p2D2 where D1 and D2 are thedemands of operator 1 and operator 2 respectively The decisions ofoperators are modelled in a dynamic two-stage game In the first stageboth operators simultaneously determine their products by choosinglocations x2 y1 and y2 In the second stage operators choose prices Thisorder reflects the fact that prices are easily changed at very short noticeScheduling decisions and quality are more difficult and require more timeto implement

The two stages of the game are subgames of the overall game Servicepatterns will only be stable if in the overall game there exists a subgameperfect Nash equilibrium in pure strategies Dynamic games are solvedby backward induction At stage 1 operators anticipate their optimalstrategies at stage 2 and establish their optimal strategies for stage 1accordingly Consequently the two stages of the overall game need to beanalysed in reverse order This generates two questions First at stage 2given any chosen locations of departures and qualities what are the

Journal of Transport Economics and Policy Volume 40 Part 1

142

equilibrium prices p1 and p2 Second at stage 1 what is the optimal choiceof locations of departures and qualities for both operators taking the effecton prices into account

Operatorsrsquo demands can be established by equating the utility functionsfor consumers with a preferred departure time of 0 lt xi 4x2 andx2 lt xi 4 1 respectively This generates the indifferent consumers whoget the same utility from using either the service of operator 1 or that ofoperator 2 that is

y frac14 p2 p1 teth1 x2THORN thorn jethy22 y21THORN2jethy2 y1THORN

for 0 lt xi 4x2

and

yy frac14 p2 p1 thorn tx2 thorn jethy22 y21THORN2jethy2 y1THORN

for x2 lt xi 4 1

It is noted that y lt yyA graphical representation in case the indifferent consumers y yy belong

to the interval [01] is given in Figure 1 where the area above the linesegments that position the indifferent consumer represents the demandfor operator 2 and the area under these line segments represent thedemand for operator 1

This figure shows that of the consumers with a preferred departure timeof 0 lt xi 4x2 a total of x2eth1 yTHORN will choose operator 2 because it offersthe closest departure The other consumers with a preferred departuretime 0 lt xi 4x2 a total of x2 y prefer to pass operator 2rsquos departureand wait for the departure of operator 1 For these consumers the bettermatch of the service of operator 1 with their quality preferences com-pensates for the longer waiting time Similarly of the consumers whohave a preferred departure time of x2 lt xi 4 1 a total of eth1 x2THORNyy prefer

Figure 1Representation of indifferent consumer if y yy 2 frac120 1

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

143

operator 1 which offers the closest departures and a total ofeth1 x2THORNeth1 yyTHORN prefer to pass the departure of operator 1 and wait forthe departure of operator 2

30 Analysis

The main question is whether there exists a stable service pattern and if sounder what conditions This boils down to looking for a subgame perfectNash equilibrium in pure strategies

Proposition 1 If consumers are sufficiently sensitive to quality that is j5 t asubgame perfect Nash equilibrium in pure strategies exists where for anylocation x2 that is the distance between the departure times of operator 1and 2 equilibrium locations in quality and fares are given by y1 frac14 0 y2 frac14 1and p1 frac14 p2 frac14 j In such an equilibrium the location x2 is undetermined Incontrast if consumers are insufficiently sensitive to quality there is nosubgame perfect Nash equilibrium in pure strategies

Proof As shown above the respective demands if y yy 2 frac120 1 will be

D1 frac14 x2

p2 p1 teth1 x2THORN thorn jethy22 y21THORN

2jethy2 y1THORN

thorn eth1 x2THORNp2 p1 thorn tx2 thorn jethy22 y21THORN

2jethy2 y1THORN

and

D2 frac14 x2

1 p2 p1 teth1 x2THORN thorn jethy22 y21THORN

2jethy2 y1THORN

thorn eth1 x2THORN1 p2 p1 thorn tx2 thorn jethy22 y21THORN

2jethy2 y1THORN

These demands for operator 1 and operator 2 can be rewritten as

D1 frac14p2 p1 thorn jethy22 y21THORN

2jethy2 y1THORNand D2 frac14 1thorn p1 p2 jethy22 y21THORN

2jethy2 y1THORN

It should be noted that these demands do not depend on x2 Con-sequently both operators are indifferent with regard to the distancebetween their departures This implies that an operator has no incentiveto change a location in reaction to the location of its competitor

Journal of Transport Economics and Policy Volume 40 Part 1

144

On the basis of these demands profits for operator 1 and operator 2 willbe

p1 frac14 p1

p2 p1 thorn jethy22 y21THORN

2jethy2 y1THORN

and p2 frac14 p2

1thorn p1 p2 jethy22 y21THORN

2jethy2 y1THORN

Maximising these profits with respect to fares gives the followingreaction curves

p1 frac14p2 thorn jethy22 y21THORN

2and p2 frac14

p1 thorn 2jethy2 y1THORN jethy22 y21THORN2

Substituting these reaction curves into each other gives the subgameperfect prices

p1 frac142jethy2 y1THORN thorn jethy22 y21THORN

3and p2 frac14

4jethy2 y1THORN jethy22 y21THORN3

Substituting the subgame perfect prices into the expression for demandand multiplying these by their own prices generates the following equili-brium profits

p1 frac14eth2jethy2 y1THORN thorn jethy22 y21THORNTHORN2

18jethy2 y1THORNand p2 frac14

eth4jethy2 y1THORN jethy22 y21THORNTHORN2

18jethy2 y1THORN

Maximising the profits with respect to the location of quality gives

p1y1

frac14 frac122jethy2 y1THORN thorn jethy22 y21THORNfrac12jethy22 y21THORN 4y1jethy2 y1THORN 2jethy2 y1THORN18jethy2 y1THORN2

and

p2y2

frac14 frac124jethy2 y1THORN jethy22 y21THORNfrac12jethy22 y21THORN 4y2jethy2 y1THORN thorn 4jethy2 y1THORN18jethy2 y1THORN2

The expressions show that p1=y1 lt 0 and p2=y2 gt 0 Henceoperator 1 will choose to offer quality y1 frac14 0 and operator 2 will offery2 frac14 1 Substituting these locations into the subgame perfect prices andequilibrium profits gives p1 frac14 p2 frac14 j and p1 frac14 p2 frac14 j=2 respectively Anoperator cannot generate higher profits by deviating from this differentia-tion in quality and associated fares if the conditions for this division ofdemand between both operators are satisfied that is y yy 2 frac120 1 Substitut-ing the equilibrium qualities y1 frac14 0 y2 frac14 1 and prices p1 frac14 p2 frac14 j into

y frac14 p2 p1 teth1 x2THORN thorn jethy22 y21THORN2jethy2 y1THORN

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

145

shows that y 2 frac120 1 if j5 teth1 x2THORN Doing the same for

yy frac14 p2 p1 thorn tx2 thorn jethy22 y21THORN2jethy2 y1THORN

shows that yy 2 frac120 1 if j5 tx2 Consequently

p1p2 frac14 j=2 if

j5 teth1 x2THORN for 04x2 lt 1=2

j5 tx2 for 1=24 x2 4 1

These conditions will be fulfilled for any x2 2 frac120 1 if j5 t so that anecessary condition for equilibrium is that the sensitivity to quality issufficiently large in relation to the perceived inconvenience of lsquowaitingrsquo

It has to be checked whether the operators cannot realise a higherprofit than p1 p

2 by choosing qualities and prices so that the indifferent

consumers y andor the indifferent consumers yy have a preferred qualityoutside the area defined by y yy 2 frac120 1 Figure 2 shows the situation inwhich one of the operators deviates from his equilibrium strategy bychoosing quality or price so that y lt 0 and yy 2 frac120 1

In Appendix A it has been shown that both operators cannot realisehigher profits by deviating from their equilibrium strategy by choosinglocations and prices so that either ethy lt 0 yy 2 frac120 1THORN or ethy 2 frac120 1 yy gt 1THORN

If the sensitivity to quality is sufficiently small in relation to theperceived inconvenience of waiting that is if

j ltt

2ethy2 y1THORN

then yy y gt 1 and it must be that ethy lt 0 yy 2 frac120 1THORN ethy 2 frac120 1 yy gt 1THORN orethy lt 0 yy gt 1THORN In Appendix A it has also been shown that no Nash

Figure 2Representation of indifferent consumer if ethy lt 0 yy 2 frac120 1THORN

Journal of Transport Economics and Policy Volume 40 Part 1

146

equilibrium in pure strategies exists if ethy lt 0 yy 2 frac120 1THORN orethy 2 frac120 1 yy gt 1THORN The division of demand if ethy lt 0 yy gt 1THORN is shown inFigure 3

In this division of demand the respective demands for operator 1and operator 2 are D1 frac14 1 x2 and D2 frac14 x2 so that the profits will bep1 frac14 p1eth1 x2THORN and p2 frac14 p2x2 It can be easily seen from these profitsthat there are no subgame perfect equilibrium prices And even if therewere then operators would not prefer the same distance x2 between depar-tures Operator 1 would like to have a zero distance that is x2 frac14 0 betweenboth operatorsrsquo locations and operator 2 would prefer maximum distancethat is x2 frac14 1 between departures Consequently no Nash equilibrium inpure strategies exists in the division of demand if ethy lt 0 yy gt 1THORN

Consequently there is a subgame perfect Nash equilibrium in purestrategies if the sensitivity to quality is sufficiently large that is if j5 tbut no Nash equilibrium in pure strategies exists if this sensitivity to qualityis sufficiently small

40 Interpretation of Results

The difference in consumersrsquo sensitivity to quality could explain whycompetition in local bus transport results in unstable service patternswhile air transport does not seem to have the same problem

41 Short-distance transport

Given the short-distances travelled operators in local bus transport havevery limited scope for meaningful product differentiation that could

Figure 3Representation of indifferent consumer if ethy lt 0 yy gt 1THORN

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

147

make consumers loyal A consumer will generally take the first bus thatarrives at the stop This occurs in the division of demand of Figure 3 Inthat case each operator prefers a different distance between departuretimes and will continuously try to attain his preferred distance The pre-ferred distance between departures for both operators is conflicting andno subgame perfect equilibrium in pure strategies with regard to thetiming of departures exists

This result corresponds to the generally-shared view on competition inurban public transport in continental Europe The European Commissionin its proposal for new regulation of the award of public service contractsin public transport by Member States articulates this view stating thatwithout exclusive rights lsquoservice patterns are unstablersquo2 This perceptionis based on the experiences in Great Britain of the deregulation of localpublic transport

Evans (1990) and Mackie et al (1995) observed that after deregulationof local public transport the number of travellers did not increase despitethe doubling of service levels (frequencies) and consequent reductions inwaiting times This lsquopuzzling resultrsquo could not be explained by the declinein bus usage due to higher real incomes and lower real motoring costsOne explanation that has been put forward was that frequency increasesare compensated by offsetting effects for example uncertainty caused topassengers by route instability such as irregular intervals frequently chan-ging timetables and so on (Evans 1990 Mackie et al 1995)

The model for low consumer sensitivity to quality predicts this instabil-ity of service patterns In the division of demand of Figure 3 the preferredlocation of operator 1 is just before the departure of operator 2 (x2 frac14 0)while operator 2 prefers a larger distance between departures (x2 gt 0)Given x2 frac14 0 operator 2 will choose a later departure but in reactionoperator 1 will follow in order to reduce the distance to x2 frac14 0 againand so on Basically every operator would like to be at a bus stop justbefore its competitor in order to take the whole market This implies thatoperators are lsquohead-runningrsquo each other

With regard to pricing Mackie et al (1995) stated that pricing is not aparticularly potent marketing weapon The first priority is on service ratherthan fares as travellers tend to board the first bus This behaviour of con-sumers is confirmed by the model for the situation in which an operatorrsquos

2Proposal from the European Commission of 26 July 2000 for a Regulation of the European Parliament

and of the Council on action by Member States concerning public service requirements and the award

of public service contracts in passenger transport by rail road and inland waterway COM(2000)7

provisional p 5

Journal of Transport Economics and Policy Volume 40 Part 1

148

demand is independent of prices and D1 frac14 1 x2 and D2 frac14 x2 In this casethe model shows that p1=p1 5 0 and p2=p25 0 Hence operators arecompeting over the timing of departures rather than pricing Evans statesthat (1990 p 266) lsquoThe operators match fares and tacitly collude to main-tain the pre-existing fare structure The operators also tacitly collude toincrease fares simultaneously at a rate at least as fast as inflation Faresremain the same on high-demand as on low-demand routes and on activelycompetitive as on non-competitive routesrsquo The model shows that theupward pressure on prices will only be limited by the maximum willingnessto pay Consequently the pricing discipline comes from external factorsfor example the existence of competition from another mode (such asprivate car cycling walking and so on) or competition between activitiesthat consumers can undertake (and that may or may not require transport)This clarifies why fares move at a similar rate to inflation and are notrelated to the level of demand on a route or the level of competition on aroute

42 Long-distance transport

In long-distance transport such as air transport consumers are moresensitive to quality Travel times are much longer and consequently con-sumers are more appreciative of comfort This allows for much greaterquality differentiation than in short-distance travel Hence consumerswill more easily take an alternative flight Non-price and non-schedulingfactors increase in importance for longer distances as can be seen for airtransport in the Table 1

The factors as distinguished in the Avmark Aviation Economist arelsquoschedulersquo lsquofarersquo lsquoairlinersquo lsquoairplanersquo and lsquootherrsquo lsquoSchedulersquo and lsquofarersquo areequivalent to the endogenous variables lsquoschedulersquo and lsquopricersquo lsquoAirlinersquo

Table 1

Most Influential Factors in Choosing a Flight

Factors asdistinguishedby the model

Factors asdistinguishedby Source

Length of flight

Under 2 hours () 2ndash5 hours () Over 5 hours ()

Schedule Schedule 701 430 193

Price Fare 114 137 165

Quality Airline 155 362 530Airplane 25 66 102Other 05 06 10

Source Avmark Aviation EconomistIAPA in Gialloreto 1988

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

149

lsquoairplanersquo and lsquootherrsquo can be clustered into the variable lsquoqualityrsquo Pressuredby competition airlines have become increasingly creative and effective indifferentiating their services in terms of quality including the creation ofconsumer loyalty

This situation is described by a sufficient sensitivity to quality that isj5 t as depicted in Figure 1 Given this division of demand operatorsmaximally differentiate in quality that is y1 frac14 0 and y2 frac14 1 This qualitydifferentiation relaxes competition over scheduling The model showsthat an operator cannot improve his position by choosing another timeof departure given the time of departure of his competitor Stronger consu-mer loyalty eliminates operatorsrsquo incentive to lsquohead-runrsquo each other whichcreates a subgame perfect equilibrium in timing departures Intuitively onewould say that an operator who moves to a later point of time increases hismarket but sufficiently strong consumersrsquo sensitivity to quality balancesthis tendency Consumers tend to wait for the departure of their preferredoperator

With regard to price the intuition cannot be confirmed that operatorsdo not seem to compete on price because pricing is too strong a marketingweapon According to the model operators do compete in price Furtheranalysis is needed in order to ascertain whether (and if so why) operatorsdo not seem to compete in price in long-distance transport One obser-vation (Brenner 1975) has been that scheduled transport operators tendto rival each other on frequency instead of price Such competitionincreases costs putting upward pressure on prices which could offset anyreduction in price that is normally associated with the introduction ofcompetition

43 Short-distance vs long-distanceThe impact of travel distance on stability can also be seen in the deregula-tion of lsquolong-distancersquo bus services in Great Britain In 1980 the Britishgovernment abolished a system of quantity control in the express coachmarket The deregulation allowed for free entry and competition onroutes served by nationalised carriers Douglas (1987) made a thoroughassessment of the effects of this deregulation on market structure faresservice quality and costs using data provided by express coach operatorsHe showed that on short-distance connections independent operatorsentering the market were unable to develop a significant market sharesince the two national carriers simply matched or undercut their faresand increased or manipulated departure times (Douglas 1997) Only 39per cent of such services to and from London survived during the firstfew years of deregulation The national carriers maintained some competi-tive advantages after deregulation such as sole access to major and centrally

Journal of Transport Economics and Policy Volume 40 Part 1

150

located bus stations a considerable network of services and an extensivesales network This made them better able to survive than the newindependent operators on the market

On long-distance connections however several independents captureda permanent place in the market Specialisation by offering a premierquality service allowed the independents to build up immunity to thepurely fare and scheduling responses of nationalised carriers and thuscapture a share of the market (Douglas 1997) In this way the indepen-dents were especially successful on the Anglo-Scottish routes The longertravel distance offered operators greater scope for product differentiationConsequently more operators were able to provide services even if theydeparted at the same time In the first few years of deregulation 67 percent of new long-distance services to or from London survived Henceproduct differentiation on long-distance connections made entrants resis-tant to the pricing and scheduling responses of incumbent operators bycreating consumer loyalty stabilising scheduling competition

50 Conclusion

For operators in scheduled passenger transport it is a great marketingchallenge to create an image that is distinct from their competitorsOperating the same or similar types of vehicles on the same routes doesnot have many elements of visible tangible differentiation vis-a-viscompetitors Many of the elements in which differences do exist are bytheir nature subjective and difficult to prove to the sceptical consumerExamples are friendliness and courtesy of personnel interior designseats mealssnacks lounges advertising image and so on Long-distanceoperators are better able than short-distance operators to realise suchproduct differentiation in a meaningful fashion Over longer distancesconsumers are generally more flexible with regard to departure times andare more appreciative of their preferred quality of service

In a two-dimensional horizontal product differentiation model withlinear waiting costs for departures and non-linear sensitivity to deviationsfrom preferred quality of service it is shown that a stable service patternrequires consumers to be sufficiently sensitive to differences in qualitybetween operators In reaction operators will differentiate their productsin terms of quality This differentiation prevents consumers from simplytaking the vehicle that is closest to their preferred departure time Consu-mers will be inclined to take an earlier or later departure if they feel morecomfortable with that operator or if there are additional benefits provided

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

151

by this operator In contrast if consumers are not sensitive to qualitydifferences operators would prefer to schedule their vehicles just beforetheir competitor in order to lsquostealrsquo its customers

On the basis of Neven and Thisse (1990) Ansari et al (1998) andIrmen and Thisse (1998) it can be expected that this result will notchange if the dimension of quality differentiation is modelled as verticaldifferentiation rather than horizontal differentiation It is clear that thequality differentiation considered has not only horizontal but also verticalaspects One example is seat width and pitch For the same price everyconsumer would appreciate more space The most dominant factordifferentiating operators is probably an operatorrsquos consumer loyaltyprogramme and that creates horizontal differentiation A formalanalysis for the case of vertical differentiation is beyond the scope of thispaper

The sensitivity to quality differences is a plausible factor that couldclarify the difference in existence of a stable equilibrium between differentmodes of scheduled transport A modal spectrum can be created on thebasis of the relevance of quality differentiation for the selection of an opera-tor The low-relevance end of this spectrum includes examples as containerfreight operations (such as liner shipping) and local public transport Thehigh-relevance end would probably include inter-continental passengerair transport For the low-relevance modes experience shows that com-petition results in unstable service patterns For the high-relevance modestability has never appeared to be a problem

References

Ansari A N Economides and J Steckel (1998) lsquoThe Max-min-min Principle of ProductDifferentiationrsquo Journal of Regional Science 38 207ndash30

Banister B (1985) lsquoDeregulating the Bus Industry in Britain (A) the ProposalsrsquoTransport Reviews 5 99ndash103

Brenner M A (1975) lsquoNeed for Continued Economic Regulation of Air TransportrsquoJournal of Air Law and Commerce 41 793ndash813

Cancian M A Bills and T Bergstrom (1995) lsquoHotelling Location Problems withDirectional Constraints an Application to Television News Schedulingrsquo Journal ofIndustrial Economics 43 121ndash4

DrsquoAspremont C J Jaskold Gabszewicz and J-F Thisse (1979) lsquoOn HotellingrsquoslsquolsquoStability in competitionrsquorsquorsquo Econometrica 47 1145ndash50

Douglas N J (1987) A Welfare Assessment of Transport Deregulation The Case of theExpress Coach Market in 1980 Aldershot Gower

Evans A (1987) lsquoA Theoretical Comparison of Competition with Other EconomicRegimes for Bus Servicesrsquo Journal of Transport Economics and Policy 21 7ndash36

Journal of Transport Economics and Policy Volume 40 Part 1

152

incurs costs of j per unit y Consequently the utility U for a consumer ilocated at ethxi yiTHORN and travelling with operator 1 or 2 respectively are

Uieth1THORN frac14 V p1 teth1 xiTHORN jethy1 yiTHORN2

Uieth2THORN frac14V p2 tethx2 xiTHORN jethy2 yiTHORN2 if 0 lt xi 4x2

V p2 teth1thorn x2 xiTHORN jethy2 yiTHORN2 if x2 lt xi 4 1

(

where V is the maximum willingness to pay p1 and p2 are the prices ofoperators 1 and 2 respectively x2 is the time difference between both opera-torsrsquo departures and y1 and y2 are the respective locations of operator 1and 2 with respect to the quality they offer The maximum willingness topay reflects the existence of competition from other modes and competitionbetween alternative ways of spending time (not all requiring transport) Forsimplicity it is assumed that V is sufficiently large The x-axis locations ofboth operatorsrsquo departures are normalised around the location of departureof operator 1 This implies that the location of operator 1 x1 is 0 byassumption and that the location of operator 2 x2 is reinterpreted as thetime between both operatorsrsquo departures This time is measured as theclockwise distance of operator 2rsquos location of departure from operator1rsquos location of departure With regard to the y-axis locations it is assumedthat y25 y1 This assumption does not influence the results in a qualitativeway because quality differentiation is horizontal

Since both operators provide a single departure and share identical pro-duction technologies the production costs of both operators are assumedto be C These production costs can be left out of consideration becausethey do not qualitatively affect the strategies of operators Consequentlyprofits are given by p1 frac14 p1D1 and p2 frac14 p2D2 where D1 and D2 are thedemands of operator 1 and operator 2 respectively The decisions ofoperators are modelled in a dynamic two-stage game In the first stageboth operators simultaneously determine their products by choosinglocations x2 y1 and y2 In the second stage operators choose prices Thisorder reflects the fact that prices are easily changed at very short noticeScheduling decisions and quality are more difficult and require more timeto implement

The two stages of the game are subgames of the overall game Servicepatterns will only be stable if in the overall game there exists a subgameperfect Nash equilibrium in pure strategies Dynamic games are solvedby backward induction At stage 1 operators anticipate their optimalstrategies at stage 2 and establish their optimal strategies for stage 1accordingly Consequently the two stages of the overall game need to beanalysed in reverse order This generates two questions First at stage 2given any chosen locations of departures and qualities what are the

Journal of Transport Economics and Policy Volume 40 Part 1

142

equilibrium prices p1 and p2 Second at stage 1 what is the optimal choiceof locations of departures and qualities for both operators taking the effecton prices into account

Operatorsrsquo demands can be established by equating the utility functionsfor consumers with a preferred departure time of 0 lt xi 4x2 andx2 lt xi 4 1 respectively This generates the indifferent consumers whoget the same utility from using either the service of operator 1 or that ofoperator 2 that is

y frac14 p2 p1 teth1 x2THORN thorn jethy22 y21THORN2jethy2 y1THORN

for 0 lt xi 4x2

and

yy frac14 p2 p1 thorn tx2 thorn jethy22 y21THORN2jethy2 y1THORN

for x2 lt xi 4 1

It is noted that y lt yyA graphical representation in case the indifferent consumers y yy belong

to the interval [01] is given in Figure 1 where the area above the linesegments that position the indifferent consumer represents the demandfor operator 2 and the area under these line segments represent thedemand for operator 1

This figure shows that of the consumers with a preferred departure timeof 0 lt xi 4x2 a total of x2eth1 yTHORN will choose operator 2 because it offersthe closest departure The other consumers with a preferred departuretime 0 lt xi 4x2 a total of x2 y prefer to pass operator 2rsquos departureand wait for the departure of operator 1 For these consumers the bettermatch of the service of operator 1 with their quality preferences com-pensates for the longer waiting time Similarly of the consumers whohave a preferred departure time of x2 lt xi 4 1 a total of eth1 x2THORNyy prefer

Figure 1Representation of indifferent consumer if y yy 2 frac120 1

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

143

operator 1 which offers the closest departures and a total ofeth1 x2THORNeth1 yyTHORN prefer to pass the departure of operator 1 and wait forthe departure of operator 2

30 Analysis

The main question is whether there exists a stable service pattern and if sounder what conditions This boils down to looking for a subgame perfectNash equilibrium in pure strategies

Proposition 1 If consumers are sufficiently sensitive to quality that is j5 t asubgame perfect Nash equilibrium in pure strategies exists where for anylocation x2 that is the distance between the departure times of operator 1and 2 equilibrium locations in quality and fares are given by y1 frac14 0 y2 frac14 1and p1 frac14 p2 frac14 j In such an equilibrium the location x2 is undetermined Incontrast if consumers are insufficiently sensitive to quality there is nosubgame perfect Nash equilibrium in pure strategies

Proof As shown above the respective demands if y yy 2 frac120 1 will be

D1 frac14 x2

p2 p1 teth1 x2THORN thorn jethy22 y21THORN

2jethy2 y1THORN

thorn eth1 x2THORNp2 p1 thorn tx2 thorn jethy22 y21THORN

2jethy2 y1THORN

and

D2 frac14 x2

1 p2 p1 teth1 x2THORN thorn jethy22 y21THORN

2jethy2 y1THORN

thorn eth1 x2THORN1 p2 p1 thorn tx2 thorn jethy22 y21THORN

2jethy2 y1THORN

These demands for operator 1 and operator 2 can be rewritten as

D1 frac14p2 p1 thorn jethy22 y21THORN

2jethy2 y1THORNand D2 frac14 1thorn p1 p2 jethy22 y21THORN

2jethy2 y1THORN

It should be noted that these demands do not depend on x2 Con-sequently both operators are indifferent with regard to the distancebetween their departures This implies that an operator has no incentiveto change a location in reaction to the location of its competitor

Journal of Transport Economics and Policy Volume 40 Part 1

144

On the basis of these demands profits for operator 1 and operator 2 willbe

p1 frac14 p1

p2 p1 thorn jethy22 y21THORN

2jethy2 y1THORN

and p2 frac14 p2

1thorn p1 p2 jethy22 y21THORN

2jethy2 y1THORN

Maximising these profits with respect to fares gives the followingreaction curves

p1 frac14p2 thorn jethy22 y21THORN

2and p2 frac14

p1 thorn 2jethy2 y1THORN jethy22 y21THORN2

Substituting these reaction curves into each other gives the subgameperfect prices

p1 frac142jethy2 y1THORN thorn jethy22 y21THORN

3and p2 frac14

4jethy2 y1THORN jethy22 y21THORN3

Substituting the subgame perfect prices into the expression for demandand multiplying these by their own prices generates the following equili-brium profits

p1 frac14eth2jethy2 y1THORN thorn jethy22 y21THORNTHORN2

18jethy2 y1THORNand p2 frac14

eth4jethy2 y1THORN jethy22 y21THORNTHORN2

18jethy2 y1THORN

Maximising the profits with respect to the location of quality gives

p1y1

frac14 frac122jethy2 y1THORN thorn jethy22 y21THORNfrac12jethy22 y21THORN 4y1jethy2 y1THORN 2jethy2 y1THORN18jethy2 y1THORN2

and

p2y2

frac14 frac124jethy2 y1THORN jethy22 y21THORNfrac12jethy22 y21THORN 4y2jethy2 y1THORN thorn 4jethy2 y1THORN18jethy2 y1THORN2

The expressions show that p1=y1 lt 0 and p2=y2 gt 0 Henceoperator 1 will choose to offer quality y1 frac14 0 and operator 2 will offery2 frac14 1 Substituting these locations into the subgame perfect prices andequilibrium profits gives p1 frac14 p2 frac14 j and p1 frac14 p2 frac14 j=2 respectively Anoperator cannot generate higher profits by deviating from this differentia-tion in quality and associated fares if the conditions for this division ofdemand between both operators are satisfied that is y yy 2 frac120 1 Substitut-ing the equilibrium qualities y1 frac14 0 y2 frac14 1 and prices p1 frac14 p2 frac14 j into

y frac14 p2 p1 teth1 x2THORN thorn jethy22 y21THORN2jethy2 y1THORN

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

145

shows that y 2 frac120 1 if j5 teth1 x2THORN Doing the same for

yy frac14 p2 p1 thorn tx2 thorn jethy22 y21THORN2jethy2 y1THORN

shows that yy 2 frac120 1 if j5 tx2 Consequently

p1p2 frac14 j=2 if

j5 teth1 x2THORN for 04x2 lt 1=2

j5 tx2 for 1=24 x2 4 1

These conditions will be fulfilled for any x2 2 frac120 1 if j5 t so that anecessary condition for equilibrium is that the sensitivity to quality issufficiently large in relation to the perceived inconvenience of lsquowaitingrsquo

It has to be checked whether the operators cannot realise a higherprofit than p1 p

2 by choosing qualities and prices so that the indifferent

consumers y andor the indifferent consumers yy have a preferred qualityoutside the area defined by y yy 2 frac120 1 Figure 2 shows the situation inwhich one of the operators deviates from his equilibrium strategy bychoosing quality or price so that y lt 0 and yy 2 frac120 1

In Appendix A it has been shown that both operators cannot realisehigher profits by deviating from their equilibrium strategy by choosinglocations and prices so that either ethy lt 0 yy 2 frac120 1THORN or ethy 2 frac120 1 yy gt 1THORN

If the sensitivity to quality is sufficiently small in relation to theperceived inconvenience of waiting that is if

j ltt

2ethy2 y1THORN

then yy y gt 1 and it must be that ethy lt 0 yy 2 frac120 1THORN ethy 2 frac120 1 yy gt 1THORN orethy lt 0 yy gt 1THORN In Appendix A it has also been shown that no Nash

Figure 2Representation of indifferent consumer if ethy lt 0 yy 2 frac120 1THORN

Journal of Transport Economics and Policy Volume 40 Part 1

146

equilibrium in pure strategies exists if ethy lt 0 yy 2 frac120 1THORN orethy 2 frac120 1 yy gt 1THORN The division of demand if ethy lt 0 yy gt 1THORN is shown inFigure 3

In this division of demand the respective demands for operator 1and operator 2 are D1 frac14 1 x2 and D2 frac14 x2 so that the profits will bep1 frac14 p1eth1 x2THORN and p2 frac14 p2x2 It can be easily seen from these profitsthat there are no subgame perfect equilibrium prices And even if therewere then operators would not prefer the same distance x2 between depar-tures Operator 1 would like to have a zero distance that is x2 frac14 0 betweenboth operatorsrsquo locations and operator 2 would prefer maximum distancethat is x2 frac14 1 between departures Consequently no Nash equilibrium inpure strategies exists in the division of demand if ethy lt 0 yy gt 1THORN

Consequently there is a subgame perfect Nash equilibrium in purestrategies if the sensitivity to quality is sufficiently large that is if j5 tbut no Nash equilibrium in pure strategies exists if this sensitivity to qualityis sufficiently small

40 Interpretation of Results

The difference in consumersrsquo sensitivity to quality could explain whycompetition in local bus transport results in unstable service patternswhile air transport does not seem to have the same problem

41 Short-distance transport

Given the short-distances travelled operators in local bus transport havevery limited scope for meaningful product differentiation that could

Figure 3Representation of indifferent consumer if ethy lt 0 yy gt 1THORN

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

147

make consumers loyal A consumer will generally take the first bus thatarrives at the stop This occurs in the division of demand of Figure 3 Inthat case each operator prefers a different distance between departuretimes and will continuously try to attain his preferred distance The pre-ferred distance between departures for both operators is conflicting andno subgame perfect equilibrium in pure strategies with regard to thetiming of departures exists

This result corresponds to the generally-shared view on competition inurban public transport in continental Europe The European Commissionin its proposal for new regulation of the award of public service contractsin public transport by Member States articulates this view stating thatwithout exclusive rights lsquoservice patterns are unstablersquo2 This perceptionis based on the experiences in Great Britain of the deregulation of localpublic transport

Evans (1990) and Mackie et al (1995) observed that after deregulationof local public transport the number of travellers did not increase despitethe doubling of service levels (frequencies) and consequent reductions inwaiting times This lsquopuzzling resultrsquo could not be explained by the declinein bus usage due to higher real incomes and lower real motoring costsOne explanation that has been put forward was that frequency increasesare compensated by offsetting effects for example uncertainty caused topassengers by route instability such as irregular intervals frequently chan-ging timetables and so on (Evans 1990 Mackie et al 1995)

The model for low consumer sensitivity to quality predicts this instabil-ity of service patterns In the division of demand of Figure 3 the preferredlocation of operator 1 is just before the departure of operator 2 (x2 frac14 0)while operator 2 prefers a larger distance between departures (x2 gt 0)Given x2 frac14 0 operator 2 will choose a later departure but in reactionoperator 1 will follow in order to reduce the distance to x2 frac14 0 againand so on Basically every operator would like to be at a bus stop justbefore its competitor in order to take the whole market This implies thatoperators are lsquohead-runningrsquo each other

With regard to pricing Mackie et al (1995) stated that pricing is not aparticularly potent marketing weapon The first priority is on service ratherthan fares as travellers tend to board the first bus This behaviour of con-sumers is confirmed by the model for the situation in which an operatorrsquos

2Proposal from the European Commission of 26 July 2000 for a Regulation of the European Parliament

and of the Council on action by Member States concerning public service requirements and the award

of public service contracts in passenger transport by rail road and inland waterway COM(2000)7

provisional p 5

Journal of Transport Economics and Policy Volume 40 Part 1

148

demand is independent of prices and D1 frac14 1 x2 and D2 frac14 x2 In this casethe model shows that p1=p1 5 0 and p2=p25 0 Hence operators arecompeting over the timing of departures rather than pricing Evans statesthat (1990 p 266) lsquoThe operators match fares and tacitly collude to main-tain the pre-existing fare structure The operators also tacitly collude toincrease fares simultaneously at a rate at least as fast as inflation Faresremain the same on high-demand as on low-demand routes and on activelycompetitive as on non-competitive routesrsquo The model shows that theupward pressure on prices will only be limited by the maximum willingnessto pay Consequently the pricing discipline comes from external factorsfor example the existence of competition from another mode (such asprivate car cycling walking and so on) or competition between activitiesthat consumers can undertake (and that may or may not require transport)This clarifies why fares move at a similar rate to inflation and are notrelated to the level of demand on a route or the level of competition on aroute

42 Long-distance transport

In long-distance transport such as air transport consumers are moresensitive to quality Travel times are much longer and consequently con-sumers are more appreciative of comfort This allows for much greaterquality differentiation than in short-distance travel Hence consumerswill more easily take an alternative flight Non-price and non-schedulingfactors increase in importance for longer distances as can be seen for airtransport in the Table 1

The factors as distinguished in the Avmark Aviation Economist arelsquoschedulersquo lsquofarersquo lsquoairlinersquo lsquoairplanersquo and lsquootherrsquo lsquoSchedulersquo and lsquofarersquo areequivalent to the endogenous variables lsquoschedulersquo and lsquopricersquo lsquoAirlinersquo

Table 1

Most Influential Factors in Choosing a Flight

Factors asdistinguishedby the model

Factors asdistinguishedby Source

Length of flight

Under 2 hours () 2ndash5 hours () Over 5 hours ()

Schedule Schedule 701 430 193

Price Fare 114 137 165

Quality Airline 155 362 530Airplane 25 66 102Other 05 06 10

Source Avmark Aviation EconomistIAPA in Gialloreto 1988

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

149

lsquoairplanersquo and lsquootherrsquo can be clustered into the variable lsquoqualityrsquo Pressuredby competition airlines have become increasingly creative and effective indifferentiating their services in terms of quality including the creation ofconsumer loyalty

This situation is described by a sufficient sensitivity to quality that isj5 t as depicted in Figure 1 Given this division of demand operatorsmaximally differentiate in quality that is y1 frac14 0 and y2 frac14 1 This qualitydifferentiation relaxes competition over scheduling The model showsthat an operator cannot improve his position by choosing another timeof departure given the time of departure of his competitor Stronger consu-mer loyalty eliminates operatorsrsquo incentive to lsquohead-runrsquo each other whichcreates a subgame perfect equilibrium in timing departures Intuitively onewould say that an operator who moves to a later point of time increases hismarket but sufficiently strong consumersrsquo sensitivity to quality balancesthis tendency Consumers tend to wait for the departure of their preferredoperator

With regard to price the intuition cannot be confirmed that operatorsdo not seem to compete on price because pricing is too strong a marketingweapon According to the model operators do compete in price Furtheranalysis is needed in order to ascertain whether (and if so why) operatorsdo not seem to compete in price in long-distance transport One obser-vation (Brenner 1975) has been that scheduled transport operators tendto rival each other on frequency instead of price Such competitionincreases costs putting upward pressure on prices which could offset anyreduction in price that is normally associated with the introduction ofcompetition

43 Short-distance vs long-distanceThe impact of travel distance on stability can also be seen in the deregula-tion of lsquolong-distancersquo bus services in Great Britain In 1980 the Britishgovernment abolished a system of quantity control in the express coachmarket The deregulation allowed for free entry and competition onroutes served by nationalised carriers Douglas (1987) made a thoroughassessment of the effects of this deregulation on market structure faresservice quality and costs using data provided by express coach operatorsHe showed that on short-distance connections independent operatorsentering the market were unable to develop a significant market sharesince the two national carriers simply matched or undercut their faresand increased or manipulated departure times (Douglas 1997) Only 39per cent of such services to and from London survived during the firstfew years of deregulation The national carriers maintained some competi-tive advantages after deregulation such as sole access to major and centrally

Journal of Transport Economics and Policy Volume 40 Part 1

150

located bus stations a considerable network of services and an extensivesales network This made them better able to survive than the newindependent operators on the market

On long-distance connections however several independents captureda permanent place in the market Specialisation by offering a premierquality service allowed the independents to build up immunity to thepurely fare and scheduling responses of nationalised carriers and thuscapture a share of the market (Douglas 1997) In this way the indepen-dents were especially successful on the Anglo-Scottish routes The longertravel distance offered operators greater scope for product differentiationConsequently more operators were able to provide services even if theydeparted at the same time In the first few years of deregulation 67 percent of new long-distance services to or from London survived Henceproduct differentiation on long-distance connections made entrants resis-tant to the pricing and scheduling responses of incumbent operators bycreating consumer loyalty stabilising scheduling competition

50 Conclusion

For operators in scheduled passenger transport it is a great marketingchallenge to create an image that is distinct from their competitorsOperating the same or similar types of vehicles on the same routes doesnot have many elements of visible tangible differentiation vis-a-viscompetitors Many of the elements in which differences do exist are bytheir nature subjective and difficult to prove to the sceptical consumerExamples are friendliness and courtesy of personnel interior designseats mealssnacks lounges advertising image and so on Long-distanceoperators are better able than short-distance operators to realise suchproduct differentiation in a meaningful fashion Over longer distancesconsumers are generally more flexible with regard to departure times andare more appreciative of their preferred quality of service

In a two-dimensional horizontal product differentiation model withlinear waiting costs for departures and non-linear sensitivity to deviationsfrom preferred quality of service it is shown that a stable service patternrequires consumers to be sufficiently sensitive to differences in qualitybetween operators In reaction operators will differentiate their productsin terms of quality This differentiation prevents consumers from simplytaking the vehicle that is closest to their preferred departure time Consu-mers will be inclined to take an earlier or later departure if they feel morecomfortable with that operator or if there are additional benefits provided

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

151

by this operator In contrast if consumers are not sensitive to qualitydifferences operators would prefer to schedule their vehicles just beforetheir competitor in order to lsquostealrsquo its customers

On the basis of Neven and Thisse (1990) Ansari et al (1998) andIrmen and Thisse (1998) it can be expected that this result will notchange if the dimension of quality differentiation is modelled as verticaldifferentiation rather than horizontal differentiation It is clear that thequality differentiation considered has not only horizontal but also verticalaspects One example is seat width and pitch For the same price everyconsumer would appreciate more space The most dominant factordifferentiating operators is probably an operatorrsquos consumer loyaltyprogramme and that creates horizontal differentiation A formalanalysis for the case of vertical differentiation is beyond the scope of thispaper

The sensitivity to quality differences is a plausible factor that couldclarify the difference in existence of a stable equilibrium between differentmodes of scheduled transport A modal spectrum can be created on thebasis of the relevance of quality differentiation for the selection of an opera-tor The low-relevance end of this spectrum includes examples as containerfreight operations (such as liner shipping) and local public transport Thehigh-relevance end would probably include inter-continental passengerair transport For the low-relevance modes experience shows that com-petition results in unstable service patterns For the high-relevance modestability has never appeared to be a problem

References

Ansari A N Economides and J Steckel (1998) lsquoThe Max-min-min Principle of ProductDifferentiationrsquo Journal of Regional Science 38 207ndash30

Banister B (1985) lsquoDeregulating the Bus Industry in Britain (A) the ProposalsrsquoTransport Reviews 5 99ndash103

Brenner M A (1975) lsquoNeed for Continued Economic Regulation of Air TransportrsquoJournal of Air Law and Commerce 41 793ndash813

Cancian M A Bills and T Bergstrom (1995) lsquoHotelling Location Problems withDirectional Constraints an Application to Television News Schedulingrsquo Journal ofIndustrial Economics 43 121ndash4

DrsquoAspremont C J Jaskold Gabszewicz and J-F Thisse (1979) lsquoOn HotellingrsquoslsquolsquoStability in competitionrsquorsquorsquo Econometrica 47 1145ndash50

Douglas N J (1987) A Welfare Assessment of Transport Deregulation The Case of theExpress Coach Market in 1980 Aldershot Gower

Evans A (1987) lsquoA Theoretical Comparison of Competition with Other EconomicRegimes for Bus Servicesrsquo Journal of Transport Economics and Policy 21 7ndash36

Journal of Transport Economics and Policy Volume 40 Part 1

152

equilibrium prices p1 and p2 Second at stage 1 what is the optimal choiceof locations of departures and qualities for both operators taking the effecton prices into account

Operatorsrsquo demands can be established by equating the utility functionsfor consumers with a preferred departure time of 0 lt xi 4x2 andx2 lt xi 4 1 respectively This generates the indifferent consumers whoget the same utility from using either the service of operator 1 or that ofoperator 2 that is

y frac14 p2 p1 teth1 x2THORN thorn jethy22 y21THORN2jethy2 y1THORN

for 0 lt xi 4x2

and

yy frac14 p2 p1 thorn tx2 thorn jethy22 y21THORN2jethy2 y1THORN

for x2 lt xi 4 1

It is noted that y lt yyA graphical representation in case the indifferent consumers y yy belong

to the interval [01] is given in Figure 1 where the area above the linesegments that position the indifferent consumer represents the demandfor operator 2 and the area under these line segments represent thedemand for operator 1

This figure shows that of the consumers with a preferred departure timeof 0 lt xi 4x2 a total of x2eth1 yTHORN will choose operator 2 because it offersthe closest departure The other consumers with a preferred departuretime 0 lt xi 4x2 a total of x2 y prefer to pass operator 2rsquos departureand wait for the departure of operator 1 For these consumers the bettermatch of the service of operator 1 with their quality preferences com-pensates for the longer waiting time Similarly of the consumers whohave a preferred departure time of x2 lt xi 4 1 a total of eth1 x2THORNyy prefer

Figure 1Representation of indifferent consumer if y yy 2 frac120 1

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

143

operator 1 which offers the closest departures and a total ofeth1 x2THORNeth1 yyTHORN prefer to pass the departure of operator 1 and wait forthe departure of operator 2

30 Analysis

The main question is whether there exists a stable service pattern and if sounder what conditions This boils down to looking for a subgame perfectNash equilibrium in pure strategies

Proposition 1 If consumers are sufficiently sensitive to quality that is j5 t asubgame perfect Nash equilibrium in pure strategies exists where for anylocation x2 that is the distance between the departure times of operator 1and 2 equilibrium locations in quality and fares are given by y1 frac14 0 y2 frac14 1and p1 frac14 p2 frac14 j In such an equilibrium the location x2 is undetermined Incontrast if consumers are insufficiently sensitive to quality there is nosubgame perfect Nash equilibrium in pure strategies

Proof As shown above the respective demands if y yy 2 frac120 1 will be

D1 frac14 x2

p2 p1 teth1 x2THORN thorn jethy22 y21THORN

2jethy2 y1THORN

thorn eth1 x2THORNp2 p1 thorn tx2 thorn jethy22 y21THORN

2jethy2 y1THORN

and

D2 frac14 x2

1 p2 p1 teth1 x2THORN thorn jethy22 y21THORN

2jethy2 y1THORN

thorn eth1 x2THORN1 p2 p1 thorn tx2 thorn jethy22 y21THORN

2jethy2 y1THORN

These demands for operator 1 and operator 2 can be rewritten as

D1 frac14p2 p1 thorn jethy22 y21THORN

2jethy2 y1THORNand D2 frac14 1thorn p1 p2 jethy22 y21THORN

2jethy2 y1THORN

It should be noted that these demands do not depend on x2 Con-sequently both operators are indifferent with regard to the distancebetween their departures This implies that an operator has no incentiveto change a location in reaction to the location of its competitor

Journal of Transport Economics and Policy Volume 40 Part 1

144

On the basis of these demands profits for operator 1 and operator 2 willbe

p1 frac14 p1

p2 p1 thorn jethy22 y21THORN

2jethy2 y1THORN

and p2 frac14 p2

1thorn p1 p2 jethy22 y21THORN

2jethy2 y1THORN

Maximising these profits with respect to fares gives the followingreaction curves

p1 frac14p2 thorn jethy22 y21THORN

2and p2 frac14

p1 thorn 2jethy2 y1THORN jethy22 y21THORN2

Substituting these reaction curves into each other gives the subgameperfect prices

p1 frac142jethy2 y1THORN thorn jethy22 y21THORN

3and p2 frac14

4jethy2 y1THORN jethy22 y21THORN3

Substituting the subgame perfect prices into the expression for demandand multiplying these by their own prices generates the following equili-brium profits

p1 frac14eth2jethy2 y1THORN thorn jethy22 y21THORNTHORN2

18jethy2 y1THORNand p2 frac14

eth4jethy2 y1THORN jethy22 y21THORNTHORN2

18jethy2 y1THORN

Maximising the profits with respect to the location of quality gives

p1y1

frac14 frac122jethy2 y1THORN thorn jethy22 y21THORNfrac12jethy22 y21THORN 4y1jethy2 y1THORN 2jethy2 y1THORN18jethy2 y1THORN2

and

p2y2

frac14 frac124jethy2 y1THORN jethy22 y21THORNfrac12jethy22 y21THORN 4y2jethy2 y1THORN thorn 4jethy2 y1THORN18jethy2 y1THORN2

The expressions show that p1=y1 lt 0 and p2=y2 gt 0 Henceoperator 1 will choose to offer quality y1 frac14 0 and operator 2 will offery2 frac14 1 Substituting these locations into the subgame perfect prices andequilibrium profits gives p1 frac14 p2 frac14 j and p1 frac14 p2 frac14 j=2 respectively Anoperator cannot generate higher profits by deviating from this differentia-tion in quality and associated fares if the conditions for this division ofdemand between both operators are satisfied that is y yy 2 frac120 1 Substitut-ing the equilibrium qualities y1 frac14 0 y2 frac14 1 and prices p1 frac14 p2 frac14 j into

y frac14 p2 p1 teth1 x2THORN thorn jethy22 y21THORN2jethy2 y1THORN

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

145

shows that y 2 frac120 1 if j5 teth1 x2THORN Doing the same for

yy frac14 p2 p1 thorn tx2 thorn jethy22 y21THORN2jethy2 y1THORN

shows that yy 2 frac120 1 if j5 tx2 Consequently

p1p2 frac14 j=2 if

j5 teth1 x2THORN for 04x2 lt 1=2

j5 tx2 for 1=24 x2 4 1

These conditions will be fulfilled for any x2 2 frac120 1 if j5 t so that anecessary condition for equilibrium is that the sensitivity to quality issufficiently large in relation to the perceived inconvenience of lsquowaitingrsquo

It has to be checked whether the operators cannot realise a higherprofit than p1 p

2 by choosing qualities and prices so that the indifferent

consumers y andor the indifferent consumers yy have a preferred qualityoutside the area defined by y yy 2 frac120 1 Figure 2 shows the situation inwhich one of the operators deviates from his equilibrium strategy bychoosing quality or price so that y lt 0 and yy 2 frac120 1

In Appendix A it has been shown that both operators cannot realisehigher profits by deviating from their equilibrium strategy by choosinglocations and prices so that either ethy lt 0 yy 2 frac120 1THORN or ethy 2 frac120 1 yy gt 1THORN

If the sensitivity to quality is sufficiently small in relation to theperceived inconvenience of waiting that is if

j ltt

2ethy2 y1THORN

then yy y gt 1 and it must be that ethy lt 0 yy 2 frac120 1THORN ethy 2 frac120 1 yy gt 1THORN orethy lt 0 yy gt 1THORN In Appendix A it has also been shown that no Nash

Figure 2Representation of indifferent consumer if ethy lt 0 yy 2 frac120 1THORN

Journal of Transport Economics and Policy Volume 40 Part 1

146

equilibrium in pure strategies exists if ethy lt 0 yy 2 frac120 1THORN orethy 2 frac120 1 yy gt 1THORN The division of demand if ethy lt 0 yy gt 1THORN is shown inFigure 3

In this division of demand the respective demands for operator 1and operator 2 are D1 frac14 1 x2 and D2 frac14 x2 so that the profits will bep1 frac14 p1eth1 x2THORN and p2 frac14 p2x2 It can be easily seen from these profitsthat there are no subgame perfect equilibrium prices And even if therewere then operators would not prefer the same distance x2 between depar-tures Operator 1 would like to have a zero distance that is x2 frac14 0 betweenboth operatorsrsquo locations and operator 2 would prefer maximum distancethat is x2 frac14 1 between departures Consequently no Nash equilibrium inpure strategies exists in the division of demand if ethy lt 0 yy gt 1THORN

Consequently there is a subgame perfect Nash equilibrium in purestrategies if the sensitivity to quality is sufficiently large that is if j5 tbut no Nash equilibrium in pure strategies exists if this sensitivity to qualityis sufficiently small

40 Interpretation of Results

The difference in consumersrsquo sensitivity to quality could explain whycompetition in local bus transport results in unstable service patternswhile air transport does not seem to have the same problem

41 Short-distance transport

Given the short-distances travelled operators in local bus transport havevery limited scope for meaningful product differentiation that could

Figure 3Representation of indifferent consumer if ethy lt 0 yy gt 1THORN

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

147

make consumers loyal A consumer will generally take the first bus thatarrives at the stop This occurs in the division of demand of Figure 3 Inthat case each operator prefers a different distance between departuretimes and will continuously try to attain his preferred distance The pre-ferred distance between departures for both operators is conflicting andno subgame perfect equilibrium in pure strategies with regard to thetiming of departures exists

This result corresponds to the generally-shared view on competition inurban public transport in continental Europe The European Commissionin its proposal for new regulation of the award of public service contractsin public transport by Member States articulates this view stating thatwithout exclusive rights lsquoservice patterns are unstablersquo2 This perceptionis based on the experiences in Great Britain of the deregulation of localpublic transport

Evans (1990) and Mackie et al (1995) observed that after deregulationof local public transport the number of travellers did not increase despitethe doubling of service levels (frequencies) and consequent reductions inwaiting times This lsquopuzzling resultrsquo could not be explained by the declinein bus usage due to higher real incomes and lower real motoring costsOne explanation that has been put forward was that frequency increasesare compensated by offsetting effects for example uncertainty caused topassengers by route instability such as irregular intervals frequently chan-ging timetables and so on (Evans 1990 Mackie et al 1995)

The model for low consumer sensitivity to quality predicts this instabil-ity of service patterns In the division of demand of Figure 3 the preferredlocation of operator 1 is just before the departure of operator 2 (x2 frac14 0)while operator 2 prefers a larger distance between departures (x2 gt 0)Given x2 frac14 0 operator 2 will choose a later departure but in reactionoperator 1 will follow in order to reduce the distance to x2 frac14 0 againand so on Basically every operator would like to be at a bus stop justbefore its competitor in order to take the whole market This implies thatoperators are lsquohead-runningrsquo each other

With regard to pricing Mackie et al (1995) stated that pricing is not aparticularly potent marketing weapon The first priority is on service ratherthan fares as travellers tend to board the first bus This behaviour of con-sumers is confirmed by the model for the situation in which an operatorrsquos

2Proposal from the European Commission of 26 July 2000 for a Regulation of the European Parliament

and of the Council on action by Member States concerning public service requirements and the award

of public service contracts in passenger transport by rail road and inland waterway COM(2000)7

provisional p 5

Journal of Transport Economics and Policy Volume 40 Part 1

148

demand is independent of prices and D1 frac14 1 x2 and D2 frac14 x2 In this casethe model shows that p1=p1 5 0 and p2=p25 0 Hence operators arecompeting over the timing of departures rather than pricing Evans statesthat (1990 p 266) lsquoThe operators match fares and tacitly collude to main-tain the pre-existing fare structure The operators also tacitly collude toincrease fares simultaneously at a rate at least as fast as inflation Faresremain the same on high-demand as on low-demand routes and on activelycompetitive as on non-competitive routesrsquo The model shows that theupward pressure on prices will only be limited by the maximum willingnessto pay Consequently the pricing discipline comes from external factorsfor example the existence of competition from another mode (such asprivate car cycling walking and so on) or competition between activitiesthat consumers can undertake (and that may or may not require transport)This clarifies why fares move at a similar rate to inflation and are notrelated to the level of demand on a route or the level of competition on aroute

42 Long-distance transport

In long-distance transport such as air transport consumers are moresensitive to quality Travel times are much longer and consequently con-sumers are more appreciative of comfort This allows for much greaterquality differentiation than in short-distance travel Hence consumerswill more easily take an alternative flight Non-price and non-schedulingfactors increase in importance for longer distances as can be seen for airtransport in the Table 1

The factors as distinguished in the Avmark Aviation Economist arelsquoschedulersquo lsquofarersquo lsquoairlinersquo lsquoairplanersquo and lsquootherrsquo lsquoSchedulersquo and lsquofarersquo areequivalent to the endogenous variables lsquoschedulersquo and lsquopricersquo lsquoAirlinersquo

Table 1

Most Influential Factors in Choosing a Flight

Factors asdistinguishedby the model

Factors asdistinguishedby Source

Length of flight

Under 2 hours () 2ndash5 hours () Over 5 hours ()

Schedule Schedule 701 430 193

Price Fare 114 137 165

Quality Airline 155 362 530Airplane 25 66 102Other 05 06 10

Source Avmark Aviation EconomistIAPA in Gialloreto 1988

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

149

lsquoairplanersquo and lsquootherrsquo can be clustered into the variable lsquoqualityrsquo Pressuredby competition airlines have become increasingly creative and effective indifferentiating their services in terms of quality including the creation ofconsumer loyalty

This situation is described by a sufficient sensitivity to quality that isj5 t as depicted in Figure 1 Given this division of demand operatorsmaximally differentiate in quality that is y1 frac14 0 and y2 frac14 1 This qualitydifferentiation relaxes competition over scheduling The model showsthat an operator cannot improve his position by choosing another timeof departure given the time of departure of his competitor Stronger consu-mer loyalty eliminates operatorsrsquo incentive to lsquohead-runrsquo each other whichcreates a subgame perfect equilibrium in timing departures Intuitively onewould say that an operator who moves to a later point of time increases hismarket but sufficiently strong consumersrsquo sensitivity to quality balancesthis tendency Consumers tend to wait for the departure of their preferredoperator

With regard to price the intuition cannot be confirmed that operatorsdo not seem to compete on price because pricing is too strong a marketingweapon According to the model operators do compete in price Furtheranalysis is needed in order to ascertain whether (and if so why) operatorsdo not seem to compete in price in long-distance transport One obser-vation (Brenner 1975) has been that scheduled transport operators tendto rival each other on frequency instead of price Such competitionincreases costs putting upward pressure on prices which could offset anyreduction in price that is normally associated with the introduction ofcompetition

43 Short-distance vs long-distanceThe impact of travel distance on stability can also be seen in the deregula-tion of lsquolong-distancersquo bus services in Great Britain In 1980 the Britishgovernment abolished a system of quantity control in the express coachmarket The deregulation allowed for free entry and competition onroutes served by nationalised carriers Douglas (1987) made a thoroughassessment of the effects of this deregulation on market structure faresservice quality and costs using data provided by express coach operatorsHe showed that on short-distance connections independent operatorsentering the market were unable to develop a significant market sharesince the two national carriers simply matched or undercut their faresand increased or manipulated departure times (Douglas 1997) Only 39per cent of such services to and from London survived during the firstfew years of deregulation The national carriers maintained some competi-tive advantages after deregulation such as sole access to major and centrally

Journal of Transport Economics and Policy Volume 40 Part 1

150

located bus stations a considerable network of services and an extensivesales network This made them better able to survive than the newindependent operators on the market

On long-distance connections however several independents captureda permanent place in the market Specialisation by offering a premierquality service allowed the independents to build up immunity to thepurely fare and scheduling responses of nationalised carriers and thuscapture a share of the market (Douglas 1997) In this way the indepen-dents were especially successful on the Anglo-Scottish routes The longertravel distance offered operators greater scope for product differentiationConsequently more operators were able to provide services even if theydeparted at the same time In the first few years of deregulation 67 percent of new long-distance services to or from London survived Henceproduct differentiation on long-distance connections made entrants resis-tant to the pricing and scheduling responses of incumbent operators bycreating consumer loyalty stabilising scheduling competition

50 Conclusion

For operators in scheduled passenger transport it is a great marketingchallenge to create an image that is distinct from their competitorsOperating the same or similar types of vehicles on the same routes doesnot have many elements of visible tangible differentiation vis-a-viscompetitors Many of the elements in which differences do exist are bytheir nature subjective and difficult to prove to the sceptical consumerExamples are friendliness and courtesy of personnel interior designseats mealssnacks lounges advertising image and so on Long-distanceoperators are better able than short-distance operators to realise suchproduct differentiation in a meaningful fashion Over longer distancesconsumers are generally more flexible with regard to departure times andare more appreciative of their preferred quality of service

In a two-dimensional horizontal product differentiation model withlinear waiting costs for departures and non-linear sensitivity to deviationsfrom preferred quality of service it is shown that a stable service patternrequires consumers to be sufficiently sensitive to differences in qualitybetween operators In reaction operators will differentiate their productsin terms of quality This differentiation prevents consumers from simplytaking the vehicle that is closest to their preferred departure time Consu-mers will be inclined to take an earlier or later departure if they feel morecomfortable with that operator or if there are additional benefits provided

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

151

by this operator In contrast if consumers are not sensitive to qualitydifferences operators would prefer to schedule their vehicles just beforetheir competitor in order to lsquostealrsquo its customers

On the basis of Neven and Thisse (1990) Ansari et al (1998) andIrmen and Thisse (1998) it can be expected that this result will notchange if the dimension of quality differentiation is modelled as verticaldifferentiation rather than horizontal differentiation It is clear that thequality differentiation considered has not only horizontal but also verticalaspects One example is seat width and pitch For the same price everyconsumer would appreciate more space The most dominant factordifferentiating operators is probably an operatorrsquos consumer loyaltyprogramme and that creates horizontal differentiation A formalanalysis for the case of vertical differentiation is beyond the scope of thispaper

The sensitivity to quality differences is a plausible factor that couldclarify the difference in existence of a stable equilibrium between differentmodes of scheduled transport A modal spectrum can be created on thebasis of the relevance of quality differentiation for the selection of an opera-tor The low-relevance end of this spectrum includes examples as containerfreight operations (such as liner shipping) and local public transport Thehigh-relevance end would probably include inter-continental passengerair transport For the low-relevance modes experience shows that com-petition results in unstable service patterns For the high-relevance modestability has never appeared to be a problem

References

Ansari A N Economides and J Steckel (1998) lsquoThe Max-min-min Principle of ProductDifferentiationrsquo Journal of Regional Science 38 207ndash30

Banister B (1985) lsquoDeregulating the Bus Industry in Britain (A) the ProposalsrsquoTransport Reviews 5 99ndash103

Brenner M A (1975) lsquoNeed for Continued Economic Regulation of Air TransportrsquoJournal of Air Law and Commerce 41 793ndash813

Cancian M A Bills and T Bergstrom (1995) lsquoHotelling Location Problems withDirectional Constraints an Application to Television News Schedulingrsquo Journal ofIndustrial Economics 43 121ndash4

DrsquoAspremont C J Jaskold Gabszewicz and J-F Thisse (1979) lsquoOn HotellingrsquoslsquolsquoStability in competitionrsquorsquorsquo Econometrica 47 1145ndash50

Douglas N J (1987) A Welfare Assessment of Transport Deregulation The Case of theExpress Coach Market in 1980 Aldershot Gower

Evans A (1987) lsquoA Theoretical Comparison of Competition with Other EconomicRegimes for Bus Servicesrsquo Journal of Transport Economics and Policy 21 7ndash36

Journal of Transport Economics and Policy Volume 40 Part 1

152

operator 1 which offers the closest departures and a total ofeth1 x2THORNeth1 yyTHORN prefer to pass the departure of operator 1 and wait forthe departure of operator 2

30 Analysis

The main question is whether there exists a stable service pattern and if sounder what conditions This boils down to looking for a subgame perfectNash equilibrium in pure strategies

Proposition 1 If consumers are sufficiently sensitive to quality that is j5 t asubgame perfect Nash equilibrium in pure strategies exists where for anylocation x2 that is the distance between the departure times of operator 1and 2 equilibrium locations in quality and fares are given by y1 frac14 0 y2 frac14 1and p1 frac14 p2 frac14 j In such an equilibrium the location x2 is undetermined Incontrast if consumers are insufficiently sensitive to quality there is nosubgame perfect Nash equilibrium in pure strategies

Proof As shown above the respective demands if y yy 2 frac120 1 will be

D1 frac14 x2

p2 p1 teth1 x2THORN thorn jethy22 y21THORN

2jethy2 y1THORN

thorn eth1 x2THORNp2 p1 thorn tx2 thorn jethy22 y21THORN

2jethy2 y1THORN

and

D2 frac14 x2

1 p2 p1 teth1 x2THORN thorn jethy22 y21THORN

2jethy2 y1THORN

thorn eth1 x2THORN1 p2 p1 thorn tx2 thorn jethy22 y21THORN

2jethy2 y1THORN

These demands for operator 1 and operator 2 can be rewritten as

D1 frac14p2 p1 thorn jethy22 y21THORN

2jethy2 y1THORNand D2 frac14 1thorn p1 p2 jethy22 y21THORN

2jethy2 y1THORN

It should be noted that these demands do not depend on x2 Con-sequently both operators are indifferent with regard to the distancebetween their departures This implies that an operator has no incentiveto change a location in reaction to the location of its competitor

Journal of Transport Economics and Policy Volume 40 Part 1

144

On the basis of these demands profits for operator 1 and operator 2 willbe

p1 frac14 p1

p2 p1 thorn jethy22 y21THORN

2jethy2 y1THORN

and p2 frac14 p2

1thorn p1 p2 jethy22 y21THORN

2jethy2 y1THORN

Maximising these profits with respect to fares gives the followingreaction curves

p1 frac14p2 thorn jethy22 y21THORN

2and p2 frac14

p1 thorn 2jethy2 y1THORN jethy22 y21THORN2

Substituting these reaction curves into each other gives the subgameperfect prices

p1 frac142jethy2 y1THORN thorn jethy22 y21THORN

3and p2 frac14

4jethy2 y1THORN jethy22 y21THORN3

Substituting the subgame perfect prices into the expression for demandand multiplying these by their own prices generates the following equili-brium profits

p1 frac14eth2jethy2 y1THORN thorn jethy22 y21THORNTHORN2

18jethy2 y1THORNand p2 frac14

eth4jethy2 y1THORN jethy22 y21THORNTHORN2

18jethy2 y1THORN

Maximising the profits with respect to the location of quality gives

p1y1

frac14 frac122jethy2 y1THORN thorn jethy22 y21THORNfrac12jethy22 y21THORN 4y1jethy2 y1THORN 2jethy2 y1THORN18jethy2 y1THORN2

and

p2y2

frac14 frac124jethy2 y1THORN jethy22 y21THORNfrac12jethy22 y21THORN 4y2jethy2 y1THORN thorn 4jethy2 y1THORN18jethy2 y1THORN2

The expressions show that p1=y1 lt 0 and p2=y2 gt 0 Henceoperator 1 will choose to offer quality y1 frac14 0 and operator 2 will offery2 frac14 1 Substituting these locations into the subgame perfect prices andequilibrium profits gives p1 frac14 p2 frac14 j and p1 frac14 p2 frac14 j=2 respectively Anoperator cannot generate higher profits by deviating from this differentia-tion in quality and associated fares if the conditions for this division ofdemand between both operators are satisfied that is y yy 2 frac120 1 Substitut-ing the equilibrium qualities y1 frac14 0 y2 frac14 1 and prices p1 frac14 p2 frac14 j into

y frac14 p2 p1 teth1 x2THORN thorn jethy22 y21THORN2jethy2 y1THORN

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

145

shows that y 2 frac120 1 if j5 teth1 x2THORN Doing the same for

yy frac14 p2 p1 thorn tx2 thorn jethy22 y21THORN2jethy2 y1THORN

shows that yy 2 frac120 1 if j5 tx2 Consequently

p1p2 frac14 j=2 if

j5 teth1 x2THORN for 04x2 lt 1=2

j5 tx2 for 1=24 x2 4 1

These conditions will be fulfilled for any x2 2 frac120 1 if j5 t so that anecessary condition for equilibrium is that the sensitivity to quality issufficiently large in relation to the perceived inconvenience of lsquowaitingrsquo

It has to be checked whether the operators cannot realise a higherprofit than p1 p

2 by choosing qualities and prices so that the indifferent

consumers y andor the indifferent consumers yy have a preferred qualityoutside the area defined by y yy 2 frac120 1 Figure 2 shows the situation inwhich one of the operators deviates from his equilibrium strategy bychoosing quality or price so that y lt 0 and yy 2 frac120 1

In Appendix A it has been shown that both operators cannot realisehigher profits by deviating from their equilibrium strategy by choosinglocations and prices so that either ethy lt 0 yy 2 frac120 1THORN or ethy 2 frac120 1 yy gt 1THORN

If the sensitivity to quality is sufficiently small in relation to theperceived inconvenience of waiting that is if

j ltt

2ethy2 y1THORN

then yy y gt 1 and it must be that ethy lt 0 yy 2 frac120 1THORN ethy 2 frac120 1 yy gt 1THORN orethy lt 0 yy gt 1THORN In Appendix A it has also been shown that no Nash

Figure 2Representation of indifferent consumer if ethy lt 0 yy 2 frac120 1THORN

Journal of Transport Economics and Policy Volume 40 Part 1

146

equilibrium in pure strategies exists if ethy lt 0 yy 2 frac120 1THORN orethy 2 frac120 1 yy gt 1THORN The division of demand if ethy lt 0 yy gt 1THORN is shown inFigure 3

In this division of demand the respective demands for operator 1and operator 2 are D1 frac14 1 x2 and D2 frac14 x2 so that the profits will bep1 frac14 p1eth1 x2THORN and p2 frac14 p2x2 It can be easily seen from these profitsthat there are no subgame perfect equilibrium prices And even if therewere then operators would not prefer the same distance x2 between depar-tures Operator 1 would like to have a zero distance that is x2 frac14 0 betweenboth operatorsrsquo locations and operator 2 would prefer maximum distancethat is x2 frac14 1 between departures Consequently no Nash equilibrium inpure strategies exists in the division of demand if ethy lt 0 yy gt 1THORN

Consequently there is a subgame perfect Nash equilibrium in purestrategies if the sensitivity to quality is sufficiently large that is if j5 tbut no Nash equilibrium in pure strategies exists if this sensitivity to qualityis sufficiently small

40 Interpretation of Results

The difference in consumersrsquo sensitivity to quality could explain whycompetition in local bus transport results in unstable service patternswhile air transport does not seem to have the same problem

41 Short-distance transport

Given the short-distances travelled operators in local bus transport havevery limited scope for meaningful product differentiation that could

Figure 3Representation of indifferent consumer if ethy lt 0 yy gt 1THORN

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

147

make consumers loyal A consumer will generally take the first bus thatarrives at the stop This occurs in the division of demand of Figure 3 Inthat case each operator prefers a different distance between departuretimes and will continuously try to attain his preferred distance The pre-ferred distance between departures for both operators is conflicting andno subgame perfect equilibrium in pure strategies with regard to thetiming of departures exists

This result corresponds to the generally-shared view on competition inurban public transport in continental Europe The European Commissionin its proposal for new regulation of the award of public service contractsin public transport by Member States articulates this view stating thatwithout exclusive rights lsquoservice patterns are unstablersquo2 This perceptionis based on the experiences in Great Britain of the deregulation of localpublic transport

Evans (1990) and Mackie et al (1995) observed that after deregulationof local public transport the number of travellers did not increase despitethe doubling of service levels (frequencies) and consequent reductions inwaiting times This lsquopuzzling resultrsquo could not be explained by the declinein bus usage due to higher real incomes and lower real motoring costsOne explanation that has been put forward was that frequency increasesare compensated by offsetting effects for example uncertainty caused topassengers by route instability such as irregular intervals frequently chan-ging timetables and so on (Evans 1990 Mackie et al 1995)

The model for low consumer sensitivity to quality predicts this instabil-ity of service patterns In the division of demand of Figure 3 the preferredlocation of operator 1 is just before the departure of operator 2 (x2 frac14 0)while operator 2 prefers a larger distance between departures (x2 gt 0)Given x2 frac14 0 operator 2 will choose a later departure but in reactionoperator 1 will follow in order to reduce the distance to x2 frac14 0 againand so on Basically every operator would like to be at a bus stop justbefore its competitor in order to take the whole market This implies thatoperators are lsquohead-runningrsquo each other

With regard to pricing Mackie et al (1995) stated that pricing is not aparticularly potent marketing weapon The first priority is on service ratherthan fares as travellers tend to board the first bus This behaviour of con-sumers is confirmed by the model for the situation in which an operatorrsquos

2Proposal from the European Commission of 26 July 2000 for a Regulation of the European Parliament

and of the Council on action by Member States concerning public service requirements and the award

of public service contracts in passenger transport by rail road and inland waterway COM(2000)7

provisional p 5

Journal of Transport Economics and Policy Volume 40 Part 1

148

demand is independent of prices and D1 frac14 1 x2 and D2 frac14 x2 In this casethe model shows that p1=p1 5 0 and p2=p25 0 Hence operators arecompeting over the timing of departures rather than pricing Evans statesthat (1990 p 266) lsquoThe operators match fares and tacitly collude to main-tain the pre-existing fare structure The operators also tacitly collude toincrease fares simultaneously at a rate at least as fast as inflation Faresremain the same on high-demand as on low-demand routes and on activelycompetitive as on non-competitive routesrsquo The model shows that theupward pressure on prices will only be limited by the maximum willingnessto pay Consequently the pricing discipline comes from external factorsfor example the existence of competition from another mode (such asprivate car cycling walking and so on) or competition between activitiesthat consumers can undertake (and that may or may not require transport)This clarifies why fares move at a similar rate to inflation and are notrelated to the level of demand on a route or the level of competition on aroute

42 Long-distance transport

In long-distance transport such as air transport consumers are moresensitive to quality Travel times are much longer and consequently con-sumers are more appreciative of comfort This allows for much greaterquality differentiation than in short-distance travel Hence consumerswill more easily take an alternative flight Non-price and non-schedulingfactors increase in importance for longer distances as can be seen for airtransport in the Table 1

The factors as distinguished in the Avmark Aviation Economist arelsquoschedulersquo lsquofarersquo lsquoairlinersquo lsquoairplanersquo and lsquootherrsquo lsquoSchedulersquo and lsquofarersquo areequivalent to the endogenous variables lsquoschedulersquo and lsquopricersquo lsquoAirlinersquo

Table 1

Most Influential Factors in Choosing a Flight

Factors asdistinguishedby the model

Factors asdistinguishedby Source

Length of flight

Under 2 hours () 2ndash5 hours () Over 5 hours ()

Schedule Schedule 701 430 193

Price Fare 114 137 165

Quality Airline 155 362 530Airplane 25 66 102Other 05 06 10

Source Avmark Aviation EconomistIAPA in Gialloreto 1988

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

149

lsquoairplanersquo and lsquootherrsquo can be clustered into the variable lsquoqualityrsquo Pressuredby competition airlines have become increasingly creative and effective indifferentiating their services in terms of quality including the creation ofconsumer loyalty

This situation is described by a sufficient sensitivity to quality that isj5 t as depicted in Figure 1 Given this division of demand operatorsmaximally differentiate in quality that is y1 frac14 0 and y2 frac14 1 This qualitydifferentiation relaxes competition over scheduling The model showsthat an operator cannot improve his position by choosing another timeof departure given the time of departure of his competitor Stronger consu-mer loyalty eliminates operatorsrsquo incentive to lsquohead-runrsquo each other whichcreates a subgame perfect equilibrium in timing departures Intuitively onewould say that an operator who moves to a later point of time increases hismarket but sufficiently strong consumersrsquo sensitivity to quality balancesthis tendency Consumers tend to wait for the departure of their preferredoperator

With regard to price the intuition cannot be confirmed that operatorsdo not seem to compete on price because pricing is too strong a marketingweapon According to the model operators do compete in price Furtheranalysis is needed in order to ascertain whether (and if so why) operatorsdo not seem to compete in price in long-distance transport One obser-vation (Brenner 1975) has been that scheduled transport operators tendto rival each other on frequency instead of price Such competitionincreases costs putting upward pressure on prices which could offset anyreduction in price that is normally associated with the introduction ofcompetition

43 Short-distance vs long-distanceThe impact of travel distance on stability can also be seen in the deregula-tion of lsquolong-distancersquo bus services in Great Britain In 1980 the Britishgovernment abolished a system of quantity control in the express coachmarket The deregulation allowed for free entry and competition onroutes served by nationalised carriers Douglas (1987) made a thoroughassessment of the effects of this deregulation on market structure faresservice quality and costs using data provided by express coach operatorsHe showed that on short-distance connections independent operatorsentering the market were unable to develop a significant market sharesince the two national carriers simply matched or undercut their faresand increased or manipulated departure times (Douglas 1997) Only 39per cent of such services to and from London survived during the firstfew years of deregulation The national carriers maintained some competi-tive advantages after deregulation such as sole access to major and centrally

Journal of Transport Economics and Policy Volume 40 Part 1

150

located bus stations a considerable network of services and an extensivesales network This made them better able to survive than the newindependent operators on the market

On long-distance connections however several independents captureda permanent place in the market Specialisation by offering a premierquality service allowed the independents to build up immunity to thepurely fare and scheduling responses of nationalised carriers and thuscapture a share of the market (Douglas 1997) In this way the indepen-dents were especially successful on the Anglo-Scottish routes The longertravel distance offered operators greater scope for product differentiationConsequently more operators were able to provide services even if theydeparted at the same time In the first few years of deregulation 67 percent of new long-distance services to or from London survived Henceproduct differentiation on long-distance connections made entrants resis-tant to the pricing and scheduling responses of incumbent operators bycreating consumer loyalty stabilising scheduling competition

50 Conclusion

For operators in scheduled passenger transport it is a great marketingchallenge to create an image that is distinct from their competitorsOperating the same or similar types of vehicles on the same routes doesnot have many elements of visible tangible differentiation vis-a-viscompetitors Many of the elements in which differences do exist are bytheir nature subjective and difficult to prove to the sceptical consumerExamples are friendliness and courtesy of personnel interior designseats mealssnacks lounges advertising image and so on Long-distanceoperators are better able than short-distance operators to realise suchproduct differentiation in a meaningful fashion Over longer distancesconsumers are generally more flexible with regard to departure times andare more appreciative of their preferred quality of service

In a two-dimensional horizontal product differentiation model withlinear waiting costs for departures and non-linear sensitivity to deviationsfrom preferred quality of service it is shown that a stable service patternrequires consumers to be sufficiently sensitive to differences in qualitybetween operators In reaction operators will differentiate their productsin terms of quality This differentiation prevents consumers from simplytaking the vehicle that is closest to their preferred departure time Consu-mers will be inclined to take an earlier or later departure if they feel morecomfortable with that operator or if there are additional benefits provided

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

151

by this operator In contrast if consumers are not sensitive to qualitydifferences operators would prefer to schedule their vehicles just beforetheir competitor in order to lsquostealrsquo its customers

On the basis of Neven and Thisse (1990) Ansari et al (1998) andIrmen and Thisse (1998) it can be expected that this result will notchange if the dimension of quality differentiation is modelled as verticaldifferentiation rather than horizontal differentiation It is clear that thequality differentiation considered has not only horizontal but also verticalaspects One example is seat width and pitch For the same price everyconsumer would appreciate more space The most dominant factordifferentiating operators is probably an operatorrsquos consumer loyaltyprogramme and that creates horizontal differentiation A formalanalysis for the case of vertical differentiation is beyond the scope of thispaper

The sensitivity to quality differences is a plausible factor that couldclarify the difference in existence of a stable equilibrium between differentmodes of scheduled transport A modal spectrum can be created on thebasis of the relevance of quality differentiation for the selection of an opera-tor The low-relevance end of this spectrum includes examples as containerfreight operations (such as liner shipping) and local public transport Thehigh-relevance end would probably include inter-continental passengerair transport For the low-relevance modes experience shows that com-petition results in unstable service patterns For the high-relevance modestability has never appeared to be a problem

References

Ansari A N Economides and J Steckel (1998) lsquoThe Max-min-min Principle of ProductDifferentiationrsquo Journal of Regional Science 38 207ndash30

Banister B (1985) lsquoDeregulating the Bus Industry in Britain (A) the ProposalsrsquoTransport Reviews 5 99ndash103

Brenner M A (1975) lsquoNeed for Continued Economic Regulation of Air TransportrsquoJournal of Air Law and Commerce 41 793ndash813

Cancian M A Bills and T Bergstrom (1995) lsquoHotelling Location Problems withDirectional Constraints an Application to Television News Schedulingrsquo Journal ofIndustrial Economics 43 121ndash4

DrsquoAspremont C J Jaskold Gabszewicz and J-F Thisse (1979) lsquoOn HotellingrsquoslsquolsquoStability in competitionrsquorsquorsquo Econometrica 47 1145ndash50

Douglas N J (1987) A Welfare Assessment of Transport Deregulation The Case of theExpress Coach Market in 1980 Aldershot Gower

Evans A (1987) lsquoA Theoretical Comparison of Competition with Other EconomicRegimes for Bus Servicesrsquo Journal of Transport Economics and Policy 21 7ndash36

Journal of Transport Economics and Policy Volume 40 Part 1

152

On the basis of these demands profits for operator 1 and operator 2 willbe

p1 frac14 p1

p2 p1 thorn jethy22 y21THORN

2jethy2 y1THORN

and p2 frac14 p2

1thorn p1 p2 jethy22 y21THORN

2jethy2 y1THORN

Maximising these profits with respect to fares gives the followingreaction curves

p1 frac14p2 thorn jethy22 y21THORN

2and p2 frac14

p1 thorn 2jethy2 y1THORN jethy22 y21THORN2

Substituting these reaction curves into each other gives the subgameperfect prices

p1 frac142jethy2 y1THORN thorn jethy22 y21THORN

3and p2 frac14

4jethy2 y1THORN jethy22 y21THORN3

Substituting the subgame perfect prices into the expression for demandand multiplying these by their own prices generates the following equili-brium profits

p1 frac14eth2jethy2 y1THORN thorn jethy22 y21THORNTHORN2

18jethy2 y1THORNand p2 frac14

eth4jethy2 y1THORN jethy22 y21THORNTHORN2

18jethy2 y1THORN

Maximising the profits with respect to the location of quality gives

p1y1

frac14 frac122jethy2 y1THORN thorn jethy22 y21THORNfrac12jethy22 y21THORN 4y1jethy2 y1THORN 2jethy2 y1THORN18jethy2 y1THORN2

and

p2y2

frac14 frac124jethy2 y1THORN jethy22 y21THORNfrac12jethy22 y21THORN 4y2jethy2 y1THORN thorn 4jethy2 y1THORN18jethy2 y1THORN2

The expressions show that p1=y1 lt 0 and p2=y2 gt 0 Henceoperator 1 will choose to offer quality y1 frac14 0 and operator 2 will offery2 frac14 1 Substituting these locations into the subgame perfect prices andequilibrium profits gives p1 frac14 p2 frac14 j and p1 frac14 p2 frac14 j=2 respectively Anoperator cannot generate higher profits by deviating from this differentia-tion in quality and associated fares if the conditions for this division ofdemand between both operators are satisfied that is y yy 2 frac120 1 Substitut-ing the equilibrium qualities y1 frac14 0 y2 frac14 1 and prices p1 frac14 p2 frac14 j into

y frac14 p2 p1 teth1 x2THORN thorn jethy22 y21THORN2jethy2 y1THORN

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

145

shows that y 2 frac120 1 if j5 teth1 x2THORN Doing the same for

yy frac14 p2 p1 thorn tx2 thorn jethy22 y21THORN2jethy2 y1THORN

shows that yy 2 frac120 1 if j5 tx2 Consequently

p1p2 frac14 j=2 if

j5 teth1 x2THORN for 04x2 lt 1=2

j5 tx2 for 1=24 x2 4 1

These conditions will be fulfilled for any x2 2 frac120 1 if j5 t so that anecessary condition for equilibrium is that the sensitivity to quality issufficiently large in relation to the perceived inconvenience of lsquowaitingrsquo

It has to be checked whether the operators cannot realise a higherprofit than p1 p

2 by choosing qualities and prices so that the indifferent

consumers y andor the indifferent consumers yy have a preferred qualityoutside the area defined by y yy 2 frac120 1 Figure 2 shows the situation inwhich one of the operators deviates from his equilibrium strategy bychoosing quality or price so that y lt 0 and yy 2 frac120 1

In Appendix A it has been shown that both operators cannot realisehigher profits by deviating from their equilibrium strategy by choosinglocations and prices so that either ethy lt 0 yy 2 frac120 1THORN or ethy 2 frac120 1 yy gt 1THORN

If the sensitivity to quality is sufficiently small in relation to theperceived inconvenience of waiting that is if

j ltt

2ethy2 y1THORN

then yy y gt 1 and it must be that ethy lt 0 yy 2 frac120 1THORN ethy 2 frac120 1 yy gt 1THORN orethy lt 0 yy gt 1THORN In Appendix A it has also been shown that no Nash

Figure 2Representation of indifferent consumer if ethy lt 0 yy 2 frac120 1THORN

Journal of Transport Economics and Policy Volume 40 Part 1

146

equilibrium in pure strategies exists if ethy lt 0 yy 2 frac120 1THORN orethy 2 frac120 1 yy gt 1THORN The division of demand if ethy lt 0 yy gt 1THORN is shown inFigure 3

In this division of demand the respective demands for operator 1and operator 2 are D1 frac14 1 x2 and D2 frac14 x2 so that the profits will bep1 frac14 p1eth1 x2THORN and p2 frac14 p2x2 It can be easily seen from these profitsthat there are no subgame perfect equilibrium prices And even if therewere then operators would not prefer the same distance x2 between depar-tures Operator 1 would like to have a zero distance that is x2 frac14 0 betweenboth operatorsrsquo locations and operator 2 would prefer maximum distancethat is x2 frac14 1 between departures Consequently no Nash equilibrium inpure strategies exists in the division of demand if ethy lt 0 yy gt 1THORN

Consequently there is a subgame perfect Nash equilibrium in purestrategies if the sensitivity to quality is sufficiently large that is if j5 tbut no Nash equilibrium in pure strategies exists if this sensitivity to qualityis sufficiently small

40 Interpretation of Results

The difference in consumersrsquo sensitivity to quality could explain whycompetition in local bus transport results in unstable service patternswhile air transport does not seem to have the same problem

41 Short-distance transport

Given the short-distances travelled operators in local bus transport havevery limited scope for meaningful product differentiation that could

Figure 3Representation of indifferent consumer if ethy lt 0 yy gt 1THORN

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

147

make consumers loyal A consumer will generally take the first bus thatarrives at the stop This occurs in the division of demand of Figure 3 Inthat case each operator prefers a different distance between departuretimes and will continuously try to attain his preferred distance The pre-ferred distance between departures for both operators is conflicting andno subgame perfect equilibrium in pure strategies with regard to thetiming of departures exists

This result corresponds to the generally-shared view on competition inurban public transport in continental Europe The European Commissionin its proposal for new regulation of the award of public service contractsin public transport by Member States articulates this view stating thatwithout exclusive rights lsquoservice patterns are unstablersquo2 This perceptionis based on the experiences in Great Britain of the deregulation of localpublic transport

Evans (1990) and Mackie et al (1995) observed that after deregulationof local public transport the number of travellers did not increase despitethe doubling of service levels (frequencies) and consequent reductions inwaiting times This lsquopuzzling resultrsquo could not be explained by the declinein bus usage due to higher real incomes and lower real motoring costsOne explanation that has been put forward was that frequency increasesare compensated by offsetting effects for example uncertainty caused topassengers by route instability such as irregular intervals frequently chan-ging timetables and so on (Evans 1990 Mackie et al 1995)

The model for low consumer sensitivity to quality predicts this instabil-ity of service patterns In the division of demand of Figure 3 the preferredlocation of operator 1 is just before the departure of operator 2 (x2 frac14 0)while operator 2 prefers a larger distance between departures (x2 gt 0)Given x2 frac14 0 operator 2 will choose a later departure but in reactionoperator 1 will follow in order to reduce the distance to x2 frac14 0 againand so on Basically every operator would like to be at a bus stop justbefore its competitor in order to take the whole market This implies thatoperators are lsquohead-runningrsquo each other

With regard to pricing Mackie et al (1995) stated that pricing is not aparticularly potent marketing weapon The first priority is on service ratherthan fares as travellers tend to board the first bus This behaviour of con-sumers is confirmed by the model for the situation in which an operatorrsquos

2Proposal from the European Commission of 26 July 2000 for a Regulation of the European Parliament

and of the Council on action by Member States concerning public service requirements and the award

of public service contracts in passenger transport by rail road and inland waterway COM(2000)7

provisional p 5

Journal of Transport Economics and Policy Volume 40 Part 1

148

demand is independent of prices and D1 frac14 1 x2 and D2 frac14 x2 In this casethe model shows that p1=p1 5 0 and p2=p25 0 Hence operators arecompeting over the timing of departures rather than pricing Evans statesthat (1990 p 266) lsquoThe operators match fares and tacitly collude to main-tain the pre-existing fare structure The operators also tacitly collude toincrease fares simultaneously at a rate at least as fast as inflation Faresremain the same on high-demand as on low-demand routes and on activelycompetitive as on non-competitive routesrsquo The model shows that theupward pressure on prices will only be limited by the maximum willingnessto pay Consequently the pricing discipline comes from external factorsfor example the existence of competition from another mode (such asprivate car cycling walking and so on) or competition between activitiesthat consumers can undertake (and that may or may not require transport)This clarifies why fares move at a similar rate to inflation and are notrelated to the level of demand on a route or the level of competition on aroute

42 Long-distance transport

In long-distance transport such as air transport consumers are moresensitive to quality Travel times are much longer and consequently con-sumers are more appreciative of comfort This allows for much greaterquality differentiation than in short-distance travel Hence consumerswill more easily take an alternative flight Non-price and non-schedulingfactors increase in importance for longer distances as can be seen for airtransport in the Table 1

The factors as distinguished in the Avmark Aviation Economist arelsquoschedulersquo lsquofarersquo lsquoairlinersquo lsquoairplanersquo and lsquootherrsquo lsquoSchedulersquo and lsquofarersquo areequivalent to the endogenous variables lsquoschedulersquo and lsquopricersquo lsquoAirlinersquo

Table 1

Most Influential Factors in Choosing a Flight

Factors asdistinguishedby the model

Factors asdistinguishedby Source

Length of flight

Under 2 hours () 2ndash5 hours () Over 5 hours ()

Schedule Schedule 701 430 193

Price Fare 114 137 165

Quality Airline 155 362 530Airplane 25 66 102Other 05 06 10

Source Avmark Aviation EconomistIAPA in Gialloreto 1988

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

149

lsquoairplanersquo and lsquootherrsquo can be clustered into the variable lsquoqualityrsquo Pressuredby competition airlines have become increasingly creative and effective indifferentiating their services in terms of quality including the creation ofconsumer loyalty

This situation is described by a sufficient sensitivity to quality that isj5 t as depicted in Figure 1 Given this division of demand operatorsmaximally differentiate in quality that is y1 frac14 0 and y2 frac14 1 This qualitydifferentiation relaxes competition over scheduling The model showsthat an operator cannot improve his position by choosing another timeof departure given the time of departure of his competitor Stronger consu-mer loyalty eliminates operatorsrsquo incentive to lsquohead-runrsquo each other whichcreates a subgame perfect equilibrium in timing departures Intuitively onewould say that an operator who moves to a later point of time increases hismarket but sufficiently strong consumersrsquo sensitivity to quality balancesthis tendency Consumers tend to wait for the departure of their preferredoperator

With regard to price the intuition cannot be confirmed that operatorsdo not seem to compete on price because pricing is too strong a marketingweapon According to the model operators do compete in price Furtheranalysis is needed in order to ascertain whether (and if so why) operatorsdo not seem to compete in price in long-distance transport One obser-vation (Brenner 1975) has been that scheduled transport operators tendto rival each other on frequency instead of price Such competitionincreases costs putting upward pressure on prices which could offset anyreduction in price that is normally associated with the introduction ofcompetition

43 Short-distance vs long-distanceThe impact of travel distance on stability can also be seen in the deregula-tion of lsquolong-distancersquo bus services in Great Britain In 1980 the Britishgovernment abolished a system of quantity control in the express coachmarket The deregulation allowed for free entry and competition onroutes served by nationalised carriers Douglas (1987) made a thoroughassessment of the effects of this deregulation on market structure faresservice quality and costs using data provided by express coach operatorsHe showed that on short-distance connections independent operatorsentering the market were unable to develop a significant market sharesince the two national carriers simply matched or undercut their faresand increased or manipulated departure times (Douglas 1997) Only 39per cent of such services to and from London survived during the firstfew years of deregulation The national carriers maintained some competi-tive advantages after deregulation such as sole access to major and centrally

Journal of Transport Economics and Policy Volume 40 Part 1

150

located bus stations a considerable network of services and an extensivesales network This made them better able to survive than the newindependent operators on the market

On long-distance connections however several independents captureda permanent place in the market Specialisation by offering a premierquality service allowed the independents to build up immunity to thepurely fare and scheduling responses of nationalised carriers and thuscapture a share of the market (Douglas 1997) In this way the indepen-dents were especially successful on the Anglo-Scottish routes The longertravel distance offered operators greater scope for product differentiationConsequently more operators were able to provide services even if theydeparted at the same time In the first few years of deregulation 67 percent of new long-distance services to or from London survived Henceproduct differentiation on long-distance connections made entrants resis-tant to the pricing and scheduling responses of incumbent operators bycreating consumer loyalty stabilising scheduling competition

50 Conclusion

For operators in scheduled passenger transport it is a great marketingchallenge to create an image that is distinct from their competitorsOperating the same or similar types of vehicles on the same routes doesnot have many elements of visible tangible differentiation vis-a-viscompetitors Many of the elements in which differences do exist are bytheir nature subjective and difficult to prove to the sceptical consumerExamples are friendliness and courtesy of personnel interior designseats mealssnacks lounges advertising image and so on Long-distanceoperators are better able than short-distance operators to realise suchproduct differentiation in a meaningful fashion Over longer distancesconsumers are generally more flexible with regard to departure times andare more appreciative of their preferred quality of service

In a two-dimensional horizontal product differentiation model withlinear waiting costs for departures and non-linear sensitivity to deviationsfrom preferred quality of service it is shown that a stable service patternrequires consumers to be sufficiently sensitive to differences in qualitybetween operators In reaction operators will differentiate their productsin terms of quality This differentiation prevents consumers from simplytaking the vehicle that is closest to their preferred departure time Consu-mers will be inclined to take an earlier or later departure if they feel morecomfortable with that operator or if there are additional benefits provided

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

151

by this operator In contrast if consumers are not sensitive to qualitydifferences operators would prefer to schedule their vehicles just beforetheir competitor in order to lsquostealrsquo its customers

On the basis of Neven and Thisse (1990) Ansari et al (1998) andIrmen and Thisse (1998) it can be expected that this result will notchange if the dimension of quality differentiation is modelled as verticaldifferentiation rather than horizontal differentiation It is clear that thequality differentiation considered has not only horizontal but also verticalaspects One example is seat width and pitch For the same price everyconsumer would appreciate more space The most dominant factordifferentiating operators is probably an operatorrsquos consumer loyaltyprogramme and that creates horizontal differentiation A formalanalysis for the case of vertical differentiation is beyond the scope of thispaper

The sensitivity to quality differences is a plausible factor that couldclarify the difference in existence of a stable equilibrium between differentmodes of scheduled transport A modal spectrum can be created on thebasis of the relevance of quality differentiation for the selection of an opera-tor The low-relevance end of this spectrum includes examples as containerfreight operations (such as liner shipping) and local public transport Thehigh-relevance end would probably include inter-continental passengerair transport For the low-relevance modes experience shows that com-petition results in unstable service patterns For the high-relevance modestability has never appeared to be a problem

References

Ansari A N Economides and J Steckel (1998) lsquoThe Max-min-min Principle of ProductDifferentiationrsquo Journal of Regional Science 38 207ndash30

Banister B (1985) lsquoDeregulating the Bus Industry in Britain (A) the ProposalsrsquoTransport Reviews 5 99ndash103

Brenner M A (1975) lsquoNeed for Continued Economic Regulation of Air TransportrsquoJournal of Air Law and Commerce 41 793ndash813

Cancian M A Bills and T Bergstrom (1995) lsquoHotelling Location Problems withDirectional Constraints an Application to Television News Schedulingrsquo Journal ofIndustrial Economics 43 121ndash4

DrsquoAspremont C J Jaskold Gabszewicz and J-F Thisse (1979) lsquoOn HotellingrsquoslsquolsquoStability in competitionrsquorsquorsquo Econometrica 47 1145ndash50

Douglas N J (1987) A Welfare Assessment of Transport Deregulation The Case of theExpress Coach Market in 1980 Aldershot Gower

Evans A (1987) lsquoA Theoretical Comparison of Competition with Other EconomicRegimes for Bus Servicesrsquo Journal of Transport Economics and Policy 21 7ndash36

Journal of Transport Economics and Policy Volume 40 Part 1

152

shows that y 2 frac120 1 if j5 teth1 x2THORN Doing the same for

yy frac14 p2 p1 thorn tx2 thorn jethy22 y21THORN2jethy2 y1THORN

shows that yy 2 frac120 1 if j5 tx2 Consequently

p1p2 frac14 j=2 if

j5 teth1 x2THORN for 04x2 lt 1=2

j5 tx2 for 1=24 x2 4 1

These conditions will be fulfilled for any x2 2 frac120 1 if j5 t so that anecessary condition for equilibrium is that the sensitivity to quality issufficiently large in relation to the perceived inconvenience of lsquowaitingrsquo

It has to be checked whether the operators cannot realise a higherprofit than p1 p

2 by choosing qualities and prices so that the indifferent

consumers y andor the indifferent consumers yy have a preferred qualityoutside the area defined by y yy 2 frac120 1 Figure 2 shows the situation inwhich one of the operators deviates from his equilibrium strategy bychoosing quality or price so that y lt 0 and yy 2 frac120 1

In Appendix A it has been shown that both operators cannot realisehigher profits by deviating from their equilibrium strategy by choosinglocations and prices so that either ethy lt 0 yy 2 frac120 1THORN or ethy 2 frac120 1 yy gt 1THORN

If the sensitivity to quality is sufficiently small in relation to theperceived inconvenience of waiting that is if

j ltt

2ethy2 y1THORN

then yy y gt 1 and it must be that ethy lt 0 yy 2 frac120 1THORN ethy 2 frac120 1 yy gt 1THORN orethy lt 0 yy gt 1THORN In Appendix A it has also been shown that no Nash

Figure 2Representation of indifferent consumer if ethy lt 0 yy 2 frac120 1THORN

Journal of Transport Economics and Policy Volume 40 Part 1

146

equilibrium in pure strategies exists if ethy lt 0 yy 2 frac120 1THORN orethy 2 frac120 1 yy gt 1THORN The division of demand if ethy lt 0 yy gt 1THORN is shown inFigure 3

In this division of demand the respective demands for operator 1and operator 2 are D1 frac14 1 x2 and D2 frac14 x2 so that the profits will bep1 frac14 p1eth1 x2THORN and p2 frac14 p2x2 It can be easily seen from these profitsthat there are no subgame perfect equilibrium prices And even if therewere then operators would not prefer the same distance x2 between depar-tures Operator 1 would like to have a zero distance that is x2 frac14 0 betweenboth operatorsrsquo locations and operator 2 would prefer maximum distancethat is x2 frac14 1 between departures Consequently no Nash equilibrium inpure strategies exists in the division of demand if ethy lt 0 yy gt 1THORN

Consequently there is a subgame perfect Nash equilibrium in purestrategies if the sensitivity to quality is sufficiently large that is if j5 tbut no Nash equilibrium in pure strategies exists if this sensitivity to qualityis sufficiently small

40 Interpretation of Results

The difference in consumersrsquo sensitivity to quality could explain whycompetition in local bus transport results in unstable service patternswhile air transport does not seem to have the same problem

41 Short-distance transport

Given the short-distances travelled operators in local bus transport havevery limited scope for meaningful product differentiation that could

Figure 3Representation of indifferent consumer if ethy lt 0 yy gt 1THORN

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

147

make consumers loyal A consumer will generally take the first bus thatarrives at the stop This occurs in the division of demand of Figure 3 Inthat case each operator prefers a different distance between departuretimes and will continuously try to attain his preferred distance The pre-ferred distance between departures for both operators is conflicting andno subgame perfect equilibrium in pure strategies with regard to thetiming of departures exists

This result corresponds to the generally-shared view on competition inurban public transport in continental Europe The European Commissionin its proposal for new regulation of the award of public service contractsin public transport by Member States articulates this view stating thatwithout exclusive rights lsquoservice patterns are unstablersquo2 This perceptionis based on the experiences in Great Britain of the deregulation of localpublic transport

Evans (1990) and Mackie et al (1995) observed that after deregulationof local public transport the number of travellers did not increase despitethe doubling of service levels (frequencies) and consequent reductions inwaiting times This lsquopuzzling resultrsquo could not be explained by the declinein bus usage due to higher real incomes and lower real motoring costsOne explanation that has been put forward was that frequency increasesare compensated by offsetting effects for example uncertainty caused topassengers by route instability such as irregular intervals frequently chan-ging timetables and so on (Evans 1990 Mackie et al 1995)

The model for low consumer sensitivity to quality predicts this instabil-ity of service patterns In the division of demand of Figure 3 the preferredlocation of operator 1 is just before the departure of operator 2 (x2 frac14 0)while operator 2 prefers a larger distance between departures (x2 gt 0)Given x2 frac14 0 operator 2 will choose a later departure but in reactionoperator 1 will follow in order to reduce the distance to x2 frac14 0 againand so on Basically every operator would like to be at a bus stop justbefore its competitor in order to take the whole market This implies thatoperators are lsquohead-runningrsquo each other

With regard to pricing Mackie et al (1995) stated that pricing is not aparticularly potent marketing weapon The first priority is on service ratherthan fares as travellers tend to board the first bus This behaviour of con-sumers is confirmed by the model for the situation in which an operatorrsquos

2Proposal from the European Commission of 26 July 2000 for a Regulation of the European Parliament

and of the Council on action by Member States concerning public service requirements and the award

of public service contracts in passenger transport by rail road and inland waterway COM(2000)7

provisional p 5

Journal of Transport Economics and Policy Volume 40 Part 1

148

demand is independent of prices and D1 frac14 1 x2 and D2 frac14 x2 In this casethe model shows that p1=p1 5 0 and p2=p25 0 Hence operators arecompeting over the timing of departures rather than pricing Evans statesthat (1990 p 266) lsquoThe operators match fares and tacitly collude to main-tain the pre-existing fare structure The operators also tacitly collude toincrease fares simultaneously at a rate at least as fast as inflation Faresremain the same on high-demand as on low-demand routes and on activelycompetitive as on non-competitive routesrsquo The model shows that theupward pressure on prices will only be limited by the maximum willingnessto pay Consequently the pricing discipline comes from external factorsfor example the existence of competition from another mode (such asprivate car cycling walking and so on) or competition between activitiesthat consumers can undertake (and that may or may not require transport)This clarifies why fares move at a similar rate to inflation and are notrelated to the level of demand on a route or the level of competition on aroute

42 Long-distance transport

In long-distance transport such as air transport consumers are moresensitive to quality Travel times are much longer and consequently con-sumers are more appreciative of comfort This allows for much greaterquality differentiation than in short-distance travel Hence consumerswill more easily take an alternative flight Non-price and non-schedulingfactors increase in importance for longer distances as can be seen for airtransport in the Table 1

The factors as distinguished in the Avmark Aviation Economist arelsquoschedulersquo lsquofarersquo lsquoairlinersquo lsquoairplanersquo and lsquootherrsquo lsquoSchedulersquo and lsquofarersquo areequivalent to the endogenous variables lsquoschedulersquo and lsquopricersquo lsquoAirlinersquo

Table 1

Most Influential Factors in Choosing a Flight

Factors asdistinguishedby the model

Factors asdistinguishedby Source

Length of flight

Under 2 hours () 2ndash5 hours () Over 5 hours ()

Schedule Schedule 701 430 193

Price Fare 114 137 165

Quality Airline 155 362 530Airplane 25 66 102Other 05 06 10

Source Avmark Aviation EconomistIAPA in Gialloreto 1988

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

149

lsquoairplanersquo and lsquootherrsquo can be clustered into the variable lsquoqualityrsquo Pressuredby competition airlines have become increasingly creative and effective indifferentiating their services in terms of quality including the creation ofconsumer loyalty

This situation is described by a sufficient sensitivity to quality that isj5 t as depicted in Figure 1 Given this division of demand operatorsmaximally differentiate in quality that is y1 frac14 0 and y2 frac14 1 This qualitydifferentiation relaxes competition over scheduling The model showsthat an operator cannot improve his position by choosing another timeof departure given the time of departure of his competitor Stronger consu-mer loyalty eliminates operatorsrsquo incentive to lsquohead-runrsquo each other whichcreates a subgame perfect equilibrium in timing departures Intuitively onewould say that an operator who moves to a later point of time increases hismarket but sufficiently strong consumersrsquo sensitivity to quality balancesthis tendency Consumers tend to wait for the departure of their preferredoperator

With regard to price the intuition cannot be confirmed that operatorsdo not seem to compete on price because pricing is too strong a marketingweapon According to the model operators do compete in price Furtheranalysis is needed in order to ascertain whether (and if so why) operatorsdo not seem to compete in price in long-distance transport One obser-vation (Brenner 1975) has been that scheduled transport operators tendto rival each other on frequency instead of price Such competitionincreases costs putting upward pressure on prices which could offset anyreduction in price that is normally associated with the introduction ofcompetition

43 Short-distance vs long-distanceThe impact of travel distance on stability can also be seen in the deregula-tion of lsquolong-distancersquo bus services in Great Britain In 1980 the Britishgovernment abolished a system of quantity control in the express coachmarket The deregulation allowed for free entry and competition onroutes served by nationalised carriers Douglas (1987) made a thoroughassessment of the effects of this deregulation on market structure faresservice quality and costs using data provided by express coach operatorsHe showed that on short-distance connections independent operatorsentering the market were unable to develop a significant market sharesince the two national carriers simply matched or undercut their faresand increased or manipulated departure times (Douglas 1997) Only 39per cent of such services to and from London survived during the firstfew years of deregulation The national carriers maintained some competi-tive advantages after deregulation such as sole access to major and centrally

Journal of Transport Economics and Policy Volume 40 Part 1

150

located bus stations a considerable network of services and an extensivesales network This made them better able to survive than the newindependent operators on the market

On long-distance connections however several independents captureda permanent place in the market Specialisation by offering a premierquality service allowed the independents to build up immunity to thepurely fare and scheduling responses of nationalised carriers and thuscapture a share of the market (Douglas 1997) In this way the indepen-dents were especially successful on the Anglo-Scottish routes The longertravel distance offered operators greater scope for product differentiationConsequently more operators were able to provide services even if theydeparted at the same time In the first few years of deregulation 67 percent of new long-distance services to or from London survived Henceproduct differentiation on long-distance connections made entrants resis-tant to the pricing and scheduling responses of incumbent operators bycreating consumer loyalty stabilising scheduling competition

50 Conclusion

For operators in scheduled passenger transport it is a great marketingchallenge to create an image that is distinct from their competitorsOperating the same or similar types of vehicles on the same routes doesnot have many elements of visible tangible differentiation vis-a-viscompetitors Many of the elements in which differences do exist are bytheir nature subjective and difficult to prove to the sceptical consumerExamples are friendliness and courtesy of personnel interior designseats mealssnacks lounges advertising image and so on Long-distanceoperators are better able than short-distance operators to realise suchproduct differentiation in a meaningful fashion Over longer distancesconsumers are generally more flexible with regard to departure times andare more appreciative of their preferred quality of service

In a two-dimensional horizontal product differentiation model withlinear waiting costs for departures and non-linear sensitivity to deviationsfrom preferred quality of service it is shown that a stable service patternrequires consumers to be sufficiently sensitive to differences in qualitybetween operators In reaction operators will differentiate their productsin terms of quality This differentiation prevents consumers from simplytaking the vehicle that is closest to their preferred departure time Consu-mers will be inclined to take an earlier or later departure if they feel morecomfortable with that operator or if there are additional benefits provided

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

151

by this operator In contrast if consumers are not sensitive to qualitydifferences operators would prefer to schedule their vehicles just beforetheir competitor in order to lsquostealrsquo its customers

On the basis of Neven and Thisse (1990) Ansari et al (1998) andIrmen and Thisse (1998) it can be expected that this result will notchange if the dimension of quality differentiation is modelled as verticaldifferentiation rather than horizontal differentiation It is clear that thequality differentiation considered has not only horizontal but also verticalaspects One example is seat width and pitch For the same price everyconsumer would appreciate more space The most dominant factordifferentiating operators is probably an operatorrsquos consumer loyaltyprogramme and that creates horizontal differentiation A formalanalysis for the case of vertical differentiation is beyond the scope of thispaper

The sensitivity to quality differences is a plausible factor that couldclarify the difference in existence of a stable equilibrium between differentmodes of scheduled transport A modal spectrum can be created on thebasis of the relevance of quality differentiation for the selection of an opera-tor The low-relevance end of this spectrum includes examples as containerfreight operations (such as liner shipping) and local public transport Thehigh-relevance end would probably include inter-continental passengerair transport For the low-relevance modes experience shows that com-petition results in unstable service patterns For the high-relevance modestability has never appeared to be a problem

References

Ansari A N Economides and J Steckel (1998) lsquoThe Max-min-min Principle of ProductDifferentiationrsquo Journal of Regional Science 38 207ndash30

Banister B (1985) lsquoDeregulating the Bus Industry in Britain (A) the ProposalsrsquoTransport Reviews 5 99ndash103

Brenner M A (1975) lsquoNeed for Continued Economic Regulation of Air TransportrsquoJournal of Air Law and Commerce 41 793ndash813

Cancian M A Bills and T Bergstrom (1995) lsquoHotelling Location Problems withDirectional Constraints an Application to Television News Schedulingrsquo Journal ofIndustrial Economics 43 121ndash4

DrsquoAspremont C J Jaskold Gabszewicz and J-F Thisse (1979) lsquoOn HotellingrsquoslsquolsquoStability in competitionrsquorsquorsquo Econometrica 47 1145ndash50

Douglas N J (1987) A Welfare Assessment of Transport Deregulation The Case of theExpress Coach Market in 1980 Aldershot Gower

Evans A (1987) lsquoA Theoretical Comparison of Competition with Other EconomicRegimes for Bus Servicesrsquo Journal of Transport Economics and Policy 21 7ndash36

Journal of Transport Economics and Policy Volume 40 Part 1

152

equilibrium in pure strategies exists if ethy lt 0 yy 2 frac120 1THORN orethy 2 frac120 1 yy gt 1THORN The division of demand if ethy lt 0 yy gt 1THORN is shown inFigure 3

In this division of demand the respective demands for operator 1and operator 2 are D1 frac14 1 x2 and D2 frac14 x2 so that the profits will bep1 frac14 p1eth1 x2THORN and p2 frac14 p2x2 It can be easily seen from these profitsthat there are no subgame perfect equilibrium prices And even if therewere then operators would not prefer the same distance x2 between depar-tures Operator 1 would like to have a zero distance that is x2 frac14 0 betweenboth operatorsrsquo locations and operator 2 would prefer maximum distancethat is x2 frac14 1 between departures Consequently no Nash equilibrium inpure strategies exists in the division of demand if ethy lt 0 yy gt 1THORN

Consequently there is a subgame perfect Nash equilibrium in purestrategies if the sensitivity to quality is sufficiently large that is if j5 tbut no Nash equilibrium in pure strategies exists if this sensitivity to qualityis sufficiently small

40 Interpretation of Results

The difference in consumersrsquo sensitivity to quality could explain whycompetition in local bus transport results in unstable service patternswhile air transport does not seem to have the same problem

41 Short-distance transport

Given the short-distances travelled operators in local bus transport havevery limited scope for meaningful product differentiation that could

Figure 3Representation of indifferent consumer if ethy lt 0 yy gt 1THORN

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

147

make consumers loyal A consumer will generally take the first bus thatarrives at the stop This occurs in the division of demand of Figure 3 Inthat case each operator prefers a different distance between departuretimes and will continuously try to attain his preferred distance The pre-ferred distance between departures for both operators is conflicting andno subgame perfect equilibrium in pure strategies with regard to thetiming of departures exists

This result corresponds to the generally-shared view on competition inurban public transport in continental Europe The European Commissionin its proposal for new regulation of the award of public service contractsin public transport by Member States articulates this view stating thatwithout exclusive rights lsquoservice patterns are unstablersquo2 This perceptionis based on the experiences in Great Britain of the deregulation of localpublic transport

Evans (1990) and Mackie et al (1995) observed that after deregulationof local public transport the number of travellers did not increase despitethe doubling of service levels (frequencies) and consequent reductions inwaiting times This lsquopuzzling resultrsquo could not be explained by the declinein bus usage due to higher real incomes and lower real motoring costsOne explanation that has been put forward was that frequency increasesare compensated by offsetting effects for example uncertainty caused topassengers by route instability such as irregular intervals frequently chan-ging timetables and so on (Evans 1990 Mackie et al 1995)

The model for low consumer sensitivity to quality predicts this instabil-ity of service patterns In the division of demand of Figure 3 the preferredlocation of operator 1 is just before the departure of operator 2 (x2 frac14 0)while operator 2 prefers a larger distance between departures (x2 gt 0)Given x2 frac14 0 operator 2 will choose a later departure but in reactionoperator 1 will follow in order to reduce the distance to x2 frac14 0 againand so on Basically every operator would like to be at a bus stop justbefore its competitor in order to take the whole market This implies thatoperators are lsquohead-runningrsquo each other

With regard to pricing Mackie et al (1995) stated that pricing is not aparticularly potent marketing weapon The first priority is on service ratherthan fares as travellers tend to board the first bus This behaviour of con-sumers is confirmed by the model for the situation in which an operatorrsquos

2Proposal from the European Commission of 26 July 2000 for a Regulation of the European Parliament

and of the Council on action by Member States concerning public service requirements and the award

of public service contracts in passenger transport by rail road and inland waterway COM(2000)7

provisional p 5

Journal of Transport Economics and Policy Volume 40 Part 1

148

demand is independent of prices and D1 frac14 1 x2 and D2 frac14 x2 In this casethe model shows that p1=p1 5 0 and p2=p25 0 Hence operators arecompeting over the timing of departures rather than pricing Evans statesthat (1990 p 266) lsquoThe operators match fares and tacitly collude to main-tain the pre-existing fare structure The operators also tacitly collude toincrease fares simultaneously at a rate at least as fast as inflation Faresremain the same on high-demand as on low-demand routes and on activelycompetitive as on non-competitive routesrsquo The model shows that theupward pressure on prices will only be limited by the maximum willingnessto pay Consequently the pricing discipline comes from external factorsfor example the existence of competition from another mode (such asprivate car cycling walking and so on) or competition between activitiesthat consumers can undertake (and that may or may not require transport)This clarifies why fares move at a similar rate to inflation and are notrelated to the level of demand on a route or the level of competition on aroute

42 Long-distance transport

In long-distance transport such as air transport consumers are moresensitive to quality Travel times are much longer and consequently con-sumers are more appreciative of comfort This allows for much greaterquality differentiation than in short-distance travel Hence consumerswill more easily take an alternative flight Non-price and non-schedulingfactors increase in importance for longer distances as can be seen for airtransport in the Table 1

The factors as distinguished in the Avmark Aviation Economist arelsquoschedulersquo lsquofarersquo lsquoairlinersquo lsquoairplanersquo and lsquootherrsquo lsquoSchedulersquo and lsquofarersquo areequivalent to the endogenous variables lsquoschedulersquo and lsquopricersquo lsquoAirlinersquo

Table 1

Most Influential Factors in Choosing a Flight

Factors asdistinguishedby the model

Factors asdistinguishedby Source

Length of flight

Under 2 hours () 2ndash5 hours () Over 5 hours ()

Schedule Schedule 701 430 193

Price Fare 114 137 165

Quality Airline 155 362 530Airplane 25 66 102Other 05 06 10

Source Avmark Aviation EconomistIAPA in Gialloreto 1988

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

149

lsquoairplanersquo and lsquootherrsquo can be clustered into the variable lsquoqualityrsquo Pressuredby competition airlines have become increasingly creative and effective indifferentiating their services in terms of quality including the creation ofconsumer loyalty

This situation is described by a sufficient sensitivity to quality that isj5 t as depicted in Figure 1 Given this division of demand operatorsmaximally differentiate in quality that is y1 frac14 0 and y2 frac14 1 This qualitydifferentiation relaxes competition over scheduling The model showsthat an operator cannot improve his position by choosing another timeof departure given the time of departure of his competitor Stronger consu-mer loyalty eliminates operatorsrsquo incentive to lsquohead-runrsquo each other whichcreates a subgame perfect equilibrium in timing departures Intuitively onewould say that an operator who moves to a later point of time increases hismarket but sufficiently strong consumersrsquo sensitivity to quality balancesthis tendency Consumers tend to wait for the departure of their preferredoperator

With regard to price the intuition cannot be confirmed that operatorsdo not seem to compete on price because pricing is too strong a marketingweapon According to the model operators do compete in price Furtheranalysis is needed in order to ascertain whether (and if so why) operatorsdo not seem to compete in price in long-distance transport One obser-vation (Brenner 1975) has been that scheduled transport operators tendto rival each other on frequency instead of price Such competitionincreases costs putting upward pressure on prices which could offset anyreduction in price that is normally associated with the introduction ofcompetition

43 Short-distance vs long-distanceThe impact of travel distance on stability can also be seen in the deregula-tion of lsquolong-distancersquo bus services in Great Britain In 1980 the Britishgovernment abolished a system of quantity control in the express coachmarket The deregulation allowed for free entry and competition onroutes served by nationalised carriers Douglas (1987) made a thoroughassessment of the effects of this deregulation on market structure faresservice quality and costs using data provided by express coach operatorsHe showed that on short-distance connections independent operatorsentering the market were unable to develop a significant market sharesince the two national carriers simply matched or undercut their faresand increased or manipulated departure times (Douglas 1997) Only 39per cent of such services to and from London survived during the firstfew years of deregulation The national carriers maintained some competi-tive advantages after deregulation such as sole access to major and centrally

Journal of Transport Economics and Policy Volume 40 Part 1

150

located bus stations a considerable network of services and an extensivesales network This made them better able to survive than the newindependent operators on the market

On long-distance connections however several independents captureda permanent place in the market Specialisation by offering a premierquality service allowed the independents to build up immunity to thepurely fare and scheduling responses of nationalised carriers and thuscapture a share of the market (Douglas 1997) In this way the indepen-dents were especially successful on the Anglo-Scottish routes The longertravel distance offered operators greater scope for product differentiationConsequently more operators were able to provide services even if theydeparted at the same time In the first few years of deregulation 67 percent of new long-distance services to or from London survived Henceproduct differentiation on long-distance connections made entrants resis-tant to the pricing and scheduling responses of incumbent operators bycreating consumer loyalty stabilising scheduling competition

50 Conclusion

For operators in scheduled passenger transport it is a great marketingchallenge to create an image that is distinct from their competitorsOperating the same or similar types of vehicles on the same routes doesnot have many elements of visible tangible differentiation vis-a-viscompetitors Many of the elements in which differences do exist are bytheir nature subjective and difficult to prove to the sceptical consumerExamples are friendliness and courtesy of personnel interior designseats mealssnacks lounges advertising image and so on Long-distanceoperators are better able than short-distance operators to realise suchproduct differentiation in a meaningful fashion Over longer distancesconsumers are generally more flexible with regard to departure times andare more appreciative of their preferred quality of service

In a two-dimensional horizontal product differentiation model withlinear waiting costs for departures and non-linear sensitivity to deviationsfrom preferred quality of service it is shown that a stable service patternrequires consumers to be sufficiently sensitive to differences in qualitybetween operators In reaction operators will differentiate their productsin terms of quality This differentiation prevents consumers from simplytaking the vehicle that is closest to their preferred departure time Consu-mers will be inclined to take an earlier or later departure if they feel morecomfortable with that operator or if there are additional benefits provided

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

151

by this operator In contrast if consumers are not sensitive to qualitydifferences operators would prefer to schedule their vehicles just beforetheir competitor in order to lsquostealrsquo its customers

On the basis of Neven and Thisse (1990) Ansari et al (1998) andIrmen and Thisse (1998) it can be expected that this result will notchange if the dimension of quality differentiation is modelled as verticaldifferentiation rather than horizontal differentiation It is clear that thequality differentiation considered has not only horizontal but also verticalaspects One example is seat width and pitch For the same price everyconsumer would appreciate more space The most dominant factordifferentiating operators is probably an operatorrsquos consumer loyaltyprogramme and that creates horizontal differentiation A formalanalysis for the case of vertical differentiation is beyond the scope of thispaper

The sensitivity to quality differences is a plausible factor that couldclarify the difference in existence of a stable equilibrium between differentmodes of scheduled transport A modal spectrum can be created on thebasis of the relevance of quality differentiation for the selection of an opera-tor The low-relevance end of this spectrum includes examples as containerfreight operations (such as liner shipping) and local public transport Thehigh-relevance end would probably include inter-continental passengerair transport For the low-relevance modes experience shows that com-petition results in unstable service patterns For the high-relevance modestability has never appeared to be a problem

References

Ansari A N Economides and J Steckel (1998) lsquoThe Max-min-min Principle of ProductDifferentiationrsquo Journal of Regional Science 38 207ndash30

Banister B (1985) lsquoDeregulating the Bus Industry in Britain (A) the ProposalsrsquoTransport Reviews 5 99ndash103

Brenner M A (1975) lsquoNeed for Continued Economic Regulation of Air TransportrsquoJournal of Air Law and Commerce 41 793ndash813

Cancian M A Bills and T Bergstrom (1995) lsquoHotelling Location Problems withDirectional Constraints an Application to Television News Schedulingrsquo Journal ofIndustrial Economics 43 121ndash4

DrsquoAspremont C J Jaskold Gabszewicz and J-F Thisse (1979) lsquoOn HotellingrsquoslsquolsquoStability in competitionrsquorsquorsquo Econometrica 47 1145ndash50

Douglas N J (1987) A Welfare Assessment of Transport Deregulation The Case of theExpress Coach Market in 1980 Aldershot Gower

Evans A (1987) lsquoA Theoretical Comparison of Competition with Other EconomicRegimes for Bus Servicesrsquo Journal of Transport Economics and Policy 21 7ndash36

Journal of Transport Economics and Policy Volume 40 Part 1

152

make consumers loyal A consumer will generally take the first bus thatarrives at the stop This occurs in the division of demand of Figure 3 Inthat case each operator prefers a different distance between departuretimes and will continuously try to attain his preferred distance The pre-ferred distance between departures for both operators is conflicting andno subgame perfect equilibrium in pure strategies with regard to thetiming of departures exists

This result corresponds to the generally-shared view on competition inurban public transport in continental Europe The European Commissionin its proposal for new regulation of the award of public service contractsin public transport by Member States articulates this view stating thatwithout exclusive rights lsquoservice patterns are unstablersquo2 This perceptionis based on the experiences in Great Britain of the deregulation of localpublic transport

Evans (1990) and Mackie et al (1995) observed that after deregulationof local public transport the number of travellers did not increase despitethe doubling of service levels (frequencies) and consequent reductions inwaiting times This lsquopuzzling resultrsquo could not be explained by the declinein bus usage due to higher real incomes and lower real motoring costsOne explanation that has been put forward was that frequency increasesare compensated by offsetting effects for example uncertainty caused topassengers by route instability such as irregular intervals frequently chan-ging timetables and so on (Evans 1990 Mackie et al 1995)

The model for low consumer sensitivity to quality predicts this instabil-ity of service patterns In the division of demand of Figure 3 the preferredlocation of operator 1 is just before the departure of operator 2 (x2 frac14 0)while operator 2 prefers a larger distance between departures (x2 gt 0)Given x2 frac14 0 operator 2 will choose a later departure but in reactionoperator 1 will follow in order to reduce the distance to x2 frac14 0 againand so on Basically every operator would like to be at a bus stop justbefore its competitor in order to take the whole market This implies thatoperators are lsquohead-runningrsquo each other

With regard to pricing Mackie et al (1995) stated that pricing is not aparticularly potent marketing weapon The first priority is on service ratherthan fares as travellers tend to board the first bus This behaviour of con-sumers is confirmed by the model for the situation in which an operatorrsquos

2Proposal from the European Commission of 26 July 2000 for a Regulation of the European Parliament

and of the Council on action by Member States concerning public service requirements and the award

of public service contracts in passenger transport by rail road and inland waterway COM(2000)7

provisional p 5

Journal of Transport Economics and Policy Volume 40 Part 1

148

demand is independent of prices and D1 frac14 1 x2 and D2 frac14 x2 In this casethe model shows that p1=p1 5 0 and p2=p25 0 Hence operators arecompeting over the timing of departures rather than pricing Evans statesthat (1990 p 266) lsquoThe operators match fares and tacitly collude to main-tain the pre-existing fare structure The operators also tacitly collude toincrease fares simultaneously at a rate at least as fast as inflation Faresremain the same on high-demand as on low-demand routes and on activelycompetitive as on non-competitive routesrsquo The model shows that theupward pressure on prices will only be limited by the maximum willingnessto pay Consequently the pricing discipline comes from external factorsfor example the existence of competition from another mode (such asprivate car cycling walking and so on) or competition between activitiesthat consumers can undertake (and that may or may not require transport)This clarifies why fares move at a similar rate to inflation and are notrelated to the level of demand on a route or the level of competition on aroute

42 Long-distance transport

In long-distance transport such as air transport consumers are moresensitive to quality Travel times are much longer and consequently con-sumers are more appreciative of comfort This allows for much greaterquality differentiation than in short-distance travel Hence consumerswill more easily take an alternative flight Non-price and non-schedulingfactors increase in importance for longer distances as can be seen for airtransport in the Table 1

The factors as distinguished in the Avmark Aviation Economist arelsquoschedulersquo lsquofarersquo lsquoairlinersquo lsquoairplanersquo and lsquootherrsquo lsquoSchedulersquo and lsquofarersquo areequivalent to the endogenous variables lsquoschedulersquo and lsquopricersquo lsquoAirlinersquo

Table 1

Most Influential Factors in Choosing a Flight

Factors asdistinguishedby the model

Factors asdistinguishedby Source

Length of flight

Under 2 hours () 2ndash5 hours () Over 5 hours ()

Schedule Schedule 701 430 193

Price Fare 114 137 165

Quality Airline 155 362 530Airplane 25 66 102Other 05 06 10

Source Avmark Aviation EconomistIAPA in Gialloreto 1988

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

149

lsquoairplanersquo and lsquootherrsquo can be clustered into the variable lsquoqualityrsquo Pressuredby competition airlines have become increasingly creative and effective indifferentiating their services in terms of quality including the creation ofconsumer loyalty

This situation is described by a sufficient sensitivity to quality that isj5 t as depicted in Figure 1 Given this division of demand operatorsmaximally differentiate in quality that is y1 frac14 0 and y2 frac14 1 This qualitydifferentiation relaxes competition over scheduling The model showsthat an operator cannot improve his position by choosing another timeof departure given the time of departure of his competitor Stronger consu-mer loyalty eliminates operatorsrsquo incentive to lsquohead-runrsquo each other whichcreates a subgame perfect equilibrium in timing departures Intuitively onewould say that an operator who moves to a later point of time increases hismarket but sufficiently strong consumersrsquo sensitivity to quality balancesthis tendency Consumers tend to wait for the departure of their preferredoperator

With regard to price the intuition cannot be confirmed that operatorsdo not seem to compete on price because pricing is too strong a marketingweapon According to the model operators do compete in price Furtheranalysis is needed in order to ascertain whether (and if so why) operatorsdo not seem to compete in price in long-distance transport One obser-vation (Brenner 1975) has been that scheduled transport operators tendto rival each other on frequency instead of price Such competitionincreases costs putting upward pressure on prices which could offset anyreduction in price that is normally associated with the introduction ofcompetition

43 Short-distance vs long-distanceThe impact of travel distance on stability can also be seen in the deregula-tion of lsquolong-distancersquo bus services in Great Britain In 1980 the Britishgovernment abolished a system of quantity control in the express coachmarket The deregulation allowed for free entry and competition onroutes served by nationalised carriers Douglas (1987) made a thoroughassessment of the effects of this deregulation on market structure faresservice quality and costs using data provided by express coach operatorsHe showed that on short-distance connections independent operatorsentering the market were unable to develop a significant market sharesince the two national carriers simply matched or undercut their faresand increased or manipulated departure times (Douglas 1997) Only 39per cent of such services to and from London survived during the firstfew years of deregulation The national carriers maintained some competi-tive advantages after deregulation such as sole access to major and centrally

Journal of Transport Economics and Policy Volume 40 Part 1

150

located bus stations a considerable network of services and an extensivesales network This made them better able to survive than the newindependent operators on the market

On long-distance connections however several independents captureda permanent place in the market Specialisation by offering a premierquality service allowed the independents to build up immunity to thepurely fare and scheduling responses of nationalised carriers and thuscapture a share of the market (Douglas 1997) In this way the indepen-dents were especially successful on the Anglo-Scottish routes The longertravel distance offered operators greater scope for product differentiationConsequently more operators were able to provide services even if theydeparted at the same time In the first few years of deregulation 67 percent of new long-distance services to or from London survived Henceproduct differentiation on long-distance connections made entrants resis-tant to the pricing and scheduling responses of incumbent operators bycreating consumer loyalty stabilising scheduling competition

50 Conclusion

For operators in scheduled passenger transport it is a great marketingchallenge to create an image that is distinct from their competitorsOperating the same or similar types of vehicles on the same routes doesnot have many elements of visible tangible differentiation vis-a-viscompetitors Many of the elements in which differences do exist are bytheir nature subjective and difficult to prove to the sceptical consumerExamples are friendliness and courtesy of personnel interior designseats mealssnacks lounges advertising image and so on Long-distanceoperators are better able than short-distance operators to realise suchproduct differentiation in a meaningful fashion Over longer distancesconsumers are generally more flexible with regard to departure times andare more appreciative of their preferred quality of service

In a two-dimensional horizontal product differentiation model withlinear waiting costs for departures and non-linear sensitivity to deviationsfrom preferred quality of service it is shown that a stable service patternrequires consumers to be sufficiently sensitive to differences in qualitybetween operators In reaction operators will differentiate their productsin terms of quality This differentiation prevents consumers from simplytaking the vehicle that is closest to their preferred departure time Consu-mers will be inclined to take an earlier or later departure if they feel morecomfortable with that operator or if there are additional benefits provided

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

151

by this operator In contrast if consumers are not sensitive to qualitydifferences operators would prefer to schedule their vehicles just beforetheir competitor in order to lsquostealrsquo its customers

On the basis of Neven and Thisse (1990) Ansari et al (1998) andIrmen and Thisse (1998) it can be expected that this result will notchange if the dimension of quality differentiation is modelled as verticaldifferentiation rather than horizontal differentiation It is clear that thequality differentiation considered has not only horizontal but also verticalaspects One example is seat width and pitch For the same price everyconsumer would appreciate more space The most dominant factordifferentiating operators is probably an operatorrsquos consumer loyaltyprogramme and that creates horizontal differentiation A formalanalysis for the case of vertical differentiation is beyond the scope of thispaper

The sensitivity to quality differences is a plausible factor that couldclarify the difference in existence of a stable equilibrium between differentmodes of scheduled transport A modal spectrum can be created on thebasis of the relevance of quality differentiation for the selection of an opera-tor The low-relevance end of this spectrum includes examples as containerfreight operations (such as liner shipping) and local public transport Thehigh-relevance end would probably include inter-continental passengerair transport For the low-relevance modes experience shows that com-petition results in unstable service patterns For the high-relevance modestability has never appeared to be a problem

References

Ansari A N Economides and J Steckel (1998) lsquoThe Max-min-min Principle of ProductDifferentiationrsquo Journal of Regional Science 38 207ndash30

Banister B (1985) lsquoDeregulating the Bus Industry in Britain (A) the ProposalsrsquoTransport Reviews 5 99ndash103

Brenner M A (1975) lsquoNeed for Continued Economic Regulation of Air TransportrsquoJournal of Air Law and Commerce 41 793ndash813

Cancian M A Bills and T Bergstrom (1995) lsquoHotelling Location Problems withDirectional Constraints an Application to Television News Schedulingrsquo Journal ofIndustrial Economics 43 121ndash4

DrsquoAspremont C J Jaskold Gabszewicz and J-F Thisse (1979) lsquoOn HotellingrsquoslsquolsquoStability in competitionrsquorsquorsquo Econometrica 47 1145ndash50

Douglas N J (1987) A Welfare Assessment of Transport Deregulation The Case of theExpress Coach Market in 1980 Aldershot Gower

Evans A (1987) lsquoA Theoretical Comparison of Competition with Other EconomicRegimes for Bus Servicesrsquo Journal of Transport Economics and Policy 21 7ndash36

Journal of Transport Economics and Policy Volume 40 Part 1

152

demand is independent of prices and D1 frac14 1 x2 and D2 frac14 x2 In this casethe model shows that p1=p1 5 0 and p2=p25 0 Hence operators arecompeting over the timing of departures rather than pricing Evans statesthat (1990 p 266) lsquoThe operators match fares and tacitly collude to main-tain the pre-existing fare structure The operators also tacitly collude toincrease fares simultaneously at a rate at least as fast as inflation Faresremain the same on high-demand as on low-demand routes and on activelycompetitive as on non-competitive routesrsquo The model shows that theupward pressure on prices will only be limited by the maximum willingnessto pay Consequently the pricing discipline comes from external factorsfor example the existence of competition from another mode (such asprivate car cycling walking and so on) or competition between activitiesthat consumers can undertake (and that may or may not require transport)This clarifies why fares move at a similar rate to inflation and are notrelated to the level of demand on a route or the level of competition on aroute

42 Long-distance transport

In long-distance transport such as air transport consumers are moresensitive to quality Travel times are much longer and consequently con-sumers are more appreciative of comfort This allows for much greaterquality differentiation than in short-distance travel Hence consumerswill more easily take an alternative flight Non-price and non-schedulingfactors increase in importance for longer distances as can be seen for airtransport in the Table 1

The factors as distinguished in the Avmark Aviation Economist arelsquoschedulersquo lsquofarersquo lsquoairlinersquo lsquoairplanersquo and lsquootherrsquo lsquoSchedulersquo and lsquofarersquo areequivalent to the endogenous variables lsquoschedulersquo and lsquopricersquo lsquoAirlinersquo

Table 1

Most Influential Factors in Choosing a Flight

Factors asdistinguishedby the model

Factors asdistinguishedby Source

Length of flight

Under 2 hours () 2ndash5 hours () Over 5 hours ()

Schedule Schedule 701 430 193

Price Fare 114 137 165

Quality Airline 155 362 530Airplane 25 66 102Other 05 06 10

Source Avmark Aviation EconomistIAPA in Gialloreto 1988

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

149

lsquoairplanersquo and lsquootherrsquo can be clustered into the variable lsquoqualityrsquo Pressuredby competition airlines have become increasingly creative and effective indifferentiating their services in terms of quality including the creation ofconsumer loyalty

This situation is described by a sufficient sensitivity to quality that isj5 t as depicted in Figure 1 Given this division of demand operatorsmaximally differentiate in quality that is y1 frac14 0 and y2 frac14 1 This qualitydifferentiation relaxes competition over scheduling The model showsthat an operator cannot improve his position by choosing another timeof departure given the time of departure of his competitor Stronger consu-mer loyalty eliminates operatorsrsquo incentive to lsquohead-runrsquo each other whichcreates a subgame perfect equilibrium in timing departures Intuitively onewould say that an operator who moves to a later point of time increases hismarket but sufficiently strong consumersrsquo sensitivity to quality balancesthis tendency Consumers tend to wait for the departure of their preferredoperator

With regard to price the intuition cannot be confirmed that operatorsdo not seem to compete on price because pricing is too strong a marketingweapon According to the model operators do compete in price Furtheranalysis is needed in order to ascertain whether (and if so why) operatorsdo not seem to compete in price in long-distance transport One obser-vation (Brenner 1975) has been that scheduled transport operators tendto rival each other on frequency instead of price Such competitionincreases costs putting upward pressure on prices which could offset anyreduction in price that is normally associated with the introduction ofcompetition

43 Short-distance vs long-distanceThe impact of travel distance on stability can also be seen in the deregula-tion of lsquolong-distancersquo bus services in Great Britain In 1980 the Britishgovernment abolished a system of quantity control in the express coachmarket The deregulation allowed for free entry and competition onroutes served by nationalised carriers Douglas (1987) made a thoroughassessment of the effects of this deregulation on market structure faresservice quality and costs using data provided by express coach operatorsHe showed that on short-distance connections independent operatorsentering the market were unable to develop a significant market sharesince the two national carriers simply matched or undercut their faresand increased or manipulated departure times (Douglas 1997) Only 39per cent of such services to and from London survived during the firstfew years of deregulation The national carriers maintained some competi-tive advantages after deregulation such as sole access to major and centrally

Journal of Transport Economics and Policy Volume 40 Part 1

150

located bus stations a considerable network of services and an extensivesales network This made them better able to survive than the newindependent operators on the market

On long-distance connections however several independents captureda permanent place in the market Specialisation by offering a premierquality service allowed the independents to build up immunity to thepurely fare and scheduling responses of nationalised carriers and thuscapture a share of the market (Douglas 1997) In this way the indepen-dents were especially successful on the Anglo-Scottish routes The longertravel distance offered operators greater scope for product differentiationConsequently more operators were able to provide services even if theydeparted at the same time In the first few years of deregulation 67 percent of new long-distance services to or from London survived Henceproduct differentiation on long-distance connections made entrants resis-tant to the pricing and scheduling responses of incumbent operators bycreating consumer loyalty stabilising scheduling competition

50 Conclusion

For operators in scheduled passenger transport it is a great marketingchallenge to create an image that is distinct from their competitorsOperating the same or similar types of vehicles on the same routes doesnot have many elements of visible tangible differentiation vis-a-viscompetitors Many of the elements in which differences do exist are bytheir nature subjective and difficult to prove to the sceptical consumerExamples are friendliness and courtesy of personnel interior designseats mealssnacks lounges advertising image and so on Long-distanceoperators are better able than short-distance operators to realise suchproduct differentiation in a meaningful fashion Over longer distancesconsumers are generally more flexible with regard to departure times andare more appreciative of their preferred quality of service

In a two-dimensional horizontal product differentiation model withlinear waiting costs for departures and non-linear sensitivity to deviationsfrom preferred quality of service it is shown that a stable service patternrequires consumers to be sufficiently sensitive to differences in qualitybetween operators In reaction operators will differentiate their productsin terms of quality This differentiation prevents consumers from simplytaking the vehicle that is closest to their preferred departure time Consu-mers will be inclined to take an earlier or later departure if they feel morecomfortable with that operator or if there are additional benefits provided

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

151

by this operator In contrast if consumers are not sensitive to qualitydifferences operators would prefer to schedule their vehicles just beforetheir competitor in order to lsquostealrsquo its customers

On the basis of Neven and Thisse (1990) Ansari et al (1998) andIrmen and Thisse (1998) it can be expected that this result will notchange if the dimension of quality differentiation is modelled as verticaldifferentiation rather than horizontal differentiation It is clear that thequality differentiation considered has not only horizontal but also verticalaspects One example is seat width and pitch For the same price everyconsumer would appreciate more space The most dominant factordifferentiating operators is probably an operatorrsquos consumer loyaltyprogramme and that creates horizontal differentiation A formalanalysis for the case of vertical differentiation is beyond the scope of thispaper

The sensitivity to quality differences is a plausible factor that couldclarify the difference in existence of a stable equilibrium between differentmodes of scheduled transport A modal spectrum can be created on thebasis of the relevance of quality differentiation for the selection of an opera-tor The low-relevance end of this spectrum includes examples as containerfreight operations (such as liner shipping) and local public transport Thehigh-relevance end would probably include inter-continental passengerair transport For the low-relevance modes experience shows that com-petition results in unstable service patterns For the high-relevance modestability has never appeared to be a problem

References

Ansari A N Economides and J Steckel (1998) lsquoThe Max-min-min Principle of ProductDifferentiationrsquo Journal of Regional Science 38 207ndash30

Banister B (1985) lsquoDeregulating the Bus Industry in Britain (A) the ProposalsrsquoTransport Reviews 5 99ndash103

Brenner M A (1975) lsquoNeed for Continued Economic Regulation of Air TransportrsquoJournal of Air Law and Commerce 41 793ndash813

Cancian M A Bills and T Bergstrom (1995) lsquoHotelling Location Problems withDirectional Constraints an Application to Television News Schedulingrsquo Journal ofIndustrial Economics 43 121ndash4

DrsquoAspremont C J Jaskold Gabszewicz and J-F Thisse (1979) lsquoOn HotellingrsquoslsquolsquoStability in competitionrsquorsquorsquo Econometrica 47 1145ndash50

Douglas N J (1987) A Welfare Assessment of Transport Deregulation The Case of theExpress Coach Market in 1980 Aldershot Gower

Evans A (1987) lsquoA Theoretical Comparison of Competition with Other EconomicRegimes for Bus Servicesrsquo Journal of Transport Economics and Policy 21 7ndash36

Journal of Transport Economics and Policy Volume 40 Part 1

152

lsquoairplanersquo and lsquootherrsquo can be clustered into the variable lsquoqualityrsquo Pressuredby competition airlines have become increasingly creative and effective indifferentiating their services in terms of quality including the creation ofconsumer loyalty

This situation is described by a sufficient sensitivity to quality that isj5 t as depicted in Figure 1 Given this division of demand operatorsmaximally differentiate in quality that is y1 frac14 0 and y2 frac14 1 This qualitydifferentiation relaxes competition over scheduling The model showsthat an operator cannot improve his position by choosing another timeof departure given the time of departure of his competitor Stronger consu-mer loyalty eliminates operatorsrsquo incentive to lsquohead-runrsquo each other whichcreates a subgame perfect equilibrium in timing departures Intuitively onewould say that an operator who moves to a later point of time increases hismarket but sufficiently strong consumersrsquo sensitivity to quality balancesthis tendency Consumers tend to wait for the departure of their preferredoperator

With regard to price the intuition cannot be confirmed that operatorsdo not seem to compete on price because pricing is too strong a marketingweapon According to the model operators do compete in price Furtheranalysis is needed in order to ascertain whether (and if so why) operatorsdo not seem to compete in price in long-distance transport One obser-vation (Brenner 1975) has been that scheduled transport operators tendto rival each other on frequency instead of price Such competitionincreases costs putting upward pressure on prices which could offset anyreduction in price that is normally associated with the introduction ofcompetition

43 Short-distance vs long-distanceThe impact of travel distance on stability can also be seen in the deregula-tion of lsquolong-distancersquo bus services in Great Britain In 1980 the Britishgovernment abolished a system of quantity control in the express coachmarket The deregulation allowed for free entry and competition onroutes served by nationalised carriers Douglas (1987) made a thoroughassessment of the effects of this deregulation on market structure faresservice quality and costs using data provided by express coach operatorsHe showed that on short-distance connections independent operatorsentering the market were unable to develop a significant market sharesince the two national carriers simply matched or undercut their faresand increased or manipulated departure times (Douglas 1997) Only 39per cent of such services to and from London survived during the firstfew years of deregulation The national carriers maintained some competi-tive advantages after deregulation such as sole access to major and centrally

Journal of Transport Economics and Policy Volume 40 Part 1

150

located bus stations a considerable network of services and an extensivesales network This made them better able to survive than the newindependent operators on the market

On long-distance connections however several independents captureda permanent place in the market Specialisation by offering a premierquality service allowed the independents to build up immunity to thepurely fare and scheduling responses of nationalised carriers and thuscapture a share of the market (Douglas 1997) In this way the indepen-dents were especially successful on the Anglo-Scottish routes The longertravel distance offered operators greater scope for product differentiationConsequently more operators were able to provide services even if theydeparted at the same time In the first few years of deregulation 67 percent of new long-distance services to or from London survived Henceproduct differentiation on long-distance connections made entrants resis-tant to the pricing and scheduling responses of incumbent operators bycreating consumer loyalty stabilising scheduling competition

50 Conclusion

For operators in scheduled passenger transport it is a great marketingchallenge to create an image that is distinct from their competitorsOperating the same or similar types of vehicles on the same routes doesnot have many elements of visible tangible differentiation vis-a-viscompetitors Many of the elements in which differences do exist are bytheir nature subjective and difficult to prove to the sceptical consumerExamples are friendliness and courtesy of personnel interior designseats mealssnacks lounges advertising image and so on Long-distanceoperators are better able than short-distance operators to realise suchproduct differentiation in a meaningful fashion Over longer distancesconsumers are generally more flexible with regard to departure times andare more appreciative of their preferred quality of service

In a two-dimensional horizontal product differentiation model withlinear waiting costs for departures and non-linear sensitivity to deviationsfrom preferred quality of service it is shown that a stable service patternrequires consumers to be sufficiently sensitive to differences in qualitybetween operators In reaction operators will differentiate their productsin terms of quality This differentiation prevents consumers from simplytaking the vehicle that is closest to their preferred departure time Consu-mers will be inclined to take an earlier or later departure if they feel morecomfortable with that operator or if there are additional benefits provided

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

151

by this operator In contrast if consumers are not sensitive to qualitydifferences operators would prefer to schedule their vehicles just beforetheir competitor in order to lsquostealrsquo its customers

On the basis of Neven and Thisse (1990) Ansari et al (1998) andIrmen and Thisse (1998) it can be expected that this result will notchange if the dimension of quality differentiation is modelled as verticaldifferentiation rather than horizontal differentiation It is clear that thequality differentiation considered has not only horizontal but also verticalaspects One example is seat width and pitch For the same price everyconsumer would appreciate more space The most dominant factordifferentiating operators is probably an operatorrsquos consumer loyaltyprogramme and that creates horizontal differentiation A formalanalysis for the case of vertical differentiation is beyond the scope of thispaper

The sensitivity to quality differences is a plausible factor that couldclarify the difference in existence of a stable equilibrium between differentmodes of scheduled transport A modal spectrum can be created on thebasis of the relevance of quality differentiation for the selection of an opera-tor The low-relevance end of this spectrum includes examples as containerfreight operations (such as liner shipping) and local public transport Thehigh-relevance end would probably include inter-continental passengerair transport For the low-relevance modes experience shows that com-petition results in unstable service patterns For the high-relevance modestability has never appeared to be a problem

References

Ansari A N Economides and J Steckel (1998) lsquoThe Max-min-min Principle of ProductDifferentiationrsquo Journal of Regional Science 38 207ndash30

Banister B (1985) lsquoDeregulating the Bus Industry in Britain (A) the ProposalsrsquoTransport Reviews 5 99ndash103

Brenner M A (1975) lsquoNeed for Continued Economic Regulation of Air TransportrsquoJournal of Air Law and Commerce 41 793ndash813

Cancian M A Bills and T Bergstrom (1995) lsquoHotelling Location Problems withDirectional Constraints an Application to Television News Schedulingrsquo Journal ofIndustrial Economics 43 121ndash4

DrsquoAspremont C J Jaskold Gabszewicz and J-F Thisse (1979) lsquoOn HotellingrsquoslsquolsquoStability in competitionrsquorsquorsquo Econometrica 47 1145ndash50

Douglas N J (1987) A Welfare Assessment of Transport Deregulation The Case of theExpress Coach Market in 1980 Aldershot Gower

Evans A (1987) lsquoA Theoretical Comparison of Competition with Other EconomicRegimes for Bus Servicesrsquo Journal of Transport Economics and Policy 21 7ndash36

Journal of Transport Economics and Policy Volume 40 Part 1

152

located bus stations a considerable network of services and an extensivesales network This made them better able to survive than the newindependent operators on the market

On long-distance connections however several independents captureda permanent place in the market Specialisation by offering a premierquality service allowed the independents to build up immunity to thepurely fare and scheduling responses of nationalised carriers and thuscapture a share of the market (Douglas 1997) In this way the indepen-dents were especially successful on the Anglo-Scottish routes The longertravel distance offered operators greater scope for product differentiationConsequently more operators were able to provide services even if theydeparted at the same time In the first few years of deregulation 67 percent of new long-distance services to or from London survived Henceproduct differentiation on long-distance connections made entrants resis-tant to the pricing and scheduling responses of incumbent operators bycreating consumer loyalty stabilising scheduling competition

50 Conclusion

For operators in scheduled passenger transport it is a great marketingchallenge to create an image that is distinct from their competitorsOperating the same or similar types of vehicles on the same routes doesnot have many elements of visible tangible differentiation vis-a-viscompetitors Many of the elements in which differences do exist are bytheir nature subjective and difficult to prove to the sceptical consumerExamples are friendliness and courtesy of personnel interior designseats mealssnacks lounges advertising image and so on Long-distanceoperators are better able than short-distance operators to realise suchproduct differentiation in a meaningful fashion Over longer distancesconsumers are generally more flexible with regard to departure times andare more appreciative of their preferred quality of service

In a two-dimensional horizontal product differentiation model withlinear waiting costs for departures and non-linear sensitivity to deviationsfrom preferred quality of service it is shown that a stable service patternrequires consumers to be sufficiently sensitive to differences in qualitybetween operators In reaction operators will differentiate their productsin terms of quality This differentiation prevents consumers from simplytaking the vehicle that is closest to their preferred departure time Consu-mers will be inclined to take an earlier or later departure if they feel morecomfortable with that operator or if there are additional benefits provided

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

151

by this operator In contrast if consumers are not sensitive to qualitydifferences operators would prefer to schedule their vehicles just beforetheir competitor in order to lsquostealrsquo its customers

On the basis of Neven and Thisse (1990) Ansari et al (1998) andIrmen and Thisse (1998) it can be expected that this result will notchange if the dimension of quality differentiation is modelled as verticaldifferentiation rather than horizontal differentiation It is clear that thequality differentiation considered has not only horizontal but also verticalaspects One example is seat width and pitch For the same price everyconsumer would appreciate more space The most dominant factordifferentiating operators is probably an operatorrsquos consumer loyaltyprogramme and that creates horizontal differentiation A formalanalysis for the case of vertical differentiation is beyond the scope of thispaper

The sensitivity to quality differences is a plausible factor that couldclarify the difference in existence of a stable equilibrium between differentmodes of scheduled transport A modal spectrum can be created on thebasis of the relevance of quality differentiation for the selection of an opera-tor The low-relevance end of this spectrum includes examples as containerfreight operations (such as liner shipping) and local public transport Thehigh-relevance end would probably include inter-continental passengerair transport For the low-relevance modes experience shows that com-petition results in unstable service patterns For the high-relevance modestability has never appeared to be a problem

References

Ansari A N Economides and J Steckel (1998) lsquoThe Max-min-min Principle of ProductDifferentiationrsquo Journal of Regional Science 38 207ndash30

Banister B (1985) lsquoDeregulating the Bus Industry in Britain (A) the ProposalsrsquoTransport Reviews 5 99ndash103

Brenner M A (1975) lsquoNeed for Continued Economic Regulation of Air TransportrsquoJournal of Air Law and Commerce 41 793ndash813

Cancian M A Bills and T Bergstrom (1995) lsquoHotelling Location Problems withDirectional Constraints an Application to Television News Schedulingrsquo Journal ofIndustrial Economics 43 121ndash4

DrsquoAspremont C J Jaskold Gabszewicz and J-F Thisse (1979) lsquoOn HotellingrsquoslsquolsquoStability in competitionrsquorsquorsquo Econometrica 47 1145ndash50

Douglas N J (1987) A Welfare Assessment of Transport Deregulation The Case of theExpress Coach Market in 1980 Aldershot Gower

Evans A (1987) lsquoA Theoretical Comparison of Competition with Other EconomicRegimes for Bus Servicesrsquo Journal of Transport Economics and Policy 21 7ndash36

Journal of Transport Economics and Policy Volume 40 Part 1

152

by this operator In contrast if consumers are not sensitive to qualitydifferences operators would prefer to schedule their vehicles just beforetheir competitor in order to lsquostealrsquo its customers

On the basis of Neven and Thisse (1990) Ansari et al (1998) andIrmen and Thisse (1998) it can be expected that this result will notchange if the dimension of quality differentiation is modelled as verticaldifferentiation rather than horizontal differentiation It is clear that thequality differentiation considered has not only horizontal but also verticalaspects One example is seat width and pitch For the same price everyconsumer would appreciate more space The most dominant factordifferentiating operators is probably an operatorrsquos consumer loyaltyprogramme and that creates horizontal differentiation A formalanalysis for the case of vertical differentiation is beyond the scope of thispaper

The sensitivity to quality differences is a plausible factor that couldclarify the difference in existence of a stable equilibrium between differentmodes of scheduled transport A modal spectrum can be created on thebasis of the relevance of quality differentiation for the selection of an opera-tor The low-relevance end of this spectrum includes examples as containerfreight operations (such as liner shipping) and local public transport Thehigh-relevance end would probably include inter-continental passengerair transport For the low-relevance modes experience shows that com-petition results in unstable service patterns For the high-relevance modestability has never appeared to be a problem

References

Ansari A N Economides and J Steckel (1998) lsquoThe Max-min-min Principle of ProductDifferentiationrsquo Journal of Regional Science 38 207ndash30

Banister B (1985) lsquoDeregulating the Bus Industry in Britain (A) the ProposalsrsquoTransport Reviews 5 99ndash103

Brenner M A (1975) lsquoNeed for Continued Economic Regulation of Air TransportrsquoJournal of Air Law and Commerce 41 793ndash813

Cancian M A Bills and T Bergstrom (1995) lsquoHotelling Location Problems withDirectional Constraints an Application to Television News Schedulingrsquo Journal ofIndustrial Economics 43 121ndash4

DrsquoAspremont C J Jaskold Gabszewicz and J-F Thisse (1979) lsquoOn HotellingrsquoslsquolsquoStability in competitionrsquorsquorsquo Econometrica 47 1145ndash50

Douglas N J (1987) A Welfare Assessment of Transport Deregulation The Case of theExpress Coach Market in 1980 Aldershot Gower

Evans A (1987) lsquoA Theoretical Comparison of Competition with Other EconomicRegimes for Bus Servicesrsquo Journal of Transport Economics and Policy 21 7ndash36

Journal of Transport Economics and Policy Volume 40 Part 1

152

Evans A (1990) lsquoCompetition and the Structure of Local Bus Marketsrsquo Journal ofTransport Economics and Policy 24 255ndash81

Foster C D (1985) lsquoThe Economics of Bus Deregulation in Britainrsquo Transport Reviews5 207ndash14

Foster C and J Golay (1986) lsquoSome Curious Old Practices and their Relevance toEquilibrium in Bus Competitionrsquo Journal of Transport Economics and Policy 20191ndash216

Gialloreto L (1988) Strategic Airline Management the Global War Begins LondonPitman

Hotelling H (1929) lsquoStability in Competitionrsquo Economic Journal 39 41ndash57Irmen A and J-F Thisse (1998) lsquoCompetition in Multi-characteristics Spaces Hotelling

was Almost Rightrsquo Journal of Economic Theory 78 76ndash102Mackie P J Preston and C Nash (1995) lsquoBus Deregulation Ten Years Onrsquo Transport

Reviews 15 229ndash51Neven D and J-F Thisse (1990) lsquoOn Quality and Variety Competitionrsquo in J J Gabsze-

wicz J-F Richard and L A Wolsey (eds) Economics Decision-making GamesEconometrics and Optimisation Amsterdam Elsevier Science Publishers

Tirole J (1988) The Theory of Industrial Organization Cambridge MA MIT PressTyson W J (1992) Bus Regulation Five Years On London Association of Metropolitan

Authorities and Passenger Transport Executive Group

Appendix A

A Linear Preference for Quality Model

The utility functions change if the costs that consumers incur for a devia-tion from their preferred quality (y-axis) are linear instead of quadraticIf discomfort increases linearly for larger deviations from preferred qualitythe utility of a consumer for using the service from operator 1 and operator2 respectively are

Uieth1THORN frac14 V p1 teth1 xiTHORN jjy1 yij

and

Uieth2THORN frac14V p2 tethx2 xiTHORN jjy2 yij if 0 lt xi 4 x2

V p2 teth1thorn x2 xiTHORN jjy2 yij if x2 lt xi 4 1

Proposition 2 There is no subgame perfect Nash equilibrium in purestrategies if the costs are linear in deviation from the preferred quality

Proof Equating the generalised costs for the intervals 0 lt xi 4x2 andx2 lt xi 4 1 allows us to establish the demand functions for both operatorsA consumer i with quality preference yi and preferred departure time xi hasthe following generalised costs if he uses the service from operator 1 or

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

153

2 respectively

If 0 lt xi 4x2

Uieth1THORN frac14 V p1 teth1 xiTHORN jethy1 yiTHORNUieth2THORN frac14 V p2 tethx2 xiTHORN jethy2 yiTHORN

if yi 4 y1 4 y2

Uieth1THORN frac14 V p1 teth1 xiTHORN jethyi y1THORNUieth2THORN frac14 V p2 tethx2 xiTHORN jethy2 yiTHORN

if y1 lt yi lt y2

Uieth1THORN frac14 V p1 teth1 xiTHORN jethyi y1THORNUieth2THORN frac14 V p2 tethx2 xiTHORN jethyi y2THORN

if y14 y2 4 yi

8gtgtgtgtgtgtgtgtltgtgtgtgtgtgtgtgt

If x2 lt xi 4 1

Uieth1THORN frac14 V p1 teth1 xiTHORN jethy1 yiTHORNUieth2THORN frac14 V p2 teth1thorn x2 xiTHORN jethy2 yiTHORN

if yi 4 y14 y2

Uieth1THORN frac14 V p1 teth1 xiTHORN jethyi y1THORNUieth2THORN frac14 V p2 teth1thorn x2 xiTHORN jethy2 yiTHORN

if y1 lt yi lt y2

Uieth1THORN frac14 V p1 teth1 xiTHORN jethyi y1THORNUieth2THORN frac14 V p2 teth1thorn x2 xiTHORN jethyi y2THORN

if y1 4 y24 yi

8gtgtgtgtgtgtgtgtltgtgtgtgtgtgtgtgt

Equating these generalised costs generates the consumers who have nopreference to using the service of operator 1 or operator 2 This gives thefollowing expressions

If 0 lt x4x2

p2 p1 frac14 teth1 x2THORN jethy2 y1THORN if y4 y14 y2p2 p1

2 teth1 x2THORN jethy1 thorn y2THORN

2frac14 y if y1 lt y lt y2

p2 p1 frac14 teth1 x2THORN thorn jethy2 y1THORN if y14 y2 4 y

8gtgtltgtgt

If x2 lt x4 1

p2 p1 frac14 tx2 jethy2 y1THORN if y4 y14 y2p2 p1

2thorn tx2 thorn jethy1 thorn y2THORN

2frac14 y if y1 lt y lt y2

p2 p1 frac14 tx2 thorn jethy2 y1THORN if y14 y24 y

8gtgtltgtgt

A consumer with quality preference yi will prefer operator 1 to operator2 if lsquofrac14rsquo is changed into lsquogtrsquo and will prefer operator 2 if lsquofrac14rsquo is changed intolsquoltrsquo The expressions show that only when y1 lt y lt y2 is there a division ofconsumers within an interval (0 lt x4x2 or x2 lt x4 1) some of whomprefer operator 1 while others prefer operator 2 and a few are indifferentIn the case of y4 y14 y2 and y1 4 y24 y there is no indifferent consumerFor example if y4 y1 4 y2 all consumers in interval 0 lt x4 x2 (x2) preferoperator 2 if p2 p1 lt teth1 x2THORN jethy2 y1THORN However if y4 y1 4 y2 notall x2 consumers will prefer operator 1 if p2 p1 gt teth1 x2THORN jethy2 y1THORN

Journal of Transport Economics and Policy Volume 40 Part 1

154

unless y1 frac14 y2 In this case if y1 lt y2 the indifferent consumer is actuallybetween y1 and y2 violating the condition y4 y1 4 y2 Hence ify4 y14 y2 or y1 4 y2 4 y y1 frac14 y2 is a necessary condition for possibledivisions of demand

On the basis of these expressions for the indifferent consumer it is nowpossible to define the following possible divisions of demand between bothoperators

If y4 y14 y2

D1 frac14 x2

D2 frac14 1 x2if y1 frac14 y2 p2 p1 gt teth1 x2THORN

p2 p1 lt tx2

D1 frac14 1 x2

D2 frac14 x2if y1 frac14 y2 p2 p1 lt teth1 x2THORN

p2 p1 gt tx2

8gtgtgtltgtgtgt

If y1 lt y lt y2

D1 frac14p2 p1 teth1 x2THORN jethy1 thorn y2THORN

2

x2

thornp2 p1 thorn tx2 thorn jethy1 thorn y2THORN

2

eth1 x2THORN

D2 frac141 p2 p1 teth1 x2THORN jethy1 thorn y2THORN

2

x2

thorn1 p2 p1 thorn tx2 thorn jethy1 thorn y2THORN

2

eth1 x2THORN

8gtgtgtgtgtgtgtgtgtgtgtgtltgtgtgtgtgtgtgtgtgtgtgtgt

If y14 y2 4 y

D1 frac14 x2

D2 frac14 1 x2if y1 frac14 y2 p2 p1 gt teth1 x2THORN

p2 p1 lt tx2

D1 frac14 1 x2

D2 frac14 x2if y1 frac14 y2 p2 p1 lt teth1 x2THORN

p2 p1 gt tx2

8gtgtgtltgtgtgt

For y4 y1 4 y2 and y14 y2 4 y the possible divisions of demand andassociated conditions are identical Analysing D1 frac14 x2 D2 frac14 1 x2 itbecomes immediately clear that the conditions p2 p1 gt teth1 x2THORN andp2 p1 lt tx2 cannot be fulfilled at the same time The divisionD1 frac14 1 x2 D2 frac14 x2 faces a similar problem Its associated conditionscan be rewritten as p2 lt p1 thorn teth1 x2THORN and p1 lt p2 thorn tx2 These pricingstrategies of operator 2 and operator 1 respectively clearly do not constituteequilibrium in the pricing subgame so prices will not be stable

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

155

This leaves us with the division of demand if y1 lt y lt y2 Operatorsrsquorespective demands can be simplified into

D1 frac14p2 p1 thorn jethy1 thorn y2THORN

2and D2 frac14 1thorn p1 p2 jethy1 thorn y2THORN

2

Profits are then

p1 frac14 p1D1 frac14 p1

p2 p1 thorn jethy1 thorn y2THORN

2

and

p2 frac14 p2D2 frac14 p2

1thorn p1 p2 jethy1 thorn y2THORN

2

Maximising these profits with respect to fares give the operatorsrsquoreaction curves

p1 frac14p2 thorn jethy1 thorn y2THORN

2and p2 frac14 1thorn p1 jethy1 thorn y2THORN

2

Substituting these reaction curves into each other gives the subgame per-fect prices

p1 frac142thorn jethy1 thorn y2THORN

3and p2 frac14

4 jethy1 thorn y2THORN3

Substituting these prices into the expressions for profits gives

p1 frac14frac122thorn jethy1 thorn y2THORN2

18and p2 frac14

frac124 jethy1 thorn y2THORN2

18

These profits show that p1 increases in y1 and that p2 decreases in y2Consequently the equilibrium locations of quality are y1 frac14 y2 Howeverthese equilibrium locations of quality violate the condition y1 lt y lt y2that defines demand If y1 frac14 y frac14 y2 the division of demand collapses into

D1 frac14 x2

D2 frac14 1 x2if p2 p1 gt teth1 x2THORN

p2 p1 lt tx2

D1 frac14 1 x2

D2 frac14 x2if p2 p1 lt teth1 x2THORN

p2 p1 gt tx2

8gtgtgtltgtgtgt

It has been shown for y4 y1 4 y2 and y14 y2 4 y that the associatedconditions for this division of demand cannot be fulfilled at the sametime so no equilibrium exists This outcome suffers from the same instabil-ity as Hotellingrsquos principle of minimum differentiation (1929) as demon-strated by drsquoAspremont et al (1979) Hence none of the three divisionsof demand generates a subgame perfect Nash equilibrium in pure strategies

Journal of Transport Economics and Policy Volume 40 Part 1

156

Appendix B

Analysis of Figure 2

Operators can choose prices locations of departures and qualities so thateither the indifferent consumers y or the indifferent consumers yy have a pre-ferred quality outside the area defined by y yy 2 frac120 1 If ethy lt 0 yy 2 frac120 1THORNthe division of demand between operator 1 and operator 2 will be

D1 frac14 eth1 x2THORNp2 p1 thorn tx2 thorn jethy22 y21THORN

2jethy2 y1THORN

and

D2 frac14 x2 thorn eth1 x2THORN1 p2 p1 thorn tx2 thorn jethy22 y21THORN

2jethy2 y1THORN

Alternatively if ethy 2 frac120 1 yy gt 1THORN the division of demand will be

D1 frac14 x2

p2 p1 teth1 x2THORN thorn jethy22 y21THORN

2jethy2 y1THORN

thorn eth1 x2THORN

and

D2 frac14 x2

1 p2 p1 teth1 x2THORN thorn jethy22 y21THORN

2jethy2 y1THORN

Proposition 3 In equilibrium operators cannot realise higher profits bydeviating so that ethy lt 0 yy 2 frac120 1THORN or ethy 2 frac120 1 yy gt 1THORNIt has to be shown that operators cannot increase their profits by deviatingfrom their equilibrium qualities and prices with the result that some indif-ferent consumers will prefer quality outside the area defined by y yy 2 frac120 1that is either ethy lt 0 yy 2 frac120 1THORN or ethy 2 frac120 1 yy gt 1THORN In the division ofdemand if ethy lt 0 yy 2 frac120 1THORN profits will be

p1 frac14 p1

eth1 x2THORN

p2 p1 thorn tx2 thorn jethy22 y21THORN

2jethy2 y1THORN

and

p2 frac14 p2

x2 thorn eth1 x2THORN

1 p2 p1 thorn tx2 thorn jethy22 y21THORN

2jethy2 y1THORN

Maximising these profits with respect to fares gives the followingreaction curves

p1 frac14p22thorn tx2 thorn jethy22 y21THORN

2

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

157

and

p2 frac14p12 tx2 thorn jethy22 y21THORN

2thorn jethy2 y1THORN

1 x2

Substituting these reaction curves into each other gives the subgameperfect prices

p1 frac14tx2 thorn jethy22 y21THORN

3thorn 2jethy2 y1THORN

3eth1 x2THORNand

p2 frac14 tx2 thorn jethy22 y21THORN3

thorn 4jethy2 y1THORN3eth1 x2THORN

Using the envelope theorem the optimal locations for operator 1 can befound by calculating (Tirole 1988 p 281)

dp1dx2

frac14 p1

D1

x2thorn D1

p2

dp2dx2

frac14 0

where D1

x2thorn D1

p2

dp2dx2

frac14 teth2 3x2THORN

6jethy2 y1THORN y1 thorn y2

6thorn 1

3eth1 x2THORNand

dp1dy1

frac14 p1

D1

y1thorn D1

p2

dp2dy1

frac14 0

whereD1

y1thorn D1

p2

dp2dy1

frac14 tx2eth1 x2THORN

6jethy2 y1THORN2thorn 1 x2

2 1thorn eth1 x2THORNy2

3ethy2 y1THORN

Similarly for operator 2

dp2dx2

frac14 p2

D2

x2thorn D2

p1

dp1dx2

frac14 0

where D2

x2thorn D2

p1

dp1dx2

frac14 teth2 3x2THORN

6jethy2 y1THORNthorn y1 thorn y2

6thorn 2

3eth1 x2THORNand

dp2dy2

frac14 p2

D2

y2thorn D2

p1

dp1dy2

frac14 0

Journal of Transport Economics and Policy Volume 40 Part 1

158

whereD2

y2thorn D2

p1

dp1dy2

frac14 tx2eth1 x2THORN

6jethy2 y1THORN2 1 x2

2thorn 2 eth1 x2THORNy1

3ethy2 y1THORN

It can be easily checked that

tx2eth1 x2THORN6jethy2 y1THORN2

thorn 1 x22

1thorn eth1 x2THORNy23ethy2 y1THORN

lt 0

so that

dp1dy1

lt 0

and that

tx2eth1 x2THORN6jethy2 y1THORN2

1 x22

thorn 2 eth1 x2THORNy13ethy2 y1THORN

gt 0

so that

dp2dy2

gt 0

Consequently operator 1 and operator 2 do not have incentive to deviatefrom y1 frac14 0 and y2 frac14 1 respectively

Substituting these equilibrium qualities into the profit functions gives

p1 frac14 p1

eth1 x2THORN

p2 p1 thorn tx2 thorn j

2j

and

p2 frac14 p2

x2 thorn eth1 x2THORN

1 p2 p1 thorn tx2 thorn j

2j

These profits can be compared with the equilibrium profits

p1p2 frac14 j=2 where

j5 teth1 x2THORN if 04x2 lt 1=2

j5 tx2 if 1=24x24 1

for a change in price of operator 1 or operator 2 with the result that y lt 0Given p2 frac14 j operator 1 will need to charge p1 gt 2j teth1 x2THORN so thaty lt 0 It can easily be checked that the resulting for operator 1 is smallerthan its equilibrium profit that is p1 lt p1 Similarly given p1 frac14 j operator2 will need to charge p2 lt teth1 x2THORN so that y lt 0 Also operator 2 does notincrease its profit by doing so as p2 lt p2

It should be noted that the division of demand if ethy lt 0 yy 2 frac120 1THORN andthe division of demand if ethy 2 frac120 1 yy gt 1THORN are simply mirror images in

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

159

which the roles of operator 1 and operator 2 are switched Consequentlyboth operators cannot realise higher profits by deviating from theirequilibrium qualities and prices

Proposition 4 There is no subgame perfect Nash equilibrium in pure strate-gies in the divisions of demand if ethy lt 0 yy 2 frac120 1THORN or ethy 2 frac120 1 yy gt 1THORN

From the expression for dp1=dx2 and dp2=dx2 it can be easily checkedthat dp1=dx2 frac14 0 is incompatible with dp2=dx2 frac14 0

dp1dx2

frac14 0 teth2 3x2THORN6jethy2 y1THORN

frac14 y2 thorn y16

1

3eth1 x2THORNand

dp2dx2

frac14 0 teth2 3x2THORN6jethy2 y1THORN

frac14 y2 thorn y16

thorn 2

3eth1 x2THORN

which can only be true if

1

1 x2frac14 0

Consequently there will not be an equilibrium location x2 that is notalso a corner-solution The existence of a corner solution requires thatx2 frac14 0 dp1=dx2 4 0 and dp2=dx24 0 or x2 frac14 1 dp1=dx2 5 0 anddp2=dx25 0

Substituting x2 frac14 0 into the total derivatives shows that dp1=dx2 gt 0Consequently there cannot be a corner solution in which x2 frac14 0 Doingthe same for x2 frac14 1 shows that dp1=dx2 gt 0 and dp2=dx2 gt 0 Howeversubstituting the subgame perfect prices into the conditions

p2 p1 teth1 x2THORN thorn jethy22 y21THORN2jethy2 y1THORN

4 0

and

p2 p1 thorn tx2 thorn jethy22 y21THORN2jethy2 y1THORN

lt 1

and substituting for x2 frac14 1 shows that these two conditions cannot be ful-filled for y1 y2 2 frac120 1 because yy y gt 1 Consequently x2 frac14 1 cannot be acorner solution either In this division of demand if ethy lt 0 yy 2 frac120 1THORN noNash equilibrium in pure strategies exists Also no Nash equilibrium inpure strategies exists in the division of demand if ethy 2 frac120 1 yy gt 1THORN becausethe analysis is similar to the division of demand if ethy lt 0 yy 2 frac120 1THORN

Journal of Transport Economics and Policy Volume 40 Part 1

160

unless y1 frac14 y2 In this case if y1 lt y2 the indifferent consumer is actuallybetween y1 and y2 violating the condition y4 y1 4 y2 Hence ify4 y14 y2 or y1 4 y2 4 y y1 frac14 y2 is a necessary condition for possibledivisions of demand

On the basis of these expressions for the indifferent consumer it is nowpossible to define the following possible divisions of demand between bothoperators

If y4 y14 y2

D1 frac14 x2

D2 frac14 1 x2if y1 frac14 y2 p2 p1 gt teth1 x2THORN

p2 p1 lt tx2

D1 frac14 1 x2

D2 frac14 x2if y1 frac14 y2 p2 p1 lt teth1 x2THORN

p2 p1 gt tx2

8gtgtgtltgtgtgt

If y1 lt y lt y2

D1 frac14p2 p1 teth1 x2THORN jethy1 thorn y2THORN

2

x2

thornp2 p1 thorn tx2 thorn jethy1 thorn y2THORN

2

eth1 x2THORN

D2 frac141 p2 p1 teth1 x2THORN jethy1 thorn y2THORN

2

x2

thorn1 p2 p1 thorn tx2 thorn jethy1 thorn y2THORN

2

eth1 x2THORN

8gtgtgtgtgtgtgtgtgtgtgtgtltgtgtgtgtgtgtgtgtgtgtgtgt

If y14 y2 4 y

D1 frac14 x2

D2 frac14 1 x2if y1 frac14 y2 p2 p1 gt teth1 x2THORN

p2 p1 lt tx2

D1 frac14 1 x2

D2 frac14 x2if y1 frac14 y2 p2 p1 lt teth1 x2THORN

p2 p1 gt tx2

8gtgtgtltgtgtgt

For y4 y1 4 y2 and y14 y2 4 y the possible divisions of demand andassociated conditions are identical Analysing D1 frac14 x2 D2 frac14 1 x2 itbecomes immediately clear that the conditions p2 p1 gt teth1 x2THORN andp2 p1 lt tx2 cannot be fulfilled at the same time The divisionD1 frac14 1 x2 D2 frac14 x2 faces a similar problem Its associated conditionscan be rewritten as p2 lt p1 thorn teth1 x2THORN and p1 lt p2 thorn tx2 These pricingstrategies of operator 2 and operator 1 respectively clearly do not constituteequilibrium in the pricing subgame so prices will not be stable

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

155

This leaves us with the division of demand if y1 lt y lt y2 Operatorsrsquorespective demands can be simplified into

D1 frac14p2 p1 thorn jethy1 thorn y2THORN

2and D2 frac14 1thorn p1 p2 jethy1 thorn y2THORN

2

Profits are then

p1 frac14 p1D1 frac14 p1

p2 p1 thorn jethy1 thorn y2THORN

2

and

p2 frac14 p2D2 frac14 p2

1thorn p1 p2 jethy1 thorn y2THORN

2

Maximising these profits with respect to fares give the operatorsrsquoreaction curves

p1 frac14p2 thorn jethy1 thorn y2THORN

2and p2 frac14 1thorn p1 jethy1 thorn y2THORN

2

Substituting these reaction curves into each other gives the subgame per-fect prices

p1 frac142thorn jethy1 thorn y2THORN

3and p2 frac14

4 jethy1 thorn y2THORN3

Substituting these prices into the expressions for profits gives

p1 frac14frac122thorn jethy1 thorn y2THORN2

18and p2 frac14

frac124 jethy1 thorn y2THORN2

18

These profits show that p1 increases in y1 and that p2 decreases in y2Consequently the equilibrium locations of quality are y1 frac14 y2 Howeverthese equilibrium locations of quality violate the condition y1 lt y lt y2that defines demand If y1 frac14 y frac14 y2 the division of demand collapses into

D1 frac14 x2

D2 frac14 1 x2if p2 p1 gt teth1 x2THORN

p2 p1 lt tx2

D1 frac14 1 x2

D2 frac14 x2if p2 p1 lt teth1 x2THORN

p2 p1 gt tx2

8gtgtgtltgtgtgt

It has been shown for y4 y1 4 y2 and y14 y2 4 y that the associatedconditions for this division of demand cannot be fulfilled at the sametime so no equilibrium exists This outcome suffers from the same instabil-ity as Hotellingrsquos principle of minimum differentiation (1929) as demon-strated by drsquoAspremont et al (1979) Hence none of the three divisionsof demand generates a subgame perfect Nash equilibrium in pure strategies

Journal of Transport Economics and Policy Volume 40 Part 1

156

Appendix B

Analysis of Figure 2

Operators can choose prices locations of departures and qualities so thateither the indifferent consumers y or the indifferent consumers yy have a pre-ferred quality outside the area defined by y yy 2 frac120 1 If ethy lt 0 yy 2 frac120 1THORNthe division of demand between operator 1 and operator 2 will be

D1 frac14 eth1 x2THORNp2 p1 thorn tx2 thorn jethy22 y21THORN

2jethy2 y1THORN

and

D2 frac14 x2 thorn eth1 x2THORN1 p2 p1 thorn tx2 thorn jethy22 y21THORN

2jethy2 y1THORN

Alternatively if ethy 2 frac120 1 yy gt 1THORN the division of demand will be

D1 frac14 x2

p2 p1 teth1 x2THORN thorn jethy22 y21THORN

2jethy2 y1THORN

thorn eth1 x2THORN

and

D2 frac14 x2

1 p2 p1 teth1 x2THORN thorn jethy22 y21THORN

2jethy2 y1THORN

Proposition 3 In equilibrium operators cannot realise higher profits bydeviating so that ethy lt 0 yy 2 frac120 1THORN or ethy 2 frac120 1 yy gt 1THORNIt has to be shown that operators cannot increase their profits by deviatingfrom their equilibrium qualities and prices with the result that some indif-ferent consumers will prefer quality outside the area defined by y yy 2 frac120 1that is either ethy lt 0 yy 2 frac120 1THORN or ethy 2 frac120 1 yy gt 1THORN In the division ofdemand if ethy lt 0 yy 2 frac120 1THORN profits will be

p1 frac14 p1

eth1 x2THORN

p2 p1 thorn tx2 thorn jethy22 y21THORN

2jethy2 y1THORN

and

p2 frac14 p2

x2 thorn eth1 x2THORN

1 p2 p1 thorn tx2 thorn jethy22 y21THORN

2jethy2 y1THORN

Maximising these profits with respect to fares gives the followingreaction curves

p1 frac14p22thorn tx2 thorn jethy22 y21THORN

2

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

157

and

p2 frac14p12 tx2 thorn jethy22 y21THORN

2thorn jethy2 y1THORN

1 x2

Substituting these reaction curves into each other gives the subgameperfect prices

p1 frac14tx2 thorn jethy22 y21THORN

3thorn 2jethy2 y1THORN

3eth1 x2THORNand

p2 frac14 tx2 thorn jethy22 y21THORN3

thorn 4jethy2 y1THORN3eth1 x2THORN

Using the envelope theorem the optimal locations for operator 1 can befound by calculating (Tirole 1988 p 281)

dp1dx2

frac14 p1

D1

x2thorn D1

p2

dp2dx2

frac14 0

where D1

x2thorn D1

p2

dp2dx2

frac14 teth2 3x2THORN

6jethy2 y1THORN y1 thorn y2

6thorn 1

3eth1 x2THORNand

dp1dy1

frac14 p1

D1

y1thorn D1

p2

dp2dy1

frac14 0

whereD1

y1thorn D1

p2

dp2dy1

frac14 tx2eth1 x2THORN

6jethy2 y1THORN2thorn 1 x2

2 1thorn eth1 x2THORNy2

3ethy2 y1THORN

Similarly for operator 2

dp2dx2

frac14 p2

D2

x2thorn D2

p1

dp1dx2

frac14 0

where D2

x2thorn D2

p1

dp1dx2

frac14 teth2 3x2THORN

6jethy2 y1THORNthorn y1 thorn y2

6thorn 2

3eth1 x2THORNand

dp2dy2

frac14 p2

D2

y2thorn D2

p1

dp1dy2

frac14 0

Journal of Transport Economics and Policy Volume 40 Part 1

158

whereD2

y2thorn D2

p1

dp1dy2

frac14 tx2eth1 x2THORN

6jethy2 y1THORN2 1 x2

2thorn 2 eth1 x2THORNy1

3ethy2 y1THORN

It can be easily checked that

tx2eth1 x2THORN6jethy2 y1THORN2

thorn 1 x22

1thorn eth1 x2THORNy23ethy2 y1THORN

lt 0

so that

dp1dy1

lt 0

and that

tx2eth1 x2THORN6jethy2 y1THORN2

1 x22

thorn 2 eth1 x2THORNy13ethy2 y1THORN

gt 0

so that

dp2dy2

gt 0

Consequently operator 1 and operator 2 do not have incentive to deviatefrom y1 frac14 0 and y2 frac14 1 respectively

Substituting these equilibrium qualities into the profit functions gives

p1 frac14 p1

eth1 x2THORN

p2 p1 thorn tx2 thorn j

2j

and

p2 frac14 p2

x2 thorn eth1 x2THORN

1 p2 p1 thorn tx2 thorn j

2j

These profits can be compared with the equilibrium profits

p1p2 frac14 j=2 where

j5 teth1 x2THORN if 04x2 lt 1=2

j5 tx2 if 1=24x24 1

for a change in price of operator 1 or operator 2 with the result that y lt 0Given p2 frac14 j operator 1 will need to charge p1 gt 2j teth1 x2THORN so thaty lt 0 It can easily be checked that the resulting for operator 1 is smallerthan its equilibrium profit that is p1 lt p1 Similarly given p1 frac14 j operator2 will need to charge p2 lt teth1 x2THORN so that y lt 0 Also operator 2 does notincrease its profit by doing so as p2 lt p2

It should be noted that the division of demand if ethy lt 0 yy 2 frac120 1THORN andthe division of demand if ethy 2 frac120 1 yy gt 1THORN are simply mirror images in

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

159

which the roles of operator 1 and operator 2 are switched Consequentlyboth operators cannot realise higher profits by deviating from theirequilibrium qualities and prices

Proposition 4 There is no subgame perfect Nash equilibrium in pure strate-gies in the divisions of demand if ethy lt 0 yy 2 frac120 1THORN or ethy 2 frac120 1 yy gt 1THORN

From the expression for dp1=dx2 and dp2=dx2 it can be easily checkedthat dp1=dx2 frac14 0 is incompatible with dp2=dx2 frac14 0

dp1dx2

frac14 0 teth2 3x2THORN6jethy2 y1THORN

frac14 y2 thorn y16

1

3eth1 x2THORNand

dp2dx2

frac14 0 teth2 3x2THORN6jethy2 y1THORN

frac14 y2 thorn y16

thorn 2

3eth1 x2THORN

which can only be true if

1

1 x2frac14 0

Consequently there will not be an equilibrium location x2 that is notalso a corner-solution The existence of a corner solution requires thatx2 frac14 0 dp1=dx2 4 0 and dp2=dx24 0 or x2 frac14 1 dp1=dx2 5 0 anddp2=dx25 0

Substituting x2 frac14 0 into the total derivatives shows that dp1=dx2 gt 0Consequently there cannot be a corner solution in which x2 frac14 0 Doingthe same for x2 frac14 1 shows that dp1=dx2 gt 0 and dp2=dx2 gt 0 Howeversubstituting the subgame perfect prices into the conditions

p2 p1 teth1 x2THORN thorn jethy22 y21THORN2jethy2 y1THORN

4 0

and

p2 p1 thorn tx2 thorn jethy22 y21THORN2jethy2 y1THORN

lt 1

and substituting for x2 frac14 1 shows that these two conditions cannot be ful-filled for y1 y2 2 frac120 1 because yy y gt 1 Consequently x2 frac14 1 cannot be acorner solution either In this division of demand if ethy lt 0 yy 2 frac120 1THORN noNash equilibrium in pure strategies exists Also no Nash equilibrium inpure strategies exists in the division of demand if ethy 2 frac120 1 yy gt 1THORN becausethe analysis is similar to the division of demand if ethy lt 0 yy 2 frac120 1THORN

Journal of Transport Economics and Policy Volume 40 Part 1

160

This leaves us with the division of demand if y1 lt y lt y2 Operatorsrsquorespective demands can be simplified into

D1 frac14p2 p1 thorn jethy1 thorn y2THORN

2and D2 frac14 1thorn p1 p2 jethy1 thorn y2THORN

2

Profits are then

p1 frac14 p1D1 frac14 p1

p2 p1 thorn jethy1 thorn y2THORN

2

and

p2 frac14 p2D2 frac14 p2

1thorn p1 p2 jethy1 thorn y2THORN

2

Maximising these profits with respect to fares give the operatorsrsquoreaction curves

p1 frac14p2 thorn jethy1 thorn y2THORN

2and p2 frac14 1thorn p1 jethy1 thorn y2THORN

2

Substituting these reaction curves into each other gives the subgame per-fect prices

p1 frac142thorn jethy1 thorn y2THORN

3and p2 frac14

4 jethy1 thorn y2THORN3

Substituting these prices into the expressions for profits gives

p1 frac14frac122thorn jethy1 thorn y2THORN2

18and p2 frac14

frac124 jethy1 thorn y2THORN2

18

These profits show that p1 increases in y1 and that p2 decreases in y2Consequently the equilibrium locations of quality are y1 frac14 y2 Howeverthese equilibrium locations of quality violate the condition y1 lt y lt y2that defines demand If y1 frac14 y frac14 y2 the division of demand collapses into

D1 frac14 x2

D2 frac14 1 x2if p2 p1 gt teth1 x2THORN

p2 p1 lt tx2

D1 frac14 1 x2

D2 frac14 x2if p2 p1 lt teth1 x2THORN

p2 p1 gt tx2

8gtgtgtltgtgtgt

It has been shown for y4 y1 4 y2 and y14 y2 4 y that the associatedconditions for this division of demand cannot be fulfilled at the sametime so no equilibrium exists This outcome suffers from the same instabil-ity as Hotellingrsquos principle of minimum differentiation (1929) as demon-strated by drsquoAspremont et al (1979) Hence none of the three divisionsof demand generates a subgame perfect Nash equilibrium in pure strategies

Journal of Transport Economics and Policy Volume 40 Part 1

156

Appendix B

Analysis of Figure 2

Operators can choose prices locations of departures and qualities so thateither the indifferent consumers y or the indifferent consumers yy have a pre-ferred quality outside the area defined by y yy 2 frac120 1 If ethy lt 0 yy 2 frac120 1THORNthe division of demand between operator 1 and operator 2 will be

D1 frac14 eth1 x2THORNp2 p1 thorn tx2 thorn jethy22 y21THORN

2jethy2 y1THORN

and

D2 frac14 x2 thorn eth1 x2THORN1 p2 p1 thorn tx2 thorn jethy22 y21THORN

2jethy2 y1THORN

Alternatively if ethy 2 frac120 1 yy gt 1THORN the division of demand will be

D1 frac14 x2

p2 p1 teth1 x2THORN thorn jethy22 y21THORN

2jethy2 y1THORN

thorn eth1 x2THORN

and

D2 frac14 x2

1 p2 p1 teth1 x2THORN thorn jethy22 y21THORN

2jethy2 y1THORN

Proposition 3 In equilibrium operators cannot realise higher profits bydeviating so that ethy lt 0 yy 2 frac120 1THORN or ethy 2 frac120 1 yy gt 1THORNIt has to be shown that operators cannot increase their profits by deviatingfrom their equilibrium qualities and prices with the result that some indif-ferent consumers will prefer quality outside the area defined by y yy 2 frac120 1that is either ethy lt 0 yy 2 frac120 1THORN or ethy 2 frac120 1 yy gt 1THORN In the division ofdemand if ethy lt 0 yy 2 frac120 1THORN profits will be

p1 frac14 p1

eth1 x2THORN

p2 p1 thorn tx2 thorn jethy22 y21THORN

2jethy2 y1THORN

and

p2 frac14 p2

x2 thorn eth1 x2THORN

1 p2 p1 thorn tx2 thorn jethy22 y21THORN

2jethy2 y1THORN

Maximising these profits with respect to fares gives the followingreaction curves

p1 frac14p22thorn tx2 thorn jethy22 y21THORN

2

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

157

and

p2 frac14p12 tx2 thorn jethy22 y21THORN

2thorn jethy2 y1THORN

1 x2

Substituting these reaction curves into each other gives the subgameperfect prices

p1 frac14tx2 thorn jethy22 y21THORN

3thorn 2jethy2 y1THORN

3eth1 x2THORNand

p2 frac14 tx2 thorn jethy22 y21THORN3

thorn 4jethy2 y1THORN3eth1 x2THORN

Using the envelope theorem the optimal locations for operator 1 can befound by calculating (Tirole 1988 p 281)

dp1dx2

frac14 p1

D1

x2thorn D1

p2

dp2dx2

frac14 0

where D1

x2thorn D1

p2

dp2dx2

frac14 teth2 3x2THORN

6jethy2 y1THORN y1 thorn y2

6thorn 1

3eth1 x2THORNand

dp1dy1

frac14 p1

D1

y1thorn D1

p2

dp2dy1

frac14 0

whereD1

y1thorn D1

p2

dp2dy1

frac14 tx2eth1 x2THORN

6jethy2 y1THORN2thorn 1 x2

2 1thorn eth1 x2THORNy2

3ethy2 y1THORN

Similarly for operator 2

dp2dx2

frac14 p2

D2

x2thorn D2

p1

dp1dx2

frac14 0

where D2

x2thorn D2

p1

dp1dx2

frac14 teth2 3x2THORN

6jethy2 y1THORNthorn y1 thorn y2

6thorn 2

3eth1 x2THORNand

dp2dy2

frac14 p2

D2

y2thorn D2

p1

dp1dy2

frac14 0

Journal of Transport Economics and Policy Volume 40 Part 1

158

whereD2

y2thorn D2

p1

dp1dy2

frac14 tx2eth1 x2THORN

6jethy2 y1THORN2 1 x2

2thorn 2 eth1 x2THORNy1

3ethy2 y1THORN

It can be easily checked that

tx2eth1 x2THORN6jethy2 y1THORN2

thorn 1 x22

1thorn eth1 x2THORNy23ethy2 y1THORN

lt 0

so that

dp1dy1

lt 0

and that

tx2eth1 x2THORN6jethy2 y1THORN2

1 x22

thorn 2 eth1 x2THORNy13ethy2 y1THORN

gt 0

so that

dp2dy2

gt 0

Consequently operator 1 and operator 2 do not have incentive to deviatefrom y1 frac14 0 and y2 frac14 1 respectively

Substituting these equilibrium qualities into the profit functions gives

p1 frac14 p1

eth1 x2THORN

p2 p1 thorn tx2 thorn j

2j

and

p2 frac14 p2

x2 thorn eth1 x2THORN

1 p2 p1 thorn tx2 thorn j

2j

These profits can be compared with the equilibrium profits

p1p2 frac14 j=2 where

j5 teth1 x2THORN if 04x2 lt 1=2

j5 tx2 if 1=24x24 1

for a change in price of operator 1 or operator 2 with the result that y lt 0Given p2 frac14 j operator 1 will need to charge p1 gt 2j teth1 x2THORN so thaty lt 0 It can easily be checked that the resulting for operator 1 is smallerthan its equilibrium profit that is p1 lt p1 Similarly given p1 frac14 j operator2 will need to charge p2 lt teth1 x2THORN so that y lt 0 Also operator 2 does notincrease its profit by doing so as p2 lt p2

It should be noted that the division of demand if ethy lt 0 yy 2 frac120 1THORN andthe division of demand if ethy 2 frac120 1 yy gt 1THORN are simply mirror images in

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

159

which the roles of operator 1 and operator 2 are switched Consequentlyboth operators cannot realise higher profits by deviating from theirequilibrium qualities and prices

Proposition 4 There is no subgame perfect Nash equilibrium in pure strate-gies in the divisions of demand if ethy lt 0 yy 2 frac120 1THORN or ethy 2 frac120 1 yy gt 1THORN

From the expression for dp1=dx2 and dp2=dx2 it can be easily checkedthat dp1=dx2 frac14 0 is incompatible with dp2=dx2 frac14 0

dp1dx2

frac14 0 teth2 3x2THORN6jethy2 y1THORN

frac14 y2 thorn y16

1

3eth1 x2THORNand

dp2dx2

frac14 0 teth2 3x2THORN6jethy2 y1THORN

frac14 y2 thorn y16

thorn 2

3eth1 x2THORN

which can only be true if

1

1 x2frac14 0

Consequently there will not be an equilibrium location x2 that is notalso a corner-solution The existence of a corner solution requires thatx2 frac14 0 dp1=dx2 4 0 and dp2=dx24 0 or x2 frac14 1 dp1=dx2 5 0 anddp2=dx25 0

Substituting x2 frac14 0 into the total derivatives shows that dp1=dx2 gt 0Consequently there cannot be a corner solution in which x2 frac14 0 Doingthe same for x2 frac14 1 shows that dp1=dx2 gt 0 and dp2=dx2 gt 0 Howeversubstituting the subgame perfect prices into the conditions

p2 p1 teth1 x2THORN thorn jethy22 y21THORN2jethy2 y1THORN

4 0

and

p2 p1 thorn tx2 thorn jethy22 y21THORN2jethy2 y1THORN

lt 1

and substituting for x2 frac14 1 shows that these two conditions cannot be ful-filled for y1 y2 2 frac120 1 because yy y gt 1 Consequently x2 frac14 1 cannot be acorner solution either In this division of demand if ethy lt 0 yy 2 frac120 1THORN noNash equilibrium in pure strategies exists Also no Nash equilibrium inpure strategies exists in the division of demand if ethy 2 frac120 1 yy gt 1THORN becausethe analysis is similar to the division of demand if ethy lt 0 yy 2 frac120 1THORN

Journal of Transport Economics and Policy Volume 40 Part 1

160

Appendix B

Analysis of Figure 2

Operators can choose prices locations of departures and qualities so thateither the indifferent consumers y or the indifferent consumers yy have a pre-ferred quality outside the area defined by y yy 2 frac120 1 If ethy lt 0 yy 2 frac120 1THORNthe division of demand between operator 1 and operator 2 will be

D1 frac14 eth1 x2THORNp2 p1 thorn tx2 thorn jethy22 y21THORN

2jethy2 y1THORN

and

D2 frac14 x2 thorn eth1 x2THORN1 p2 p1 thorn tx2 thorn jethy22 y21THORN

2jethy2 y1THORN

Alternatively if ethy 2 frac120 1 yy gt 1THORN the division of demand will be

D1 frac14 x2

p2 p1 teth1 x2THORN thorn jethy22 y21THORN

2jethy2 y1THORN

thorn eth1 x2THORN

and

D2 frac14 x2

1 p2 p1 teth1 x2THORN thorn jethy22 y21THORN

2jethy2 y1THORN

Proposition 3 In equilibrium operators cannot realise higher profits bydeviating so that ethy lt 0 yy 2 frac120 1THORN or ethy 2 frac120 1 yy gt 1THORNIt has to be shown that operators cannot increase their profits by deviatingfrom their equilibrium qualities and prices with the result that some indif-ferent consumers will prefer quality outside the area defined by y yy 2 frac120 1that is either ethy lt 0 yy 2 frac120 1THORN or ethy 2 frac120 1 yy gt 1THORN In the division ofdemand if ethy lt 0 yy 2 frac120 1THORN profits will be

p1 frac14 p1

eth1 x2THORN

p2 p1 thorn tx2 thorn jethy22 y21THORN

2jethy2 y1THORN

and

p2 frac14 p2

x2 thorn eth1 x2THORN

1 p2 p1 thorn tx2 thorn jethy22 y21THORN

2jethy2 y1THORN

Maximising these profits with respect to fares gives the followingreaction curves

p1 frac14p22thorn tx2 thorn jethy22 y21THORN

2

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

157

and

p2 frac14p12 tx2 thorn jethy22 y21THORN

2thorn jethy2 y1THORN

1 x2

Substituting these reaction curves into each other gives the subgameperfect prices

p1 frac14tx2 thorn jethy22 y21THORN

3thorn 2jethy2 y1THORN

3eth1 x2THORNand

p2 frac14 tx2 thorn jethy22 y21THORN3

thorn 4jethy2 y1THORN3eth1 x2THORN

Using the envelope theorem the optimal locations for operator 1 can befound by calculating (Tirole 1988 p 281)

dp1dx2

frac14 p1

D1

x2thorn D1

p2

dp2dx2

frac14 0

where D1

x2thorn D1

p2

dp2dx2

frac14 teth2 3x2THORN

6jethy2 y1THORN y1 thorn y2

6thorn 1

3eth1 x2THORNand

dp1dy1

frac14 p1

D1

y1thorn D1

p2

dp2dy1

frac14 0

whereD1

y1thorn D1

p2

dp2dy1

frac14 tx2eth1 x2THORN

6jethy2 y1THORN2thorn 1 x2

2 1thorn eth1 x2THORNy2

3ethy2 y1THORN

Similarly for operator 2

dp2dx2

frac14 p2

D2

x2thorn D2

p1

dp1dx2

frac14 0

where D2

x2thorn D2

p1

dp1dx2

frac14 teth2 3x2THORN

6jethy2 y1THORNthorn y1 thorn y2

6thorn 2

3eth1 x2THORNand

dp2dy2

frac14 p2

D2

y2thorn D2

p1

dp1dy2

frac14 0

Journal of Transport Economics and Policy Volume 40 Part 1

158

whereD2

y2thorn D2

p1

dp1dy2

frac14 tx2eth1 x2THORN

6jethy2 y1THORN2 1 x2

2thorn 2 eth1 x2THORNy1

3ethy2 y1THORN

It can be easily checked that

tx2eth1 x2THORN6jethy2 y1THORN2

thorn 1 x22

1thorn eth1 x2THORNy23ethy2 y1THORN

lt 0

so that

dp1dy1

lt 0

and that

tx2eth1 x2THORN6jethy2 y1THORN2

1 x22

thorn 2 eth1 x2THORNy13ethy2 y1THORN

gt 0

so that

dp2dy2

gt 0

Consequently operator 1 and operator 2 do not have incentive to deviatefrom y1 frac14 0 and y2 frac14 1 respectively

Substituting these equilibrium qualities into the profit functions gives

p1 frac14 p1

eth1 x2THORN

p2 p1 thorn tx2 thorn j

2j

and

p2 frac14 p2

x2 thorn eth1 x2THORN

1 p2 p1 thorn tx2 thorn j

2j

These profits can be compared with the equilibrium profits

p1p2 frac14 j=2 where

j5 teth1 x2THORN if 04x2 lt 1=2

j5 tx2 if 1=24x24 1

for a change in price of operator 1 or operator 2 with the result that y lt 0Given p2 frac14 j operator 1 will need to charge p1 gt 2j teth1 x2THORN so thaty lt 0 It can easily be checked that the resulting for operator 1 is smallerthan its equilibrium profit that is p1 lt p1 Similarly given p1 frac14 j operator2 will need to charge p2 lt teth1 x2THORN so that y lt 0 Also operator 2 does notincrease its profit by doing so as p2 lt p2

It should be noted that the division of demand if ethy lt 0 yy 2 frac120 1THORN andthe division of demand if ethy 2 frac120 1 yy gt 1THORN are simply mirror images in

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

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which the roles of operator 1 and operator 2 are switched Consequentlyboth operators cannot realise higher profits by deviating from theirequilibrium qualities and prices

Proposition 4 There is no subgame perfect Nash equilibrium in pure strate-gies in the divisions of demand if ethy lt 0 yy 2 frac120 1THORN or ethy 2 frac120 1 yy gt 1THORN

From the expression for dp1=dx2 and dp2=dx2 it can be easily checkedthat dp1=dx2 frac14 0 is incompatible with dp2=dx2 frac14 0

dp1dx2

frac14 0 teth2 3x2THORN6jethy2 y1THORN

frac14 y2 thorn y16

1

3eth1 x2THORNand

dp2dx2

frac14 0 teth2 3x2THORN6jethy2 y1THORN

frac14 y2 thorn y16

thorn 2

3eth1 x2THORN

which can only be true if

1

1 x2frac14 0

Consequently there will not be an equilibrium location x2 that is notalso a corner-solution The existence of a corner solution requires thatx2 frac14 0 dp1=dx2 4 0 and dp2=dx24 0 or x2 frac14 1 dp1=dx2 5 0 anddp2=dx25 0

Substituting x2 frac14 0 into the total derivatives shows that dp1=dx2 gt 0Consequently there cannot be a corner solution in which x2 frac14 0 Doingthe same for x2 frac14 1 shows that dp1=dx2 gt 0 and dp2=dx2 gt 0 Howeversubstituting the subgame perfect prices into the conditions

p2 p1 teth1 x2THORN thorn jethy22 y21THORN2jethy2 y1THORN

4 0

and

p2 p1 thorn tx2 thorn jethy22 y21THORN2jethy2 y1THORN

lt 1

and substituting for x2 frac14 1 shows that these two conditions cannot be ful-filled for y1 y2 2 frac120 1 because yy y gt 1 Consequently x2 frac14 1 cannot be acorner solution either In this division of demand if ethy lt 0 yy 2 frac120 1THORN noNash equilibrium in pure strategies exists Also no Nash equilibrium inpure strategies exists in the division of demand if ethy 2 frac120 1 yy gt 1THORN becausethe analysis is similar to the division of demand if ethy lt 0 yy 2 frac120 1THORN

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and

p2 frac14p12 tx2 thorn jethy22 y21THORN

2thorn jethy2 y1THORN

1 x2

Substituting these reaction curves into each other gives the subgameperfect prices

p1 frac14tx2 thorn jethy22 y21THORN

3thorn 2jethy2 y1THORN

3eth1 x2THORNand

p2 frac14 tx2 thorn jethy22 y21THORN3

thorn 4jethy2 y1THORN3eth1 x2THORN

Using the envelope theorem the optimal locations for operator 1 can befound by calculating (Tirole 1988 p 281)

dp1dx2

frac14 p1

D1

x2thorn D1

p2

dp2dx2

frac14 0

where D1

x2thorn D1

p2

dp2dx2

frac14 teth2 3x2THORN

6jethy2 y1THORN y1 thorn y2

6thorn 1

3eth1 x2THORNand

dp1dy1

frac14 p1

D1

y1thorn D1

p2

dp2dy1

frac14 0

whereD1

y1thorn D1

p2

dp2dy1

frac14 tx2eth1 x2THORN

6jethy2 y1THORN2thorn 1 x2

2 1thorn eth1 x2THORNy2

3ethy2 y1THORN

Similarly for operator 2

dp2dx2

frac14 p2

D2

x2thorn D2

p1

dp1dx2

frac14 0

where D2

x2thorn D2

p1

dp1dx2

frac14 teth2 3x2THORN

6jethy2 y1THORNthorn y1 thorn y2

6thorn 2

3eth1 x2THORNand

dp2dy2

frac14 p2

D2

y2thorn D2

p1

dp1dy2

frac14 0

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whereD2

y2thorn D2

p1

dp1dy2

frac14 tx2eth1 x2THORN

6jethy2 y1THORN2 1 x2

2thorn 2 eth1 x2THORNy1

3ethy2 y1THORN

It can be easily checked that

tx2eth1 x2THORN6jethy2 y1THORN2

thorn 1 x22

1thorn eth1 x2THORNy23ethy2 y1THORN

lt 0

so that

dp1dy1

lt 0

and that

tx2eth1 x2THORN6jethy2 y1THORN2

1 x22

thorn 2 eth1 x2THORNy13ethy2 y1THORN

gt 0

so that

dp2dy2

gt 0

Consequently operator 1 and operator 2 do not have incentive to deviatefrom y1 frac14 0 and y2 frac14 1 respectively

Substituting these equilibrium qualities into the profit functions gives

p1 frac14 p1

eth1 x2THORN

p2 p1 thorn tx2 thorn j

2j

and

p2 frac14 p2

x2 thorn eth1 x2THORN

1 p2 p1 thorn tx2 thorn j

2j

These profits can be compared with the equilibrium profits

p1p2 frac14 j=2 where

j5 teth1 x2THORN if 04x2 lt 1=2

j5 tx2 if 1=24x24 1

for a change in price of operator 1 or operator 2 with the result that y lt 0Given p2 frac14 j operator 1 will need to charge p1 gt 2j teth1 x2THORN so thaty lt 0 It can easily be checked that the resulting for operator 1 is smallerthan its equilibrium profit that is p1 lt p1 Similarly given p1 frac14 j operator2 will need to charge p2 lt teth1 x2THORN so that y lt 0 Also operator 2 does notincrease its profit by doing so as p2 lt p2

It should be noted that the division of demand if ethy lt 0 yy 2 frac120 1THORN andthe division of demand if ethy 2 frac120 1 yy gt 1THORN are simply mirror images in

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

159

which the roles of operator 1 and operator 2 are switched Consequentlyboth operators cannot realise higher profits by deviating from theirequilibrium qualities and prices

Proposition 4 There is no subgame perfect Nash equilibrium in pure strate-gies in the divisions of demand if ethy lt 0 yy 2 frac120 1THORN or ethy 2 frac120 1 yy gt 1THORN

From the expression for dp1=dx2 and dp2=dx2 it can be easily checkedthat dp1=dx2 frac14 0 is incompatible with dp2=dx2 frac14 0

dp1dx2

frac14 0 teth2 3x2THORN6jethy2 y1THORN

frac14 y2 thorn y16

1

3eth1 x2THORNand

dp2dx2

frac14 0 teth2 3x2THORN6jethy2 y1THORN

frac14 y2 thorn y16

thorn 2

3eth1 x2THORN

which can only be true if

1

1 x2frac14 0

Consequently there will not be an equilibrium location x2 that is notalso a corner-solution The existence of a corner solution requires thatx2 frac14 0 dp1=dx2 4 0 and dp2=dx24 0 or x2 frac14 1 dp1=dx2 5 0 anddp2=dx25 0

Substituting x2 frac14 0 into the total derivatives shows that dp1=dx2 gt 0Consequently there cannot be a corner solution in which x2 frac14 0 Doingthe same for x2 frac14 1 shows that dp1=dx2 gt 0 and dp2=dx2 gt 0 Howeversubstituting the subgame perfect prices into the conditions

p2 p1 teth1 x2THORN thorn jethy22 y21THORN2jethy2 y1THORN

4 0

and

p2 p1 thorn tx2 thorn jethy22 y21THORN2jethy2 y1THORN

lt 1

and substituting for x2 frac14 1 shows that these two conditions cannot be ful-filled for y1 y2 2 frac120 1 because yy y gt 1 Consequently x2 frac14 1 cannot be acorner solution either In this division of demand if ethy lt 0 yy 2 frac120 1THORN noNash equilibrium in pure strategies exists Also no Nash equilibrium inpure strategies exists in the division of demand if ethy 2 frac120 1 yy gt 1THORN becausethe analysis is similar to the division of demand if ethy lt 0 yy 2 frac120 1THORN

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whereD2

y2thorn D2

p1

dp1dy2

frac14 tx2eth1 x2THORN

6jethy2 y1THORN2 1 x2

2thorn 2 eth1 x2THORNy1

3ethy2 y1THORN

It can be easily checked that

tx2eth1 x2THORN6jethy2 y1THORN2

thorn 1 x22

1thorn eth1 x2THORNy23ethy2 y1THORN

lt 0

so that

dp1dy1

lt 0

and that

tx2eth1 x2THORN6jethy2 y1THORN2

1 x22

thorn 2 eth1 x2THORNy13ethy2 y1THORN

gt 0

so that

dp2dy2

gt 0

Consequently operator 1 and operator 2 do not have incentive to deviatefrom y1 frac14 0 and y2 frac14 1 respectively

Substituting these equilibrium qualities into the profit functions gives

p1 frac14 p1

eth1 x2THORN

p2 p1 thorn tx2 thorn j

2j

and

p2 frac14 p2

x2 thorn eth1 x2THORN

1 p2 p1 thorn tx2 thorn j

2j

These profits can be compared with the equilibrium profits

p1p2 frac14 j=2 where

j5 teth1 x2THORN if 04x2 lt 1=2

j5 tx2 if 1=24x24 1

for a change in price of operator 1 or operator 2 with the result that y lt 0Given p2 frac14 j operator 1 will need to charge p1 gt 2j teth1 x2THORN so thaty lt 0 It can easily be checked that the resulting for operator 1 is smallerthan its equilibrium profit that is p1 lt p1 Similarly given p1 frac14 j operator2 will need to charge p2 lt teth1 x2THORN so that y lt 0 Also operator 2 does notincrease its profit by doing so as p2 lt p2

It should be noted that the division of demand if ethy lt 0 yy 2 frac120 1THORN andthe division of demand if ethy 2 frac120 1 yy gt 1THORN are simply mirror images in

Stable Service Patterns in Scheduled Transport Competition Reeven and Janssen

159

which the roles of operator 1 and operator 2 are switched Consequentlyboth operators cannot realise higher profits by deviating from theirequilibrium qualities and prices

Proposition 4 There is no subgame perfect Nash equilibrium in pure strate-gies in the divisions of demand if ethy lt 0 yy 2 frac120 1THORN or ethy 2 frac120 1 yy gt 1THORN

From the expression for dp1=dx2 and dp2=dx2 it can be easily checkedthat dp1=dx2 frac14 0 is incompatible with dp2=dx2 frac14 0

dp1dx2

frac14 0 teth2 3x2THORN6jethy2 y1THORN

frac14 y2 thorn y16

1

3eth1 x2THORNand

dp2dx2

frac14 0 teth2 3x2THORN6jethy2 y1THORN

frac14 y2 thorn y16

thorn 2

3eth1 x2THORN

which can only be true if

1

1 x2frac14 0

Consequently there will not be an equilibrium location x2 that is notalso a corner-solution The existence of a corner solution requires thatx2 frac14 0 dp1=dx2 4 0 and dp2=dx24 0 or x2 frac14 1 dp1=dx2 5 0 anddp2=dx25 0

Substituting x2 frac14 0 into the total derivatives shows that dp1=dx2 gt 0Consequently there cannot be a corner solution in which x2 frac14 0 Doingthe same for x2 frac14 1 shows that dp1=dx2 gt 0 and dp2=dx2 gt 0 Howeversubstituting the subgame perfect prices into the conditions

p2 p1 teth1 x2THORN thorn jethy22 y21THORN2jethy2 y1THORN

4 0

and

p2 p1 thorn tx2 thorn jethy22 y21THORN2jethy2 y1THORN

lt 1

and substituting for x2 frac14 1 shows that these two conditions cannot be ful-filled for y1 y2 2 frac120 1 because yy y gt 1 Consequently x2 frac14 1 cannot be acorner solution either In this division of demand if ethy lt 0 yy 2 frac120 1THORN noNash equilibrium in pure strategies exists Also no Nash equilibrium inpure strategies exists in the division of demand if ethy 2 frac120 1 yy gt 1THORN becausethe analysis is similar to the division of demand if ethy lt 0 yy 2 frac120 1THORN

Journal of Transport Economics and Policy Volume 40 Part 1

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which the roles of operator 1 and operator 2 are switched Consequentlyboth operators cannot realise higher profits by deviating from theirequilibrium qualities and prices

Proposition 4 There is no subgame perfect Nash equilibrium in pure strate-gies in the divisions of demand if ethy lt 0 yy 2 frac120 1THORN or ethy 2 frac120 1 yy gt 1THORN

From the expression for dp1=dx2 and dp2=dx2 it can be easily checkedthat dp1=dx2 frac14 0 is incompatible with dp2=dx2 frac14 0

dp1dx2

frac14 0 teth2 3x2THORN6jethy2 y1THORN

frac14 y2 thorn y16

1

3eth1 x2THORNand

dp2dx2

frac14 0 teth2 3x2THORN6jethy2 y1THORN

frac14 y2 thorn y16

thorn 2

3eth1 x2THORN

which can only be true if

1

1 x2frac14 0

Consequently there will not be an equilibrium location x2 that is notalso a corner-solution The existence of a corner solution requires thatx2 frac14 0 dp1=dx2 4 0 and dp2=dx24 0 or x2 frac14 1 dp1=dx2 5 0 anddp2=dx25 0

Substituting x2 frac14 0 into the total derivatives shows that dp1=dx2 gt 0Consequently there cannot be a corner solution in which x2 frac14 0 Doingthe same for x2 frac14 1 shows that dp1=dx2 gt 0 and dp2=dx2 gt 0 Howeversubstituting the subgame perfect prices into the conditions

p2 p1 teth1 x2THORN thorn jethy22 y21THORN2jethy2 y1THORN

4 0

and

p2 p1 thorn tx2 thorn jethy22 y21THORN2jethy2 y1THORN

lt 1

and substituting for x2 frac14 1 shows that these two conditions cannot be ful-filled for y1 y2 2 frac120 1 because yy y gt 1 Consequently x2 frac14 1 cannot be acorner solution either In this division of demand if ethy lt 0 yy 2 frac120 1THORN noNash equilibrium in pure strategies exists Also no Nash equilibrium inpure strategies exists in the division of demand if ethy 2 frac120 1 yy gt 1THORN becausethe analysis is similar to the division of demand if ethy lt 0 yy 2 frac120 1THORN

Journal of Transport Economics and Policy Volume 40 Part 1

160