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Bargaining versus price competition in markets with quality uncertainty

Bester, H.

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Citation for published version (APA):Bester, H. (1993). Bargaining versus price competition in markets with quality uncertainty. (Reprint Series).CentER for Economic Research.

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88231993137

o~Resw.~h lilllllllllll~l~l~l~~l nlll l~llllllilll

Bargaining versus PriceCompetition in Markets with

Quality Uncertainty

byHelmut Bester

Reprinted from The AmericanEconomic Review,

Vol. 83, No. 1, March 1993

Reprint Series~ 5~,~Q~~J~ ~ no. 137

CENTER FOR ECONOMIC RESEARCH

BoardIlarry BarkemaFlelmut BesterEric van Damme, chairmanFrank van der Duvn SchoutenJeffrey lames

ManagementEric van Damme (graduate education)Arie Kapteyn (scientific director)Marie-Louise Kemperman (administration)

Scientific CouncilAnton BartenEduard BomhoffWillem BuiterJacques DrèzeTheo van de KlundertSimon Kuiperslean-Jacques LaffontMerton MillerStephen NickellPieter RuysJacques Sijben

Université Catholique de I,ouvainErasmus University RotterdamYale UniversityUniversité Catholique de LouvainTilburg UniversityGroningen UniversityUniversité des Sciences Sociales de ToulouseUniversity of ChicagoUniversity of OxfordTilburg UniversityTilburg University

Residential FellowsLans BovenbergWerner GiithJan MagnusShigeo MutoTheodore ToKarl WíimerydKarl-Erik Wiirneryd

Research CoordinatorsEric van DammeFrank van der Duyn SchoutenFlarry FluizingaArie Kapteyn

CentER, Erasmus University RotterdamUniversity of FrankfurtCentER, LSETohoku UniversityUniversity of PittsburghStockholm School of EconomicsStockholm School of Economics

Address : Warandelaan 2, P.O. Box 90153, 5000 LE Tilburg, The NetherlandsPhone : t31 13 663050Telex : 52426 kub nlTelefax : t31 13 663066E-mail : "center~a htikub5.bitnet"

ISSN 0924-7874

1993

Bargaining versus PriceCompetition in Markets with

Quality Uncertainty

byHelmut Bester

Reprinted from The AmericanEconomic Review,

Vol. 83, No. 1, March 1993

Reprint Seriesno. 137

K.U.B.BIBLIOTHEEK :TILBURG

Bargaining versus Price Competition in Marketswith Quality Uncertainty

fIr flr.l.ti)uT Besrrti~

7-his paper fixuscs trn thc cndugcr.uusdctcrmination of trading rulcs. In munymarkets, as for cxample in lhe retail husi-ness, prices are simply posted by scllcrs, andthe buyer has little direct in(luence on howmuch he has to pay. In other markets pricesarc the outcomc of hilatcral ncgotiations, sothat both thc scller and thc buyer takc anactive part in setting the price. Examplesincludc not only the bazaar of a less dcvel-oped nation, bul also the markets for usedcars, real estate, antiques, and ínputs formanufacturing firms. This papcr providcs atheoretical explanation of which pricing in-stitution is likely to emerge in a markctwhere buyers are imperfectly informedabout the quality of goods ur services. 1compare the performance characteristics ofpostcd-offer pricing with negotiated pricingand find that each arrangement has specificmerits. ~'hese determine the equilibriumpricing policy as the outcome of compctiliveinteractions between the market partici-pants.

The kcy insight of my analysis is that theprice-determination aspects of market orga-nization can also afíect yuality. Suppose thebuyer has to visit a firm to determine itschoice of product quality and that hc cxpc-riences switching costs when moving fromune seller to anothcr. The incentive to pro-vidc quality in the posted-price regimc isthat the consumer may walk away to an-other store if the quality is too low. Switch-ing COSIS may Undermine IhÍS incentive be-cause they creatc a lock-in eficct. A scllerwhu has a locked-in customer may rcducehis cost by choosing a lower quality. This

'Center (or Ecorwmic Rexearch. Tilburg Universily.P.O. 13ux Q0153, 5(xx) LE Tilburg. The Netherlands. Ithank Dilip Monkherite, Larry Samuekon, JonalhanThc~ma~. Gric van Uamme. and lw~i referees (or thcircomments

argumcnt is oftcn uscd tu adwK:tlc sclf-cnfurccd hans tin pricc advcrtising forproviders of pro(cssional scrviccs such asdocton and lawyers.' While posted-pricingpromotes er crnre price competition, it mayIcad to a dctcrioration in product quality.

ln contrast with posted pricing, bargain-ing determines the price of the good ajtrrthc buycr has arrived at a storc and learnedits qualily. Hcre lhc incen[ive lo provideyuality is gencratcd by lhc fact that thcscllcr gcts some fraction of the total sur-plus. He will seck to maximize Ihis surplusby selectíng the scxially cfficicnt quality. Asa result, thc ncgotiatcd-pricc markct ducsnot exhibit the moral-hazard problem thatcharacterizes the posted-price market.However, the locked-in consumer tinds him-sclf in a situation of partial hilateralmonopoly with the scller. This allows theseller to exploit his customer, and the har-gaining may result in a relatively high price.The different impact of switching costs onprice and quality in the posted- and thencgotiated-price markets determincs thecompetítivencss of these trading rules.2

"f-hcre is a considerable literature study-ing the formation of prices in decentralizedmarkcts where peirs of agents bargain overthc gains from trade.' 'fhis literature takes

~Yuk-Shec Chan anJ Hayne Leland (19N2) andWilliam Rogeruro (198R) ezamine thi~ argumenl.

' For a comparison o( pnsred and nego[iated pricingin a IaMtratory experiment, sec James Hong andCharles Plnlt 1198?).

~This includes work hy Peter Diamond and EricM;ukin f1Q7y1. Ariel Ruhinstein and Asher Wolinskv

( 1985), Unuglas Gale (14K6a.b). and myself (19HR). AdilTerent cunlexl ic considered in my 19ti9 paper. wbereI replace rhe price-sening stage o! the standard spalialeompetilinn modcl with a F:vgaining gamc. Furthcrreferences and a aetailed discussion of bargaining in emarkel setting are (ound in the moaograpb by MartinOsborne and Ruhinstein (I~Nq.

17R

1 Y)l.. Rr NO. I RIi.S7'Flt: li,-tRr;.41NING I'IíR.SC~.S PItICI: COM1f!'li'I'!77ON 2T)

lhc Irading rulc as exogcnously givcn; thcsellers arc prohibited from competing witheach other hy pusting prices. -I~he uptimalsclling sUategy vf a monopvlistic scllcr isstudicd hy John Riley and Richard Zcck-hauscr (19R3) and hy Drcw fudcnbcrg cl al.

l 1987). 'I~hcir analysis is cunccrncd with thcyucstion of whether a fixcd postcd priccyiclds a higher payofi for the seller than ahaggling strategy. Bcginning with thc workof William Vickrey (19(iU, the choice ofsclling mechanisms is an important topicalsv in the auction literature.' It turns outthat posting a fixed price is the optimalstrategy for a monopolistic seller of a singlegood when he faces a single potential buyer.Similarly, with many buyers, posted pricingis optimal for the monopvlist when he pro-duccs the good tmdcr constant rcturns toscalc and can freely vary thc amount olferedfor salc (see Millon Harris and Arthur F2a-viv, 1981a,b). Paul Milgrom (19R7) cmbcdsthe auction model in a noncooperative-bargaining modcl in which thc owner of thcgood always has the right tv resell thc itcmlo other traders. He finds that conductingan auction allows a weak bargainer to benc-fit from Ihe presence of stronger bargainers,sv that typically the sale will be by auctionrather than by priva[e olfer. Thc followingfeatures distinguish my model (rom this lit-cralure: there are many producers operat-ing uncler constant rcturm to scalc; thcscproducers can compc[c hy advcrtising priccs;huyers are imperlectly infonned aboutpruduc[ yuality: and buycrs facc switchingcosts and cannot negotiate with several sell-crs at the same time.

To address the problcm, 1 study a simplcmodel that allows one to derive an eyuilib-rium solution both for negotiated and postedpricing. It is presented in Section l. Sections11 and 111 investigate the equilibrium out-comc undcr both trading rules. Bascd onthis analysis, I endogenizc the determina-tion vf tracling rulcs in Scction IV, whcrc I

'Stc I'nston McAfcc and John McMillaa (1987)and Paul Milgrum t 1987) for a sun~iy.

show that Cor each parame[er constcllationthere is a unique equilibrium pricing mech-anism. Concluding remarks are contained inScction V.

1. The M11oJcl

Considcr a markct with N 1 2 identicalfirms. Each firm produces a singlc gcxid atconslant rcturns to scale. Before the markctopens, each firm decides once-and-for-allon lhe quality q e(qt„ q~) of its oulput,where qt, ~ 4~. The cost vf producing oneunil of quality q is c(q) with c(qh) ~ c(q~).In the model all consumers arc identical.~~hey do not interact slrategically with eachother. This together with thc assumption ofconslant returns to scale allows one to con-sidcr each buyer in isolation independenllyof thc total number of consumcrs. Eachconsumer purchases at most one unit of thegood. His utility from purchasing quality qat the price p is given hy q- p. Alterna-tively, hc may not purchase the good frumany of Ihe N firms and rnnsume some 'but-side good'" instcad. The price and the qual-ity uf the outside gvod are exogenously fixedso that the consumer enjvys the net bencfitr frvm buying it.

The buycr docs not directly observe lhcfirms' choice of yuality. He Icarns the qual-

ity q sold at a parlicular storc only by visit-ing Ihc storc. Thcrc is a cosl lo visiting astorc. Switching from onc of thc N scllcrsto anothcr or to consuming the outside gvodtakes one time unit. As the buycr discounls(uturc bcncfits by the discount faclor 11 ~

S c I, this creates a swilching cosL We willview S as a mcasurc of thcsc costs andinvestigate its impact on the formation ofprices in this market. This is dvnc undcr thcfullowing assumplion:

Íl) 9h-c(qn)~r'~q~-c~qe)~0.

Thus, in the full-information cyuilihriumwith pcrfect competition all firms wouldproducc quality qt,, and lhe consumcr wouldbuy thc high-yuality gcxid at lhc price p-c(qt,). Consuming thc vutsidc good wouldyicld a lowcr utility Icvel. In addition, lhe

2xn rnr: ,t,~fran~a.v I;cuNn,tllc arvtrn~ et~tac )I I9vt

surplus from producing thc luw-yuality gooclis takcn to bc too low tu competc with theuutsidc gcxtd. This implics th:u undcr im-pcrfcct informatiun lhc htrycr will ncvcr visita storc that hc suspccls to olier yualiry q,..Accordingly. 1 can con(inc thc analysis tusituatiuns whcrc thc srllcrs lind cluxningyuatity qt, to he uptimal.

It. The Ncgotiated-t'rice hlarket

In the negotiated-price market the con-sumer has the option of purchasing the out-side good or visiting one of the N stures tubargain aboui the pricc uf [he goud. Uponentering a sture, he observes the quality qactually chosen by the seller and su theprice negotiations proceed under symmelricinformation. The "disagrecmcnt puint" inthis bilatcral bargaining siluatiun represcntsthe payofís of the buyer and thc seller.respectivcly, if no sale lakes place and thcbuyer quils; it will he dcnoted :ts (d.(I). Ofcuursc, the buyer's payolf d depcnds upunhis switching cost and lhe net henefit thathe expects from hargaining with anolherscllcr or simply frum cunsuming thc outsidcgoud. Accordingly, in cquilihrium, d will bedctermined cndogenously. The seller's profittrom nat making a sale is zero. He kceps aconstant inventory of the good so that aftereach sale he incurs the cost c(q) of produc-ing one unit. Suppose the gcneralizcd Nashbargaining solution is the outcome of thebargaining.5 Then the price upon which theparties agree isR

(~) ~Plq.~)-argmaxr,[q-p-cl]`.

X[n-~(q)J'-"

`Tbe generalized Nash solution is studied by JohnHarsanyi and Reinhard Selten (197Z). An axiomatiza-tion of this solution is given by fhud Kalai (1977) andAlvin Roth U9791. Kenneth Hinmore et al. lI9R(,)derive the generalized Nash bargaining sotution as thenonccxiperative equilihrium nf an extensive game inwhich the parties alternate in making o(Ters and rnun-teroffers.

"Of courxe. an agrecment will hc reachcJ unly if lhesurplus q-r~q)-d i~ nonncgutivc Tbi. cundition isalways fulfilled in the eyuitibrium delined bclow.

with ll G a C I. This solution splits lhc sur-plus su that thc huycr reccivcs thc fractionrr. 'I"he paramcter cr may thereforc he inter-prclcd as cxpressing lhc huycr's " h:ug:tiningpuwcr"; by varying a from zero tu unity.une can ohtain any pricc that is irtdivicluallyraliunal hulh litr thc huycr and thc sdlcr.Much of my :utalysis will focus vn thc juintimpact uf thc hargaining paramclcr rr andIhc fric;tion paramctcr fi on lhc markct out-comc.

In thc event of breakdown in thc ncgutia-tions, the huyer can either switch to anolherbargaining partner or he can purchase theoutsidc guud. As the surplus q~ - c(q~ ) isless than t~, the huyer will not go tu one ofthe N stores unless he is cunvinced that hewill tind quality qh.~ In thc cyuilibrium olthc negotiatcd-price markct the buycr cx-pccls high qualily, and hc anlicipatcs lhalthc hargaining will result in sumc pricc p.Given these expectations and the delay costuf switching, his cxpcctcd ulitity frum dis-:tgrcemcnt is

(3) cl( P) -max[fit.. rs(q~,- n)1.

tn cquilibrium thc consumcr's pricc-qualilyexpectations have to be consistent with themarket outcome.

Ucfirritiurt: (~ is a rrc~olirrtcd-pricc cquilih-riton if (i) 9j, - p~ t~ and ~i ? c(yt, ): (ii)

1r - W(qt,. rl ) and cf - d( p); and (iii) j~ -..c(c;i~)- ~..ar.rri- ctqr r.

The first of these conditions ensures thatboth the sellers and the buyers are willingto participate in thc markct. If (i) fails tohold, then nune of the N sellers is activc,and the consumcr purchascs thc outsidcgood. By ( ii), the equilihrium price p isdetermined by the bargaining sulution, tak-ing inlo account that the buyer's threat puint

~As will be shown Fxluw, ch~~sing qi, is a Jominanlslr.dcEy fur each seller. This precludes thc rxrssibilily~if a mixcd equilihrium ín which vimc sctlcrs ehixisc q~,and ulhen ch~wtie q,.

I'r~l. .et n'c~. I ItF..~77 R: R.4RG:UNlNG 1'I:R.~[r.5' I'R1CI' ['lrAfl'I[777'InN 2ftl

b

II

IV

aPicuae I. Nrt(a~nnren Pe~('wc Is nN

Fo(~n uu(n~~i iN RrowNS II ,~NU IV: P(i~rnuPuu mc Is nN Gotm.~nHn~~i rv Rr(:I(~Nti 1 nNU 1!

in the price negotiation is d( ~i). Finally, liii)guarantces that each single seller finds il inhis own interest to select yuality y~,. Inequilihrium, the buyer is inditferent amungall stores so that the sellers share thc mar-kct cyually. ~1-o state thc main result of thisscction, 1 define the function

r - a~qn - c(9n)~(4) Sn(a)- (l-a)r'

Liy assumption ( I), fi~( ~) is decreasing,S~((l)- l. -cnd S,~(a)? O for all a 5 r~(qi, - c(q~,)]. In Figure I the tunction S-S~(a) reprcsents thc borderline betwcen thchvo rcgions I f 11I and tI f tV.

PROPOSITION I: There is a negnliaied-price equifibr'iunt if and only if s~ r~(a). IfS ~ S1(a), the negoriarect-price equilihrium istrnique ~rirh

n (I-a)(I-S)qntac'(qn)

l~- I-(I-a)S

PROOF:~~hc gcncraiízcd Nash bargaining solution

is defined by the necessary and suflicient

first-order condition

(5) N(d.d)-(I-cr)(q-~)fac(q)-

Accordingly,

W(q.d)-c(q) -( I -a)~q-c(q)-d]

so that by assumption (U equilibrium condi-tion (iii) is satisfied for any p satisfyingconditian (ii). By the first inequality of con-dition (i), one must have d( ji) - S(qn - p).Therefore, solving (ii) for p yields theuniyue solution stated in thc proposition."I'his solution always satisfics thc second in-eyuality in (i); the first incquality in (i) isidcntical to a(q~, - cn]~[I -(1 - a)S]? r. Bythe definition of S~, this is eyuivatent to

fi ~ S~(a).

1'he inequality S? S~(a) is satistied inregions 11 and IV of Figure L For theseparameter constellations, Ihe consumer pur-chases the high-quality good at the price p.As ~~ exceeds c(qn), the presence of marketfrictions enables the sellers to earn positiveprofits. These are higher, the lower are Sand a. lnterestingly, p approaches c(qn)both in the limit when S-~ I and in thelimit when a-~ 1. 1'he first of these proper-ties justifics viewing the perfectly competi-tivc outcomc as the limiting point of a mar-ket with negligihle switching costs.

Why docs the consumer purchase theoulsidc guod for valucs of S and a in re-gions I and III, where a ncgotiated-priceequilibrium fails to exist? The reason is thatthese parameter values violate equilibriumcondition (i). With high switching costs and

litlle bargaining power the buyer cannot geta favorahle deal once he has entered astore. Knowing this es anre keeps him fromgoing to a store and induces him to con-sume the outside good. This kind of marketfailure is well known from the standardsearch model (see e.g., Joseph Stiglitz, 1979)in which prices are unilaterally set by sell-

ers, and buycrs have to visit stores to oh-scrve priccs. lndccd, in lhc limiting situa-tion whcre a- 0 the negotiated-price

282 THIi AAIERIC.4N F.CONOAIlC REVIF.N' AIARCII 1993

markcl becomcs idcntical to the simplest 111. "fhe Pnsted-Price Marketscarch modcl with iclcntical huycrs and scll~crs. When a- 0 thc seller has all thebargaining powcr and ctfcctivcly makcs atake-it-or-leave-it ulfer lo his customers.Proposition I shows that in this case j~ - qrili.c., cach scller would charge the con-sumer's rescrvalion price). ~~his observationis thc wcll-known "monopoly pricc paradox"of Diamond (1971): cvcn with arbitrarilysmall scarch costs and a large numbcr offirms, in market eyuilibrium the price is themonopoly price. If the buyer has to pay acost for entering the market or can opt forsome outside good, this paradox predictstotal market failure." In regions 1l and IVthis unsatisfactory outcome is avoided be-cause cr is large enough to guarantee thebuyer a sutlicient share of the gains from[rade.

lmportantly, the proof of Propositíon 1reveals that the negotiated-príce market in-volves no prohlem of mor.tl hazard; that is,the incentive constrainl (iii) is never bind-ing. This perhaps surprising obscrvation hasa simple intuition: the bargaining outcomeguarantees the scller a fraction ( I- cr) ofthe hargaining surplus. As a result, he isalways better off by producing qh becausethis quality yields a higher surplus than doesq~. Chcxising quality qh is a dominant strat-egy for the seller in the negotiated-pricemarket.y This fact distinguishes this marketfrom the posled-price market, which 1 turnto in the next section, where prices are sethejore the consumer becumes aware of qual-ities.tl'

"In the Iiteraturc, the typical way to avoid theUiamund result has been to assume that snme con-sumers are well informed alxiut prices (see StevenSelop and Stigliti, 1977; ftal Varian, 19K0; Uale Stahl,19ri9).

vThis conclucion is robust against altine transfnrma-tinns of the sellcr's and buycr's utilities. The reason isthat the generalixd Nash bargaining solution satisfiesthe axiom of independence of utility rescalings.

tnThc relati~mship betwecn cr ruur and er lxisrpricing in a mrxlcl without qualilativc unccrtaíniy isexplored by Gadc U9a}t1.

In Ihe posted-price market, the scllers actas Bcrtrand compctilors by posting prices.Advcrtising price information enables thescllcr to guarantec his custumers a pricebefore they visit his store. In contrast weassume that communication of quality infor-matiun is infcasihlc. 'I~his assumption is rcl-evant in markets where yuality is cithcr tcxtcostly lo communicatc or is not veriliablc tothird parties. If a court finds it hard todetermine whether a seller actually provides"high" quality, then buyers must distrustquality advertisements because they cannotbc enforced.

The buyer obscrves the sellers' price quo-tations and compares their attractivenesswith the outside-option utility r. After en-tering a store and learning its quality he caneither make a purchase at the posted priceor switch to another seller. By assumption( I), he will not go to a store if he anticipatesfinding quality q~.'t ln the posted-priceequilibrium the buyer expects qh in eachstore, and so all sellers post the same pricep'. As all stores appear identical to thebuyer, he visits one of them at random. Toconfirm his expectations, competition mustinduce the suppliers to offer quality qh.12 Asq is not directly observable, each single sellerhas an incentive to select qh at the postedprice n` only if the buyer would quit afterobserving quality q~. Given his expcctationsabout qualities at other stores, the buyerwill ccrtainly do so if q~ - p' ~ d( p~ ). Infact, we will assume that the buyer refusesto purchase low quality unless he is notactually worse ofTby departing.t' This means

'~Of course. the buyer presumes thal no scller of-fers the gond al a price below ccnt.

til assume that each seller selects yh when he isindilfcrent belween q~, and q~.

t'This tie-breaking nde is necessary to avoid theopen-set problem diat would occur if there were nolowest pricc that signals high yuality. Indecd, equilib-

rium cunditiun (iiil in the next (txisteJ-price equilib-

rium) definitiun is impossiblc to sertisfy if condition (ii)

is repL~ced hy p' ] irt ps )

l'Ol.. 8.7 N'O. 1 (iliSTfR: IIARG~UNINC~ tTR.SU.S PRfCL COMPf:TITION 2R3

that each single seller will choose quality q~,if and only if the equilibrium price p' satis-tics the restriction p' ? rr( p' ), where

(6) ~(p')-qr-d(p`).

Whilc p~` ?~rr(Ir`) cnsures thc provisiunof high quality, a key factor in the determi-nation of p` is that priccs arc a signal oFquality. Should sonic scllcr dcvíatc from p"by posting p G p`, then the buyers will usethe obscrved price to draw inferences aboutthis scllcr's quality. If they interprct p as asignal of quality qr, thcy will not be a[-tracted even though p ~ p'. The oppositehappens if p is regarded as a signal ofquality q,,. As in other signaling games. suchan indeterminacy of out-of-eyuilibrium be-liefs may lead to a multiplicity of equilib-rium prices p~`. To avoid this prohlcm, 1 willrestrict the buycrs' bcliefs tu satisfy the "in-tuitivc criterion" proposcd by ln-Koo Choand Uavid Krcps ( 19R7). Supposc somesellcr wants to undercut his competitors bysome price p slightly bclow p' and, at thesame time, wishes to convince the consumer[hat he ofters high quality. Then one mayreasonably assume that this selVer succeedsif he would not gain by posting p andsclecting quality qr, even if his otfer attractsthe entire market. This prerequisite is ful-lillcd if low quality dcters the customer frompaying p for thc good, that is, if p? rr( p' ).Summing up. in the posted-price equilib-rium p~ only prices p? rr( P~` ) arc consid-crcd as a signal of high quali[y.

Ucfrrritiorl: p` is a po.ucd-price cquilibriumif (i) yh - p~ ~ r~ and p` ? c(qh); ( ii) p` ?rr( p~` ) ; and ( iii) there is no p?~r( p~`) suchthat p c p~ and p- c(qh) ~[ p' -

c(qh)I~N.

The first of these conditions is the sameas in the definition of the negotiated-priceequilihrium. Requirement ( ii) represents thesellcrs' inccntive-compatihility constraint toprovide high quality. Condition ( iii) pre-cludes any of the sellers gaining by unilater-ally posting sume price p below ps thatsignals high quality. Here we assume that ifall sellers post the same price p`, each

sture has the same chance of atlracting con-sumers so that its market share equals l ~N.The equilibrium outcome depends on thelevel of switching costs. Let

(7) Su-l-(qn-9e)rl'-

'l~hcn, SI, c I bccausc qh ~ qr.

PROPOSITION 2: 7llere is a posted-priceequilihriuni if aud ouly if S? Se. IJ S ~ Sn,

the postednrice equilibrilun is latique with

p' - ma~c[c(qh),(qr - Sqn)~(1- S)].

PROOF:By the first inequality in equilibrium con-

dition (i), one has -rr( p`) - 9r - S(qn - p~ )~As p~` ? c(qh) and N? 2, condition (iii) is

satistied if and only if p` minimizes p sub-

jcct to p Z c(qh) and p z~r( p` )- For S?

[4t - c(q~,)]~[qh - c(qh)j, only the first con-

straint is binding and so one has p' - c(qh).Otherwise, only the second constraint is

binding so that p~ - rr( p` ), that is, p~` -(qr - Sqh)~( l- S). lf p` - c(qn), the firslinequality in (i) is always satisfied. For p~ ~c(yh) this inequality becomes qh - p' -(qh - qr)~(1 - S)? u which, by definition of

fiu, is identical to S 2 Se.

1'he posted-price equilibrium may fail to

exist for low values of S if Sri 1 0, that is, if

(8)qh-qlGU.

This condition implies that the consumerprefers buying the outside good to purchas-

ing quality qh at a price p~ qr. It limits thcuse of prices as signals of quality in theposted-price market. Even though the buyer

may reasonably be convinced that prices

above qr indicate high quality, because hewould always quit a low-quality store with

p~ qr, he cannot be attracted by such a

price offer. More generally, the lock-in

e(fect becomes more serious when the dif-

ference between qh and qr is decreased.This is so because the consumer's utility

gain from quitting a low-quality seller and

ZRJ ritt:,t,tll:Itl['-1N li('ONUM1t!(' ItFI'llai' M1LIR(71 l~rl?

going to a high-qualily seller becomessmaller.t~

Regions 1 and 11 of Figurc I dcxribc thcarea where a posted-price equilibrium cx-ists. For values of S hclow fit; thc lock-inelíect hecomes too strong and Icacts tu :tdctcrioration of prucluct quality. As a con-sequencc, thc inslitutiun uf puslcd-olirrpricing prccludcs thc scllcrs from hcing ac-live in the markcl and resuh~ in consun?p-tion of the outside g(xrd in rcgions llland IV.

For S close enough to unity, thc postedprice p~ equals c(qh). For lower values ofS, however, one observes that price exceedsmarginal costs. ~~he inerease in the priccabove the cost of producing high qualitygives the firms an incentive not to otíer lowquality. This is a familiar fcaturc of scarchmodcls in which priccs signal procluct qual-ity (see Ashcr Wulinsky, I9R3; Rogcrson,1988). A similar mechanism appcars :llso inexpcricncc gtxrd tnarkcts with rcpcal ptn-chases, in which quality is Icarned after thcgoud is bought. In thc Bcnjamin Klein andKcith B. L,eHler (19HU model, consumerspay a quality premium which prcvcnts thesellcr from culting quality. Michael Riordan(I9R6) assumes that firms make price andquality decisions which cannot be alteredover the relevant period. A high price thensignals a high quality since consumers wouldrefuse a .cecond purchase of low quality at ahigh price. In my model, the consumerlearns about quality before buying the goodand so he necer purchases luw quality at ahigh price.

The negotiated-price market is clcarlymore efiicient than the posted-price regimein region IV of Figure I. Here the N firmsremain inactive in the posted-price market,whereas negotiated pricing results in pro-duction of the high-quality good with posi-tive payofís both for the sellers and thcbuyers. In contrast, the posted-price market

~aThe same argument shows lhat the eyuilihrium

quality musl unravel lo q; whcn yu:dily is a arntinuoucehoice variable within some intcrval Iq~.~h,L T,t aw,idlotal market taiture in this situalion, unc has lo asumelhat some consumers are well infonned ahout quality.

appears to be supcrior in rcgiun I, whcrcthc huycr rcfrains from enlcring ncgotia-tiuns hccausc his hargaining puwer is tooluw. "I hc kcy insight from Nropusitions Iand 2 is tha[ thc Iwo categorics uf tradinginslitutions involve a tradc-u(f. I'ricc har-gaining avoids thc mural-hazard prohlcm inthc lirms' sclcction uf qualitics; yct, as lhcpricc is dclcrmincd er pn.~r aflcr thc huycrh:lv choscn lhc scllcr, il may nut guaranlcclhc huycr a sullicicnt fraclion of thc surplustu make bargaining attractivic ex ante. Esanre pricing, as in the posted-pricc market,docs not suH-er from this drawback; but,whcn the price is fixed e.t- arrte, the lock-inctícct may havc a ncgative impact on thcscllcr's incentivc lo producc high quality.The relative imporlance of thcse consiclera-tions dcpends on the parameters fi and n.l'hc fulluwing scction will dcmunstralc thatthc trade-otí bctwccn thc twu pricing insti-tutions can cxplain which will cmcrgc as ancctuilibrium lrading rttlc in a givcn cnvirun-mcnt.

IV. Thc Stability or Competilion

This section is dcvoled to analyzing whichpricing mechanism is stable against compe-tition. A parlicular trading rule can survivconly if no tradcr can gain by deviating andusing anothcr Irading rulc. Applying lhisidea to the negotiated-price markcl mcansthat no scllcr should hc ablc to prolit fromposting a price e.r orue in a situation whcrcall thc othcr scllcrs rcly on er pu.ct pricing.l'hal is. it nwst be impussiblc to attractprofitably the demand of all cunsumen hyundcrcutting the negotiated-price equilib-rium p and posting p G j~. The rcason whysuch an atlempt may fail is that prices he-luw j~ may be viewed as an indication of lowquality. Using thc same restrictiuns on hc-liefs as in Section [ll. I will assume that lhcposted otícr p convinces the consumer ofquality yh only if p ~~rr( ji), whcrc ~rr(. ) isdefined by (6).

DeJinitior?: Thc negoliatcd-price equilib-rium p is srahle against pricc compctition ifthcre is no p G p such that (i) p? rr( ji) and(ii) p-c(qt,)~[p-c(qh)1rN.

VC)L. R3 A'O. I iiE.ti77:R: R~1Rl:AlNING l~7iRSl1,S 1'RI('F ('OAIPFTI"1'ION

lio)r if and n)rh~ ij a z a` and S 5 Sc-(a).

Flci~ar. 2. Nrcc,rlnir.u Peu.IN~~ Is Si'nin r iN

Rrc.u,N. II nun IV; Pusrru 1'luc.wu ls S~rnu,.rIN RI.,'~I(,N~ I nNll Ilx

zR5

PROOF:As j) 7 c(qr,) and N? 2, thcrc is ahvays a

p G~) satisfying (ii) in the definition of sta-bility. As qr, -~) ? t~, condition (i) is idcnti-cal lu p~ r!, - ~S(rrr, - n). '1'hcrcli)rc, j) is

stable if and only if therc is no p G jr satis-fying (i). 'I'his means onc must havc j~ 5qr - S(q~, - j)). Using j) from Proposilion 1,this condition is eyuivalent to

a

In uthcr words, the institution of ncgoti-

ated pricing cannot be eroded by price-posting if any otfer below j) is either vicwedas a low-quali[y signal or fails to increase

the seller's prolit even when he scrves thcwhole market. To determinc the range ofparametcr values for which this is true, 1

define thc function

(~~)

a(9i,-c~(9i,))-(9i,-9r)

S~(a)- a(qn-r(rln))-(I -a)(qi,-9i)

Note that for

a` -(4)~-9r')I~d)1-9i }9n-c(rla)-t'~

onc has

S:1(a')-Srr-Sc(a~).

Moreover, S~da) ~ t) fur all a e(a', ll. In

Figure 2 the function S- S~.(a) is depictedfur a e(a~, I); it divides the former region

ll of Figure I into the regions 1l~ and II.

PROPOSITION 3: Tlrr neguliul~~~l-pricrequilibrirun f~ is s,r,nh r,b~)i,r.~r ~)i~~ rr,),rl)e,i-

(10) S~a(qh-c(9n)~-(I-a)(Qn-qt)~

~ a(Nn - c(9i,)Í-(9r, - 9r).

As S ~ I, this inequality cannot hold if thcIcft-hand side is negative. Accordingly, bythc dcfinition of Sc-(a), ( 1O) holds if andonly if a )(Rn - 9r)r(r!n - c(qi,)} qh - 9~ )- ir and S 5 Sr-(a). Note thatSr.(a) is strictly incrcasing for a 1 á andthat Ss(a`)- Sc-(cr~). Accordingly, byProposition 1 there is no negotiated-priceequilibrium p for a e ( á, a~` ) and fi ~ Sc-(a)."1'his means that condition ( IO) applics ifand only if a? a` and fi 5 fic.(a).

Pmposition 3 statcs that ncgotiated pric-ing cannot bc sustained as a Nash cquilib-rium in thc firms' choicc of pricing policicsfor paramctcr cunstcllations in rcgions Iand II' of [~igurc 2. Ncgotiatcd pricing con-stitutes a stable equilibrium only in regions

II and 1V. At first sight it may appcarparadoxical that for S G Sc(1) the scllcrswill rely on price bargaining when thebuycr's bargaining power is rathcr high. Thisis so, however, because competition forcesscllers to adopt a trading rulc that is advan-tageous for the buyer.

Interestingly, notice that a stable negoti-ated price market necessitatcs a certainamount of markct frictions. As Srdl)GI,hargaining is not a stablc pricing institutionwhen S is cluse to unily. Negotialed pricingis unlikely to survive in a highly competitive,almost frictionlcss cnvironmcnt. ' I'he cmpir-ical implicntion is that hargaining tcncls tobe replaced by posted pricing when im-

286 THE AMLRICAN f.CONOhfIC RLl'IFW' hfARCH l99i

provements in the communication andtransportation technology reduce the buyer'sscarch cost. Swilching costs in combinalionwith impcrfect quality information prrnidc a

role for negotiated pricing in regions II andIV. l'his may explain wliy thcre is relativelylíttle haggling in markets whcre the cun-sumer is well informed about product qual-ity as, for example, in thc market for nlass-produced brand goods. Also, bargaining isobserved less frequently in the market fornew automobiles than in the used-car mar-ket, where quality uncertainty is more im-portant. Other examples for negotiatedpricing are the markets for antiques andreal estate, where the buyer has to inspectquality before making a purchase.

To complete the analysis, I now investi-gate the stability of posted pricing. 1 assumethat posting p` legally commits the selleronly in the sense that he cannot ask hiscustomers to pay more than p`. However,this does not constrain the parties not lorevise jointly the terms of the transaction. Ifin the course of bargaining they hoth reachan agreement, then this replaces the postedprice. Accordingly, [he buyer accepts lheseller's posted offer p' only if he does notsee a chance to pay less after bargaining.

Defenition: The posted-price equilibrium p'is stable against hargaining if, given d-d(p` ), it is the case that cp( qn, d)? p".

Given that the buyer cannot induce a pricereduction by bargaining, he has to pay p'after switching to another store. Therefore,his threat point in a stable posted-priceequilibrium is d(p' ), as defined by (3).

PROPOSITION 4: The posred-price equilib-rium p' is stable against bargaining ij anda~ly if either a 5 a' or a~ a` artd S zSc(a ).

PROOF:Using ( 5), p' is stable if and only if

p~ 5(I - ax9n - d(P`)) f ac(9n). Asd(p' )- S(qn - p' ), this is equivalen[ to

(ll) p'S[(l-a)(1-S)qn

-Fac(9n)[,[1-(I-a)S].

By Proposition 2 this condition always holdsif ó?[q~ - c(qn))r[qn - c(qn)] becausethen p~-c(qn). For Se(5~;,[qi -c(qn)]~[qn - c(qn))), onc has p` -(qt - Sqn)~( I- S), so lhat ( 1 I) is identical tu

(l2) S[a(Cln-c(qn))-(I-a)(9n-4~)~

~ a(qn - c(~7n))-~~In - q~).

As 0 G S c 1, (12) always holds if the left-hand side is negative, that is, if

a 5[qn - 4~],[qn -c(9n) t qn -9r~ -á.

For a 1 á, (12) is equivalent to S ~ Sc(a).By Proposition 2, p' exists if and only ifS~ Sy. As Su ~ Sc(a) for a E(ir,a'), anypY is stable if a 5 a~. For a E[a', 1), onehas S„ 5 Sc.(a) c [q~ - c(qn)]r[qn - c(qn)),so that over this range (I I) holds if and onlyif S ? Sc.(a).

Propositions 3 and 4 demonstrate that,whenever the N sellers are active in themarket, a unique stable pricing institutionemerges. As the stahility crilerion elimi-nates posted pricing in region II of Figure 2,our model predicts that Bertrand competi-tion will prevail in regions I and II~ and

negotiated pricing will prevail in regions IIand IV. Using Propositions 1 and 2, it iseasily established that p' ~ p in region II'whereas p c p' in region IÍ. The endoge-nous determination of trading rules thusmaximizes the consumer's equilihrium util-ity. ]n region ll' the sellers are trapped in aprisoner's dilemma type of situatíon. Theyall end up with lower profits because thenegotiated price p makes undercuttingprofitable. In contrast, in region Il the sig-naling effect associated with posted pricingresults in a price level p' that makes bar-gaining more efticient for coping with themoral-hazard problem.

V. Conclusion

[ have explored how difTerent pricingmechanisms affect the determination ofquality and price in a markct with qualityuncertainty and switching costs. In sum-

I r)t.. .Cr n(t t rrF.c77-tt: H.urc,tf.vthc: I F.rr.cU.1I'RIr'li fY)M1!1'h77"flr)N ?w~

m;fry, pustcd pricing imv,lvcs nwral hazard,whcrcas ncgc~tiatcd pricing is nut vcry cc,m-pctitivc. 1 havc shown that in nty nunlcl thislraclc-ulf hclwccn Ihc Iwu lracling inslitu-

ticros uniyucly dctcrmincs thc cquilihriumpricing pl,liry. ~('hc cyuilihrium traclingmcchanism has thc intcresling propcrty tII:Itit cnsures thc cc,nsumcr thc highcsl pussihlculilily Icvcl.

Mv muclcl sU'csses lhc rulc I,f qualityunccrlainly for the dctcrmination ulpricing rulcs. Of coursc, this Icavcs out a

numhcr of other considcratiuns that may bcimpl,rtant. For inslancc, I h:IVC :fssumcdthat bargaining proceeds undcr symmctricinfurmation su that ncgotiations arc cosl-

less. Asvmmctric-infurmatian bargainingmodcls can gcncratc c:osts in thc lorm ofdclay in :tgrecment." This may favor postedpricing. In gcncral. howcvcr, it is not clear apriuri which is thc most c(licicnl pricinginslitution whcn infurmation and inccntivcpruhlcros arc invc,lvccl.

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Reprint Series, CentER, Tilburg University, The Netherlands:

No. 1 G. Marini and F. van der Ploeg, Monetary, and fiscal policy in an optimising modelwith capital accumulation and finite lives, 71te Economic Journal, vol. 98, no. 392,1988, PP. 772 - 786.

No. 2 F. van der Ploeg, International policy coordination in interdependent monetaryeconomies, lournal of lnternational Economics, vol. 25, 1988, pp. 1- 23.

No. 3 A.P. Barten, The history of Dutch macroeconomic modelling (1936-1986), in W.Driehuis, M.M.G. Fase and H. den Hartog (eds.), Challenges for MacroecortomicModelling, Contributions to Economic Analysis 178, Amstetdam: North-Hollaod,1988, PP. 39 - 88.

. No. 4 F. van der Ploeg, Disposable íncome, unemployment, inflation and state spending ina dynamic political-economic model, Public Choice, vol. 60, 1989, pp. 2l1 - 239.

No. 5 Th. ten Raa and F. van der Ploeg, A statistical approach to the problem of negativesin input-output analysis, Econontic Modelling, vol. 6, no. 1, 1989, pp. 2- 19.

No. 6 E. van Damme, Renegotiation-proof equilibria in repeated prisoners' dilemma,Journal of Economic Theory, vol. 47, no. 1, 1989, pp. 206 - 217.

No. 7 C. Mulder and F. van der Ploeg, Trade unions, investment and employment in asmall open economy: a Dutch perspective, inl. Muysken and C. de Neubourg (eds.),Unentployment in Europe, London: The Macmillan Press Ltd, 1989, pp. 200 - 229.

No. 8 Th. van de Klundert and F. van der Ploeg, Wage rigidity and capital mobility in anoptimizing model of a small open economy, De Economist, vol. l37, nr. 1, 1989, pp.47 - 75.

No. 9 G. Dhaene and A.P. Barten, When it all began: the 1936 Tinbergen model revisited,Economic Modelling, vol. 6, no. 2, 1989, pp. 203 - 219.

No. 10 F. van der Ploeg and A.J. de Zeeuw, Conflict over arms accumulation in market andcommand economies, in F. van der Ploeg and A.J. de Zeeuw (eds.), Dynamic PolicyGames in Econornics, Contributions to Economic Analysis 181, Amster- dam:Elsevier Science Publishers B.V. (North-Holland), 1989, pp. 91 - 119.

No. il 1. Driffill, Macroeconomic policy games with incomplete information: someeztensions, in F. van der Ploeg and A.J. de Zeeuw (eds.), Dynamic Policy Games inEconomics, Contributions to Economic Analysis 181, Amsterdam: Elsevier SciencePublishers B.V. (North-Holland), 1989, pp. 289 - 322.

No. 12 F. van der Plceg, Towards monetary integration in Europe, in P. De Grauwe et al.,De Europese Monetaire lntegrarie.~ vier visies, Wetenschappelijke Raad voor hetRegeringsbeleid V 66, 's-Gravenhage: SDU uitgeverij, 1989, pp. 8l - 106.

No. !3 R.J.M. Alessie and A. Kapteyn, Consumption, savings and demography, in A.

Wenig, K. F. Zimmermann (eds.), Demographic Change and Economic Developtnent,BerlinlHeidelberg: Springer-Verlag, 1989, pp. 272 - 305.

No. 14 A. Hoque, J. R. Magnus and B. Pesaran, The exact multi-period mean-square forecast

error for the first-order autoregressive model, Journalof Econometrics, vol. 39, no.

3, 1988, pp. 327 - 346.

No. t5 R. Alessie, A. Kapteyn and B. Melenberg, The effects of liquidity constraints on

consumption: estimation from household panel data, European Economic Review, vol.

33, no. 213, 1989, pp. 547 - 555.

No. 16 A. Holly and J.R. Magnus, A note on instrumental variables and trtaximum likeli-

hood estimation procedures, Annales d'Économie et de Statisrique, no. 10,April-June, 1988, pp. 121 - 138.

No. 17 P. ten Hacken, A. Kapteyn and I. Woittiez, Unemployment benefits and the labor

tnarket, a microlmacro approach, in B.A. Gustafsson and N. Anders Klevmarken

(eds.), The Polirica[Economy ofSocial Security, Contributions to Economic Analysis

179, Amsterdam: Elsevier Science Publishers B.V. (North-Holland), 1989, pp. 143

- 164.

No. 18 T. Wansbeek and A. Kapteyn, Estimation of the error-components model with

incomplete panels, Journal af Econometrics, vol. 41, no. 3, 1989, pp. 341 - 361.

No. 19 A. Kapteyn, P. Kooreman and R. Willemse, Some methodological issues in the

implementation of subjective poverty deftnitions, The Journalof Human Resources,

vol. 23, no. 2, 1988, pp. 222 - 242.

No. 20 Th. van de Klundert and F. van der Ploeg, Fiscal policy and finíte lives in

interdependent economies with real and nominal wage rigidity, Oxford Econornic

Papers,vol. 41, no. 3, 1989, pp. 459 - 489.

No. 21 J.R. Magnus and B. Pesaran, The exact multi-period mean-square forecast error forthe first-order autoregressive model with an intercept, Journalof Econometrics, vol.42, no. 2, 1989, pp. 157 - 179.

No. 22 F. van der Plceg, Two essays on political economy: (í) The political economy of

overvaluation, Tht Economic lournal, vol. 99, tto. 397, 1989, pp. 850 - 855; (ii)

Election outcomes and the stockmarket, EuropeanJoutna! ofPolitical Economy, vol.

5, no. 1, 1989, pp. 21 - 30.

No.23 I.R. Magnus and A.D. Woodlartd, On the maximum likelihood estimation of

multivariate regression models containing serially correlated error components,

Jn[ernationalEconomic Review, vol. 29, no. 4, 1988, pp. 707 - 725.

No. 24 A.J.J. Talman and Y. Yamamoto, A simplicial algorithm for stationary pointproblems on polytopes, Mathematies of Operations Research, vol. 14, no. 3, 1989,pp. 383 - 399.

No. 25 E. van Damme, Stable equilibria and forward induction, Journalof Economic 7lteory,

vol. 48, no. 2, 1989, pp. 476 - 496.

No. 26 A. P. Barten and L.1. Bettendorf, Price formation of fish: An application of an inversedemand system, European Economic Review, vol. 33, no. 8, 1989, pp. 1509 - 1525.

No. 27 G. Noldeke and E. van Damme, Signalling in a dynamic labour market, Review ojEconomic Studies, vol. 57 (1), tro. 189, 1990, pp. l- 23.

No. 28 P. Kop lansen and Th. ten Raa, The choice of model in the construction ofinput-output coefficients matrices, Irtternationa! Economic Review, vol. 31, no. l,

1990, PP. 213 - 227.

No. 29 F. van der Ploeg and A.l. de Zeeuw, Perfect equilibrium in a model of competitiveatms aeeumulation, Internatiotta! Economie Review, vol. 3l, no. l, 1990, pp. 131 -146.

No. 30 J.R. Magnus and A.D. Woodland, Separability and aggregation, Economica, vol. 57,' no. 226, 1990, pp. 239 - 247.

No. 31 F. van der Plceg, International interdependence and policy coordination in economieswith real and nominal wage rigidity, Greek Economic Review, vol. I0, no. 1, lune1988, pp. 1 - 48.

No. 32 E. van Damme, Signaling and forward induction in a market entry context.Operations Researdt Proceedings 1989, Berlin-Heidelberg: Springer-Verlag, 1990,pp. 45 - 59.

No. 33 A.P. Banen, Toward a levels version of the Rotterdam and related demand systems,Cotttributions to Operations Research and Economics, Cambridge: MIT Press, 1989,pp. 441 - 465.

No. 34 F. van der Ploeg, International coordination of monetary policies under alternativeexchange-rate regimes, in F. van der Ploeg (ed.), Advanced Lectures irt QuantitativeEcorton:ics, London-Orlando: Academic Press Ltd., 1990, pp. 91 - 121.

No. 35 Th. van de Klundert, On socioeconomic causes of 'wai[ unemployment', EuropeanEconomic Review, vol. 34, no. 5, 1990, pp. 1011 - 1022.

No. 36 R.J.M. Alessie, A. Kapteyn, J.B. van Lochem and T.J. Wansbeek, Individual effectsin utility consistent models of demand, in J. Hartog, G. Ridder and J. Theeuwes(eds.), Panel Data and labor Market S[udies, Amsterdam: Elsevier SciencePublishers B.V. (North-Holland), 1990, pp. 253 - 278.

No. 37 F. van der Ploeg, Capital accumulation, inflation and long-run contlict ininternationat objectives, Ozford Econotnic Papers, vol. 42, no. 3, 1990, pp. 501 -

525.

No. 38 Th. Nijman and F. Palm, Parameter identification in ARMA Processes in thepresence of regular but incomplete sampling, Journa! of Tme Series Analysis, vot.11, no. 3, 1990, pp. 239 - 248.

No. 39 Th. van de Klundert, Wage differentials and employment in a two-sector model with

a dual labour market, Metroeconomica, vol. 40, no. 3, 1989, pp. 235 - 256.

No.40 Th. Nijman and M.F.J. Steel, Exclusion restrictions in instrumental variablesequations, Econometric Reviews, vol. 9, no. 1, 1990, pp. 37 - 55.

No. 41 A. van Soest, I. Woittiez and A. Kapteyq, Labor supply, income tazes, and hoursrestrictions in the Netherlands, Journalof Human Resources, vol. 25, no. 3, 1990,pp. 517 - 558.

No. 42 Th.C.M.I. van de Klundert and A.B.T.M. van Schaik, Unemployment persistenceand loss of productive capacity: a Keynesian approach, Journa!ofMacro- economics,vol. 12, no. 3, 1990, pp. 363 - 380.

No. 43 Th. Nijman and M. Verbeek, Estimation of time-dependent parameters in linearmodels using cross-sections, panels, or both, Journal of Econometrics, vol. 46, no.3, 1990, pp. 333 - 346.

' No. 44 E. van Datnme, R. Selten and E. Winter, Alternating bid bargaining with a smallestmoney unit, Cames and Econontic Behavior, vol. 2, no. 2, 1990, pp. 188 - 201.

No. 45 C. Dang, The D,-triangulation of R" for simplicial algorithrtu for computing solutionsof nonlinear equations, Marhematics ojOperations Research, vol. 16, no. l, 1991,pp. 148 - 161.

No. 46 Th. Nijman and F. Palm, Predictive accuracy gain from disaggregate sampling inAR1MA models, JournalojBusiness 6c Economic Starisrics, vol. 8, no. 4, 1990, pp.405 - 415.

No. 47 J.R. Magnus, On certain moments relating to ratios of quadratic fotmc in normalvariables: further results, Sankhya: The Indian Journal af Statistics, vol. 52, seriesB, Part. 1, 1990, pp. 1- 13.

No. 48 M.F.1. Steel, A Bayesian analysis of simultaneous equation models by combiningrecursive analytical and numerical approaches, Journalof Econometrics, vol. 48, no.1l2, 1991, pp. 83 - 117.

No. 49 F. van der Ploeg and C. Withagen, Pollution control and the ratnsey problem,Environmental and Resource Economics, vol. 1, no. 2, 1991, pp. 215 - 236.

No. 50 F. van der Plceg, Money and capital in interdependent economies with overlappinggenerations, Economica, vol. 58, no. 230, 1991, pp. 233 - 256.

No. 51 A. Kapteyn and A. de Zeeuw, Changing incentives for economic research in theNetherlands, European Economic Review, vol. 35, no. 2l3, 1991, pp. 603 - 611.

No. 52 C.G. de Vries, On the relation between GARCH and stable processes, Journal ofEconometrics, vol. 48, no. 3, 1991, pp. 313 - 324.

No. 53 R. Alessie and A. Kapteyn, Habit formation, interdependent preferences anddemographic effects in the almost ideal demand system, The Economic Journal, vol.101, no. 406, 1991, pp. 404 - 419.

No. 54 W. van Grcenendaal and A. de Zeeuw, Control, coordination and conflict oninternational commodity markets, Economic Modelling, vol. 8, no. 1, 1991, pp. 90- 101.

No. 55 F. van der Ploeg and A.J. Markink, Dynamic policy in linear models with rationalexpectations of future events: A computer package, Computer Science in Economicsartd Management, vol. 4, no. 3, 1991, pp. l75 - 199.

No. 56 H.A. Keuzenkamp and F. van der Plceg, Savings, investment, government finance,and the current account: The Dutch experience, in G. Alogoskoufis, L. Papademosand R. Portes (eds.), External Constraints on Macroeconomic Policy: The EuropeanExperience, Cambridge: Cambridge University Press, 1991, pp. 2l9 - 263.

No. 57 Th. Nijman, M. Verbeek and A. van Soest, The efficiency of rotating-panel designsin an analysis-of-variance model, Journal of Econometrics, vol. 49, no. 3, 1991, pp.373 - 399.

No. 58 M.F.J. Steel and J.-F. Richard, Bayesian multivariate exogeneity analysis - anapplication to a UK money demand equation, ]ournal of Econometrics, vol. 49, no.1~2, 199 t, pp. 239 - 274.

No. 59 Th. Nijman and F. Palm, Generalized least squares estimation of linear modelscontaining rational future cxpectations, International Economic Review, vol. 32, no.2, 1991, pp. 383 - 389.

No. 60 E. van Datrtme, Equilibrium selection in 2 x 2 games, Revista Espanola deEconomia, vol. 8, no. 1, 1991, pp. 37 - 52.

No. 61 E. Bennett and E. van Damme, Demand cotnmitment bargaining: the case of apexgames, in R. Selten (ed.), Game Equilibrium Models lIt - Strategic Bargaining,Berlin: Springer-Verlag, 1991, pp. 118 - 140.

No. 62 W. Guth and E. van Damme, Gorby games - a game theoretic analysis ofdisarmament campaigns and the defense efficiency - hypothesis -, in R. Avenhaus,H. Karkar and M. Rudnianski (eds.), Defense Decision Making - Analytical Supportand Crísis Management, Berlin: Springer-Verlag, 1991, pp. 215 - 240.

No. 63 A. Roell, Dual-capacity trading and the quality of the market, Journalof l:tnancialIntennediation, vol. 1, no. 2, 1990, pp. LOS - 124.

No. 64 Y. Dai, G. van der Laan, A.J.J. Talman and Y. Yamamoto, A simplicial algorithmfor the nonlinear stationary point problem on an unbounded polyhedron, Siam Journalof Optirnization, vol. 1, no. 2, 1991, pp. i5l - 165.

No.65 M. McAleer and C.R. McKenzie, Keynesian and new classical models ofunemployment revisited, The Economic Journal, vol. LO1, no. 406, 1991, pp. 359

' - 381.

No. 66 A.1.J. Talman, General equilibrium programming, Nieuw Archief voor Wiskunde, vol.

8, no. 3, 1990, pp. 387 - 397.

No. 67 J.R. Magnus and B. Pesaran, The biaz of forecasts from a first-order autoregression,Econometrie 7iteory, vol. 7, no. 2, 1991, pp. 222 - 235.

No. 68 F. van der Ploeg, Macroeconomic policy coordination issues during the various

phases of economíc and monetary integration in Europe, European Economy - TheEconomiu of EMU, Commission of the European Communities, special edition no.

l, 1991, pp. l36 - 164. ,

No. 69 H. Keuunkamp, A precursor to Muth: Tinbergen's 1932 model of rational

expectations, l)te Economic Journal, vol. IOI, no. 408, 1991, pp. 1245 - 1253.

No. 70 L. Zou, The target-incentive system vs. the price-incentive system under adverse

selection and the ratchet effec[, Journal of Public Economics, vol. 46, no. 1, 1991,

PP- 51 - 89.

No. 7I E. Bomhoff, Between price refonn and privatization: Eastem Europe in transition,

Finanzmarkt und Portfolio Management, vol. 5, no. 3, 199I, pp. 241 - 251.

' No. 72 E. Bomhoff, Stability of velocity in the major industrial counlries: a Kalman filterapproach, International Monetary Fund Staff Papers, vol. 38, no. 3, 1991, pp. 626

- 642.

No. 73 E. Bomhoff, Curcency convertibility: when and how? A contribution to the Bulgarian

debate, Kredit uttd Kapital, vol. 24, no. 3, 1991, pp. 412 - 431.

No. 74 H. Keuunkamp and F. van der Plceg, Perceived constraints for Dutch unemploymentpolicy, in C. de Neubourg (ed.), The Art of Full Employment - Unemployment Policy

in Open Economies, Contributions to Economic Analysis 203, Amsterdam: Elsevier

Science Publishers B.V. (North-Holland), 1991, pp. 7- 37.

No. 75 H. Peters and E. van Damme, Characterizing the Nash and Raiffa bargaining

solutions by disagreement point axions, Mathematics of t7perations Research, vol. 16,

no. 3, 1991, pp. 447 - 461.

No. 76 P.J. Deschamps, On the estimated variances of regression coefficients in misspecified

error components models, Econometric 7ieeory, vol. 7, no. 3, 1991, pp. 369 - 384.

No. 77 A. de Zeeuw, Note on 'Nash and Stackelberg solutions in a differential game model

of capitalism', Journal of Economic Dynamics and Control, vol. 16, no. I, 1992, pp.

139 - 145.

No. 78 ].R. Magnus, On the fundamental bordered matrix of linear estimation, in F. van der

Plceg (ed.), Advanced Lecrures in Quanritarive Economics, London-Orlando:Academic Press Ltd., 1990, pp. 583 - 604.

No. 79 F. van der Plceg and A. de Zeeuw, A differential game of intemational pollution

control, Systems and Conrrol Letters, vol. 17, no. 6, 199t, pp. 409 - 414.

No. 80 Th. Nijman and M. Verbeek, The optimal choice of controls and pre-ezperimen- tal

observations, Journal of Econometrics, vol. Sl, no. 112, 1992, pp. 183 - 189.

No. 81 M. Verbeek and Th. Nijtnan, Can whort data be treated as genuine panel data?,

Empirical Economics, vol. 17, no. 1, 1992, pp. 9- 23.

No. 82 E. van Damme and W. Giith, Equilibrium selection in the Spence signaling game, inR. Selten (ed.), Game Equilibréum Models 11- Metltods, Morals, and Markets, Berlin:Springer-Verlag, 1991, pp. 263 - 288.

No. 83 R.P. Gilles and P.H.M. Ruys, Charactérization of economic agents in arbitrarycommunication structures, Nieuw Archief voor ~skunde, vol. 8, no. 3, 1990, pp. 325- 345.

No. 84 A. de Zeeuw and F. van der Ploeg, Difference games and policy evaluation: aconceptual framework, O.tford Economic Papers, vol. 43, no. 4, 1991, pp. 612 -636.

No. 85 E. van Damme, Fair division under asytnmetric information, in R. Selten (ed.),Rational Interactian - Essays in Honor of John C. Harsanyi, Berlin~Heidelberg:Springer-Verlag, l992, pp. 121 - 144.

No. 86 F. de Jong, A. Kemna and T. Kloek, A contribution to event study methodology withan application to the Dutch stoek market, Journalof Banking and Finance, vol. l6,no. 1, 1992, pp. I1 - 36.

No. 87 A.P. Barten, The estimation of mixed demand systems, in R. Bewley and T. VanHoa (eds.), Catrributions to Consumer Detnand and Econometrics, Essays in HonourojHeitri Theil, Basingstoke: The Macmillan Press Ltd., 1992, pp. 31 - 57.

No. 88 T. Wansbeek and A. Kapteyn, Simple estimators for dynamic panel data models witherrors in variables, in R. Bewley and T. Van Hoa (eds.), Contributions to CortsumerDemand and Econornetrics, Essays in Honour of Henri Theil, Basingstoke: TheMacmillan Press Ltd., 1992, pp. 238 - 251.

No. 89 S. Chib, J. Osiewalski and M. Steel, Posterior inference on the degrees of freedomparameter in multivariate-t regression models, Economics Letters, vol. 37, no. 4,1991, pp. 391 - 397.

No. 90 H. Peters and P. Wakker, Independence of irrelevant altematives and revealed grouppreferences, Econometrica, vol. 59, no. 6, 1991, pp. 1787 - 1801.

No. 91 G. Alogoskoufis and F. van der Ploeg, On budgetary policies, growth, and externaldeficits in an interdependent world, Journal of the lapanese and InrernationalEco~tomies, vol. 5, no. 4, 1991, pp. 305 - 324.

No. 92 R.P. Gilles, G. Owen and R. van den Brink, Games with permission sttvctures: Theconjunctive approach, International Journal ojGame Theory, vol. 20, no. 3, 1992,

PP. 277 - 293.

No. 93 J.A.M. Potters, I.J. Curiel and S.H. Tijs, Traveling salesman games, MathematicalProgramming, vol. 53, no. 2, 1992, pp. 199 - 211.

No. 94 A.P. Jurg, M.J.M. Jansen, ].A.M. Potters and S.H. Tijs, A symmetrization for finitetwo-person games, Zeitschrift frlr Operatiorrs Research - Methods and Models ofOperations Research, vol. 36, no. 2, 1992, pp. 111 - 123.

No. 95 A. van den Nouweland, P. Borm and S. Tijs, Allocation rvles for hypergraphcommunication situatioac, International Journa! of Came Theory, vol. 20, no. 3,1992, pp. 255 - 268.

No. 96 E.l. Bomhoff, Monetary reform in Eastern Europe, European Economic Review, vol.

36, no. 213, 1992, pp. 454 - 458.

No. 97 F. van der Ploeg and A. de Zeeuw, International aspects of pollution control,

Environmenral mid Resource Economics, vol. 2, no. 2, 1992, pp. 1 l7 - 139.

No. 98 P.E.M. Borm and S.H. Tijs, Strategic claim games corresponding to an NTU-game,Games and Economic Behavior, vol. 4, no. 1, 1992, pp. 58 - 7l.

No. 99 A. van Soest and P. Kooreman, Coherency of the indirect translog demand system

with binding nonnegativity constraints, Journal oj Econometrics, vol. 44, no. 3,

1990, pp. 391 - 400.

No. 100 Th. ten Raa and E.N. Wolff, Secondary products and the measurement ofproductivity growth, Regionaf Science and Uróan Economics, vol. 21, no. 4, 1991,pp. 581 - 6I5.

No. 101 P. Kooreman and A. Kapteyn, On the empirical implementation of some gametheoretic models of household labor supply, 7he Journal of Human Resources, vol.25, no. 4, 1990, pp. 584 - 598.

No. 102 H. Bester, Bertrand equilibrium in a differentiated duopoly, International Economic

Review, vol. 33, no. 2, 1992, pp. 433 - 448.

No. l03 1.A.M. Potters and S.H. Tijs, The nucleolus of a matrix game and other nucleoli,Mathematics of Operations Research, vol. 17, no. 1, 1992, pp. 164 - 174.

No. 104 A. Kapteyn, P. Kooreman and A. van Soest, Quantity rationing and concavity in a

flexible household labor supply model, Review of Economics and Statistics, vol. 72,

no. 1, L990, pp. 55 - 62.

No. 105 A. Kapteyn and P. Kooreman, Household labor supply: What kind of data can tellus how many decision makers there are?, European Economic Review, vol. 36, no.213, 1992, pp. 365 - 371.

No. 106 Th. van de Klundert and S. Smulders, Reconstructing growth theory: A survey, DeEconomist, vol. 140, no. 2, 1992, pp. 177 - 203.

No. I07 N. Rankin. Imperfect competition, expectations and the multiple effects of monetary

growth, The Economic Journal, voi. 102, no. 413, 1492, pp. 743 - 753.

No. 108 1. Greenberg, On the sensitivity of von Neumann and Morgenstern abstract stabie

sets: The stable and the individual stable bargaining set, International Journal of

Game Theory, vol. 21, no. I, 1992, pp. 41 - 55.

No. !09 S. van Wijnbergen, Trade reform, policy uncertainty, and the current account: Anon-expected-utility approach, American Economic Review, vol. 82, no. 3. 1992, pp.

626 - 633.

No. Il0 M. Verbeek and Th. Nijman, Testing for selectivity bias in panel data models,International Econornic Review, vol. 33, no. 3, 1992, pp. 68l - 703.

No. 1 I 1 Th. Nijman and M. Verbeek, Nonresponse in panel data: The impact on estimates ofa life cycle consumption function, Journal of Applied Econometrics, vol. 7, no. 3,1992, pp. 243 - 257.

No. (12 I. Bomze and E. van Damme, A dynamical characterization of evolutionarily stablestates, Anrtals of Operatiorts Research, vol. 37, 1992, pp. 229 - 244.

No. I13 P.l. Deschamps, Expectations and intertemporal separability in an empirical modelof consumption and investment under uncertainty, Empirical Ecortornics, vol. 17, no.3, 1992, pp. 4l9 - 450.

No. 114 K. Kamiya and D. Talman, Simplicial algorithm for computing a core element in a' balanced game, Journaf of the Operations Research, vol. 34, no. 2, 1991, pp. 222 -

228.

No. 1IS G.W. imbens, An efficient method of moments estimator for discrete choice modelswith choice-based sampling, Econometrica, vol. 60, no. 5, 1992, pp. 1187 -1214.

No. 116 P. Borm, On perfectness concepts for bimatrix games, OR Spektrurn, vol. 14, no.1, 1992, pp. 33 - 42.

No. 117 A.P. ]urg, I. Garcia Jurado and P.E.M. Borm, On modifications of the concepts ofperfect and proper equilibria, OR Spektrum, vol. 14, no. 2, 1992, pp. 85 - 90.

No. l 18 P. Borm, H. Keiding, R.P. McLean, S. Oortwijn and S. Tijs, The compromise valuefor NTU-games, lnternational Journal of Game Theory, vol. 21, no. 2, 1992, pp.175 - 189.

No. 119 M. Maschler, J.A.M. Potters and S.H. Tijs, The general nucleolus and the reducedgame property, lnternationalJournalof Game Theory, vol. 21, no. 1, 1992, pp. 85 -106.

No. 120 K. Wárneryd, Communication, correlation and symmetry in bargaining, EconomicsLetters, vol. 39, no. 3, 1992, pp. 295 - 300.

No. I21 M.R. Baye, D. Kovenock and C.G. de Vries, It takes two to tango: equilibria in amodel of sales, Games and Economic Behavior, vol. 4, no. 4, 1992, pp. 493 - 510.

No. 122 M. Verbeek, Pseudo panel data, in L. Mátyás and P. Sevestre (eds.), TheEconontetrics of Pattel Data, Dordrecht: Kluwer Academic Publishers, 1992, pp. 303- 315.

No. 123 S. van Wijnbergen, Intertemporal speculation, shortages and the political economyof price reform, The Economíc Journat, vol. 102, no. 415, 1992, pp. 1395 - 1406.

No. 124 M. Verbeek and Th. Nijman, Incomplete panels and selection bias, in L. Mátyás andP. Sevestre (eds.), The Econometrics of Pane! Data, Dordrecht: Kluwer AcademicPublishers, 1992, pp. 262 - 302.

No. 125 1.1. Sijben, Monetary policy in a game-theoretic fratnework, Jahrbiicher fur

Nationa(óknnornie und Statisrik, vol. 210, no. 314, 1992, pp. 233 - 253.

No. l26 H.A.A. Verbon and M.1.M. Verhoeven, Decision making on pension scltemes under

rational expectations, Jonrna! of Econornics, vol. 56, no. l, 1992, pp. 71 - 97.

No. l27 L. Zou, Ownership structure and efficiency: An incentive mechanism approach,

Journal of Conrparative Economics, vol. 16, no. 3, 1993, pp. 399 - 431.

No. 128 C. Fersttttnan and A. de Zeeuw, Capital accumulation and entry deterrence: A

clarifying note, in G. Feichtinger (ed.), Dynarnic Econornic MOdels and Optinral

Control, Amsterdam: Elsevier Science Publishers B.V. (North-Holland), 1992, pp.

281 - 296.

No. 129 L. Bovenberg and C. Petersen, Public debt and pension policy, Fiscal Studies, vol.

13, no. 3, 1992, pp. 1- 14.

No. 130 R. Gradus and A. de Zeeuw, An employment game between government and firtns,

Optinral Control Applicntions á Metlrods, vol. 13, no. 1, 1992, pp. 55 - 71.

No. 131 Th. Nijman and R. Beetsma, Empirical tests of a simple pricing moclel for sugar

futures, Anrrales d'Écaronue et de Staristique, no. 24, 1991, pp. l2l - 131.

No. 132 F. Groot, C. Withagen and A. de Zeeuw, Note on the open-loop Von Stackelberg

equilibrium in the Cartel versus Fringe model, Tlre Economic Jounral,vol. 102, no.

415, 1992, pp. 1478 - 1484.

No. 133 S. Eijffinger and N. Gruijters, On the effectiveness of daily intervention by the

Deutsche Bundesbank and the Federal Reserve System in the US dollar - deutsche

mark exchange market, in BaltenspergerlSinn (eds), Exchartge-Rate Regimes aud

Currency Uniwes, Basingstoke: The Macmillan Press Ltd., 1992, pp. 13l - 156.

No. 134 M. R. Baye, D. Kovenock and C. G. de Vries, It takes two to tango: equilibria in

a model of sales, Games and Econanic Behavior, vol 4, 1992, pp. 493 - 5(0.

No. l35 A. K. Bera and S. Lee, [nformation matrix test, parameter heterogeneity and ARCH:

a synthesis, Revietv of Ecot:ornic Studies, 60, 1993, pp. 229 - 240.

No. 136 H. G. Blcemen and A. Kapteyn, The joint estimation of a non-linear labour supply

function and a wage equation using simulated response probabilities, Anna[es

d'Écarontie et de Statistique, No. 29, 1993, pp. l75 - 205.

No. 137 H. Bester, Bargaining versus price competition in markets with quality uncertainty,

The American Ecortomic Revieiv, Vol. 83, No. I, March 1993, pp. 278 - 288.

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