intertemporal mixed bundling & the summer rock concert...

Intertemporal Mixed Bundling & the Summer Rock Concert Market

A Discussion with the Center for eBusiness at MIT

Rafi A. MohammedCambridge Strategy & Economics

Product Bundling Strategy: Theory & Evidence 2

From Internet Marketing: Building Advantage in a Networked Economy


Intertemporal Mixed Bundling and the Summer Rock Concert Market

Common BundlingModel Features

Common BundlingModel Features

Mixed bundling, pure bundlingUnderlying principle of mixed bundling is price discriminationBundle price is less than the sum of the individual component pricesBundle is targeted towards consumers that have a lower valuation of the goods. Individual sales targeted towards higher valuation consumers

Mixed bundling, pure bundlingUnderlying principle of mixed bundling is price discriminationBundle price is less than the sum of the individual component pricesBundle is targeted towards consumers that have a lower valuation of the goods. Individual sales targeted towards higher valuation consumers

Theoretical ModelWinter 1999, Rand Journal of Economics

(Joint with P. DeGraba)

Theoretical ModelWinter 1999, Rand Journal of Economics

(Joint with P. DeGraba)

Under certain parameterizations, the bundle price is greater than the sum of the individual component pricesBundle is targeted towards consumers that have a higher valuation of goods and individual components targeted towards lower value consumersBuying frenzies may be a result of profit maximization. A profit maximization may result in excess demandThis strategy creates uncertainty in a market not previously characterized by uncertaintyIntroduces the concept of intertemporal mixed bundling

Under certain parameterizations, the bundle price is greater than the sum of the individual component pricesBundle is targeted towards consumers that have a higher valuation of goods and individual components targeted towards lower value consumersBuying frenzies may be a result of profit maximization. A profit maximization may result in excess demandThis strategy creates uncertainty in a market not previously characterized by uncertaintyIntroduces the concept of intertemporal mixed bundling


Intertemporal Mixed Bundling and the Summer Rock Concert Market

Empirical WorkEmpirical WorkMonitor Working Paper: July 2002

Presents one of the first “objective” empirical tests of the effects of bundling to the academic literature


Agenda

Theoretical Work

Empirical Work


Underlying IntuitionTheoretical and Empirical Models

Concerts

Concert 1. Uncertainty regarding ticket availabilityConcert 2.Popular but no chance of selling out

Fans

Diehard FansNormal Fans

Two Period Ticket Selling Strategy

Period 1. Only bundles containing both `concert tickets are sold. Bundle price > than sum of individual prices

Period 2. Remaining tickets are sold individually

Increased Profits

All diehard fans purchase bundle

Uncertainty is created in a market not previously characterized by uncertainty

More tickets and ancillaries are sold

PRODUCT / PLAYERS

PRODUCT / PLAYERS STRATEGY STRATEGY OUTCOME OUTCOME


Theory ExampleDemand Assumptions

StonesNormal

100(B) 60(D) 160 60

BruceDiehard

90(C) 200(A) 290 20

BruceNormal

60(D) 100(B) 160 70

Stones Diehard

Consumer Type

Consumer Type

Expected Number of Customers

Expected Number of Customers

Reservation PricesReservation PricesRPstones RPbruce RPbothRPstones RPbruce RPboth

200(A) 90(C) 290 (0.5 * 20) + (0.5 * 60) = 40

Stones Capacity = Bruce Capacity = 100 = K


Theory ExampleIntertemporal Mixed Bundling (IMB) Framework

\IMB Time Line

Announce Selling Strategy

Consumer Decision

Period 2 Price Set

Sell RemainingTickets Individually

at $100

ConsumerDecision

Period 1 Price Set

Set BundlePrice (Stones &Bruce Ticket) at

202.50 - ε

Stones/Springsteen

Example

We assume that once tickets are purchased, they cannot be resold


Theory ExampleDiehard Stones & Bruce Fans’ Decision

Diehard Stones Fans: Purchasing the bundle is their Dominant Strategy

Stones Diehard FansWait Until Period 2

Stones Diehard FansWait Until Period 2

12.5% chance of not getting ticketPrior probability: 50%( 60 DH), 50%(20 DH)Posterior probability = (0.5 * 60) / [(0.5 * 60) + (0.5 * 20)] = 0.75If 60 diehards, probability of not getting ticket is [1 – (100/120)] Probability of not getting ticket = 0.75 * [1 –(100/120)] = 12.5%

Expected surplus from waiting until period 2 to purchase individually: 87.5% * [200 (reservation price) - $100 (ticket price) ] = $87.50

12.5% chance of not getting ticketPrior probability: 50%( 60 DH), 50%(20 DH)Posterior probability = (0.5 * 60) / [(0.5 * 60) + (0.5 * 20)] = 0.75If 60 diehards, probability of not getting ticket is [1 – (100/120)] Probability of not getting ticket = 0.75 * [1 –(100/120)] = 12.5%

Expected surplus from waiting until period 2 to purchase individually: 87.5% * [200 (reservation price) - $100 (ticket price) ] = $87.50

Stones Diehard Fans Purchase Bundle

Stones Diehard Fans Purchase BundleSurplus from purchasing bundle: $200 (RPstones) + $90 (RPbruce) - [202.50 - ε] = $87.50 + ε

Purchasing the bundle is their Dominant Strategy

Surplus from purchasing bundle: $200 (RPstones) + $90 (RPbruce) - [202.50 - ε] = $87.50 + ε

Purchasing the bundle is their Dominant Strategy


Theory ExampleDiehard Stones & Bruce Fans’ Decision

Bruce Diehard FansWait Until Period 2

Bruce Diehard FansWait Until Period 2

Bruce Diehard FansPurchase Bundle

Bruce Diehard FansPurchase Bundle

Diehard Bruce Fans: Purchasing the bundle is their Best Response

Diehard Stones fans bundle purchases (expected value = 40) extract from Bruce concert capacity. Thus, 60 tickets left

. 33% chance of not getting ticket (90 people vying for 60 tickets)

Expected surplus from waiting until period 2 to purchase individually: 66% * [200 (reservation price) - $100 (ticket price) ] = $66.66

Diehard Stones fans bundle purchases (expected value = 40) extract from Bruce concert capacity. Thus, 60 tickets left

. 33% chance of not getting ticket (90 people vying for 60 tickets)

Expected surplus from waiting until period 2 to purchase individually: 66% * [200 (reservation price) - $100 (ticket price) ] = $66.66

Surplus from purchasing bundle: $200 (RPbruce) + $90 (RPstones) - [202.50 - ε] = $87.50 + ε

Purchasing the bundle is their Best Response

Surplus from purchasing bundle: $200 (RPbruce) + $90 (RPstones) - [202.50 - ε] = $87.50 + ε

Purchasing the bundle is their Best Response


Theory ExampleIMB: A Profitable Strategy

Profits from IMB Dominate Other

Selling Strategies

Single product sales profits: $19,000 Pure bundling profits: $17,400IMB: $20,150 - 60ε

More ProfitableSeller Equilibriums

Rational expectations over time Risk aversion assumptions

Bundle price greater than individual good pricesBundle aimed at higher value consumers, individual sales towards lower value consumersProfit maximizing strategy characterized by excess demandCreates uncertainty in a market not previously

characterized by uncertainty

ExampleSummary


IMB: Subgame Perfect Nash EquilibriumKey Theorems and Assumptions

Proposition 1 Proposition 1

If the bundle price (Pb) in period 1 = B + C + min (CP1, CP2) - ε and in period 2, good are sold individually at B, all diehards purchase the bundle and normal customers wait until period 2 to purchase individually

In our example: Pb (202.50 - ε) = B (100) + C (90) + 12.50[min (CP1, CP2)] - ε

If the bundle price (Pb) in period 1 = B + C + min (CP1, CP2) - ε and in period 2, good are sold individually at B, all diehards purchase the bundle and normal customers wait until period 2 to purchase individually

In our example: Pb (202.50 - ε) = B (100) + C (90) + 12.50[min (CP1, CP2)] - ε

Proposition 2 (Central Theorem) Proposition 2 (Central Theorem)

If for all diehard consumers, the expected probability of not getting the good in period 2 is greater than the ratio of (B + ε - C)/(A-B), a subgame Nash equilibrium will involve IMB

Proposition Intuition: Want to set a bundle price that is greater than the sum of the second period individual prices in a manner that it is in the best interests for all Diehard customers to purchase the bundle

From Proposition 1: B + C + CP - ε > 2B. This equals B + C + (probability of not getting the good) * (A - B) > 2B. Proposition 2 is derived from rearranging

If for all diehard consumers, the expected probability of not getting the good in period 2 is greater than the ratio of (B + ε - C)/(A-B), a subgame Nash equilibrium will involve IMB

Proposition Intuition: Want to set a bundle price that is greater than the sum of the second period individual prices in a manner that it is in the best interests for all Diehard customers to purchase the bundle

From Proposition 1: B + C + CP - ε > 2B. This equals B + C + (probability of not getting the good) * (A - B) > 2B. Proposition 2 is derived from rearranging

Parameter Restrictions Parameter Restrictions

Maximum profit from individual sales: 2BK (in our example $20,000)

Maximum profit from pure bundling: 2BK (in our example, $20,000)

In a intertemporal mixed bundling strategy, all remaining goods are sold in period 2 at B.

Maximum profit from individual sales: 2BK (in our example $20,000)

Maximum profit from pure bundling: 2BK (in our example, $20,000)

In a intertemporal mixed bundling strategy, all remaining goods are sold in period 2 at B.


Agenda

Theoretical Work

Empirical Work


Empirical AnalysisTestable Implications & Data

IMB is used in approximately 30% of U.S. amphitheaters.

When IMB is used, the number of tickets sold will be higher

Increased number of tickets sold that is attributable to IMB

is positively correlated with the popularity of the other bundle concerts

Cases when the bundle price is greater than the sum of the individual ticket prices

Personally collected data

Summer 1991 data. Focused on concert markets in MSAs with population greater than 1 million and concert facilities with capacity greater than 10,000

Data Sources: Pollstar, newspaper reports, proprietary data from management and agents, Radio & Records, and Billboard

The Data The Data Model: Testable Implications Model: Testable Implications


The Jimmy Buffett Concert Experience


Empirical WorkKey Variables

Variable Variable Description ATTENDANCE Dependent variable – specific concert’s attendance

LAST ATTENDANCE

Average regional attendance on the performer’s last concert tour. Excludes concerts that were sold using IMB and dependent variable concert city. This variable is divided by 10.

LAST PRICE Average regional price for the performer’s last concert tour adjusted to 1991 dollars.

CORE LAST ATTENDANCE * LAST PRICE. A proxy for a performers core audience.

UNEMPLOYM-ENT

Unemployment rate in the concert city multiplied by 10. Indicator of economic healthiness.

RADIO # of weeks artist has been regularly played on the top local radio station in their primary format from January 1991 to concert date

DEMO Percentage of radio listeners that listen to performer’s radio format in concert city multiplied by 10

RADIO REACH

(RADIO * RADIO) * DEMO

PRICE Normalized pavilion ticket price for a specific rock concert



Variable Variable Description POPULATION City population in thousands

NO ALBUM Indicator variable denoting if the artists did not have a new album on the sales chart since January 1991

BUNDLING Indicator variable denoting if IMB was used to sell concert tickets

BUNDLED CONCERTS

(Last area attendance of the other concerts in the bundle)/(pavilion capacity). A gauge of the popularity of the other concerts in the bundle and uncertainty

LOW INDEX Indicator variable designating that BUNDLED CONCERTS variable is in the bottom 50% of the BUNDLED CONCERTS variable range

HIGH INDEX Indicator variable designating that BUNDLED CONCERTS variable is in the upper 50% of the BUNDLED CONCERTS variable range


Parameter EstimatesConcert Demand Focusing on IMB Indicator Variable

Dependent Variable: ATTENDANCE

Parameter Estimate Standard Errors

INTERCEPT 8104.08 (2272.16) ***

BUNDLING 1308.75 (701.47) **

CORE 2.45 (0.35)***

UNEMPLOYMENT -162.14 (112.53)

RADIO REACH 24.44 (5.32)***

PRICE -131.75 (78.34)*

NO ALBUM 2251.70 (806.25)***

POPULATION 0.76 (0.20) ***--------------------------------------------------------------------------------------------------Observations: 142, R2: 0.4265, , Adj R2: 0 .3968, F: 14.342***1% level. **5% level. *10% level.



BUNDLED CONCERTS

BUNDLED CONCERTS is a proxy of uncertainty

Example Bundle = Concerts A,B,C & D

BUNDLED CONCERTSA =

(LAB + LAC + LAD)Pavilion Capacity

Intuition: summing the last attendance of all of the other acts in the bundle provides an indicator of the popularity of the other acts in the bundle

Intuition: given the popularity of the bundle, the higher the pavilion capacity, the lower the uncertainty


Empirical WorkKey Variables & Intuition

HIGH INDEXIndicator variable designating that observation is in

the top 50% of BUNDLED CONCERTS variable. Very attractive concert bundles

LOW INDEXIndicator variable designating that observation is in

the bottom 50% of BUNDLED CONCERTS variable. Less attractive concert bundles

Individual concert demand (i.e., The Who in Boston) is a function of several demand variables including if the show is being sold as part of a highly desirable or less desirable concert bundle

.The Whoboston = F(Xi, HIGH INDEX, LOW INDEX)

EmpiricalIntuition


Parameter EstimatesConcert Demand Focusing on Low & High Bundle Popularity Variables



INTERCEPT 7921.64 (2241.74)***

LOW INDEX 760.10 (751.43)

HIGH INDEX 3185.51 (1302.31)**

CORE 2.39 (0.32)***


RADIO REACH 25.27 (5.04)***

PRICE -136.61 (76.31)*

NO ALBUM 2414.93 (798.02)***

POPULATION 0.87 (0.18)***--------------------------------------------------------------------------------------------------Observations: 142, R2: 0.4329, Adj R2: 0.4060, F: 12.91***1% level. **5% level. *10% level.


Price: An Endogenous Variable?Assumptions and 2SLS Analysis

Recursive Systems (Wold 1954)Model refers to a sequence of years, months, or other unitsModel has only one casual relationship for each endogenous variable

Concert MarketTicket prices set 6-8 months in advance. Between time prices set and concert date, two key variables are often realized: (1) New CD sales and (2) Radio airplayOnce ticket prices are set, they are never adjusted

Two Stage Least Squares ModelFirst Stage - Instrument for potentially endogenous variable, price, PIVSecond Stage - Use instrumented variable (PIV) in model2SLS presented on following slide. Coefficient estimates are robust and qualitative results remain the same

Recursive Systems Recursive Systems Two Stage Least Squares Analysis Two Stage Least

Squares Analysis


Two Stage Least Squares Parameter Estimates Concert Demand Focusing on Bundle Popularity Variables



INTERCEPT 6315.67 (9,214.04)

LOW INDEX 721.31 (892.51)

HIGH INDEX 3331.04 (1241.41)***

CORE 2.51 (0.54)***


RADIO REACH 24.51 (8.21)***

PRICE -132.41 (332.21)

NO ALBUM 2305.85 (885.02)**

POPULATION 0.78 (0.40)*--------------------------------------------------------------------------------------------------Observations: 142, R2: 0.4387, Adj R2: 0.3980, F: 12.71***1% level. **5% level. *10% level.


Parameter Estimates forIV Analysis of Price


INTERCEPT 19.87 (1.74)***

NO ANCILLARY 1.50 (0.75)**

ARENA -3.66 (1.36)***

COMP -1.17 (0.98)

LOW INDEX -1.71 (0.88)**

HIGH INDEX -0.57 (1.41)

CORE 0.00066 (0.0004)***


RADIO REACH 0.018 (0.006)***

NO ALBUM -0.45 (0.86)

POPULATION 0.00098 (0.0002)***------------------------------------------------------------------------------------------------------------------Observations: 142, R2: 0.4297, Adj R2: 0.3960, F: 12.62***1% level. **5% level. *10% level.

Dependent Variable: Price


Hausman Test Parameter Estimates


INTERCEPT 8314.14 (5723.11)

PREDICTED PRICE -22.80 (276.25)

LOW INDEX 709.28 (799.28)

HIGH INDEX 3184.25 (1313.51)**

CORE 2.47 (0.40)***


RADIO REACH 25.23 (6.54)***

PRICE -135.77 (80.21)*

NO ALBUM 2377.51 (837.25)***

POPULATION 0.87 (0.33)***--------------------------------------------------------------------------------------------------Observations: 142, R2: 0.4297, Adj R2: 0.3960, F: 12.62***1% level. **5% level. *10% level.


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