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Entry and Vertical Differentiation

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ENTRY AND VERTICAL DIFFERENTIATION BYDIRK BERGEMANN and JUUSO VÄLIMÄKI COWLES FOUNDATION PAPER NO. 1056 COWLES FOUNDATION FOR RESEARCH IN ECONOMICS YALE UNIVERSITY Box 208281 New Haven, Connecticut 06520-8281 2003http://cowles.econ.yale.edu/91⁄0022-0531/02 $35.00© 2002 Elsevier Science (USA)All rights reserved.Journal of Economic Theory 106, 91–125 (2002)doi:10.1006/jeth.2001.2865Entry and Vertical Differentiation11The authors thank Phillipe Aghion, Glenn Ellison, Ezra Friedman, Ariel Pakes, andRobin Mason, in particular, as well as two anonymous referees for many helpful comments.Financial support from NSF Grants SBR 9709887 and 9709340, respectively, is gratefullyacknowledged. The first author thanks the Department of Economics at the University ofMannheim for its hospitality and the Sloan Foundation for financial support through aFaculty Research Fellowship. The second author thanks ESRC for financial support throughGrant R000223448.Dirk BergemannDepartment of Economics, Yale University, New Haven, Connecticut [email protected] VälimäkiDepartment of Economics, University of Southampton,Southampton SO17 1BJ, United [email protected] October 1, 2000; final version received April 23, 2001;published online March 13, 2002This paper analyzes the entry of new products into vertically differentiatedmarkets where an entrant and an incumbent compete in quantities. The value of thenew product is initially uncertain and new information is generated throughpurchases in the market. We derive the (unique) Markov perfect equilibrium of theinfinite horizon game under the strong long run average payoff criterion.The quali-tative features of the optimal entry strategy are shown to depend exclusively on therelative ranking of established and new products based on current beliefs. Superiorproducts are launched relatively slowly and at high initial prices whereas substitutesfor existing products are launched aggressively at low initial prices.The robustnessof these results with respect to different model specifications is discussed. Journal ofEconomic Literature Classification Numbers: C72, C73, D43, D83. © 2002 ElsevierScience (USA)Key Words: entry; duopoly; quantity competition; vertical differentiation;Bayesian learning; Markov perfect equilibrium; experimentation; experience goods.1. INTRODUCTION1.1. MotivationIn this paper, we analyze the optimal entry strategies for differenttypes of experience goods in a dynamic Cournot duopoly with verticallydifferentiated buyers. Our main goal is to obtain a characterization of thefeatures of the new product that lead to qualitatively different entrystrategies. We show that a new product that represents a certain improve-ment to an existing product is launched in the market at prices above thestatic equilibrium level and sales quantities below the static level. A newproduct that has a positive probability of being the leading brand in themarket, but also a positive probability of being revealed to be inferior tothe current product, is launched with a more aggressive strategy wherethe initial prices are low and initial sales exceed the static equilibriumquantities.The firms compete in a continuous time model with an infinite horizon.The uncertainty about the new product is common to all buyers in themarket. Additional information about the quality of the new product isgenerated only through experiments, i.e., through purchases in the market.The information generated is assumed to be public, and while the exactmechanism of information transmission is left unmodelled it is motivatedby considerations such as word of mouth communication between thebuyers and consumer report services. As a consequence all buyers haveidentical beliefs about the new product, and we can represent the stagegame as a vertically differentiated quantity game parametrized by thecommon belief about the new product. Examples of markets where theassumptions of common value (aside from the aspect of vertical differen-tiation) and common information may be valid include markets for trans-portation or communications services. To take a precise example, supposebuyers evaluate the services of an airline carrier on the basis of the proba-bility of on-time departure and arrival and/or the probability of lost ormisplaced baggage. The uncertainty about the quality of the service is thencommon to all customers of the airline, provided that the uncertainties arenot route specific. The (expected) performance or reliability of the newservice is then best predicted by aggregate and publicly available statisticssuch as the percentage of on-time performances by an airline. In particular,all idiosyncratic experiences are of equal value in providing informationand can therefore be replaced by sufficient aggregate statistics. Our modelonly requires that all consumers rank reliability of the airlines or conges-tion in the provision of internet services according to the same scale, yetthey can differ in their willingness to pay for different service qualities.Hence the model displays vertical but not horizontal differentiation.92 BERGEMANN AND VA¨LIMA¨KIWe have chosen a model of quantity competition as the stage game.With this choice, we extend the scope of viable new products. In particular,quantity competition allows for the possibility of launching an innovationwhich brings the two competitors closer to each other without a change inthe leadership. In a model of price competition, such innovations wouldnever be profitable, and as a result improved substitutes would never beobserved. In those models, the profits of both firms vanish as the substitu-tability of the two products increases, and as a result the static profit func-tions of the two firms are nonmonotonic in the level of differentiation. Webelieve that a model where each firm’s profit is increasing in its own qualityis better suited for a dynamic investigation of a market with verticaldifferentiation.In order to simplify the analysis, we assume that there is no discounting.As we want to stay close to the model with small discounting, we use thestrong long-run average criterion as defined in Dutta [10] as the intertem-poral evaluation criterion. This criterion can be justified as the limit ofmodels where the discount rate is tending to zero, and it retains the recursiveformulation of standard discounted dynamic programming. Under theassumptions of no discounting and quantity


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