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Price Competition for an Informed Buyer

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We investigate the outcomes of simultaneous price competition in the presence of private information on the demand side. Each of two sellers offers a different variety of a good to a buyer endowed with a private binary signal on their relative quality. We analyze how the unique equilibrium of the game changes as a function of the (common) prior belief on the relative quality of the goods and the precision of the private information of the buyer. Competition is fierce, and the buyer enjoys high rents, when the prior belief is biased in favor of one good and private signals are not very informative: the ex ante superior seller cannot resist the temptation to clear the market, and triggers an aggressive response by the competitor. When instead the distribution of ex post valuations is highly spread, due to a vague prior belief and strong signals, the sellers become local monopolists and extract high rents from the buyer. We provide a full characterization of the mixed-strategy equilibrium which arises when the two goods are mildly differentiated ex post. Overall, the market-clearing temptation effect destroys the monotonicity and convexity of the equilibrium profit of a seller in the prior belief. As a consequence, a competing seller does not necessarily benefit from revelation of public information, sometimes even if biased in its favor. This paper analyzes the behavior of posterior distributions under the Jeffreys prior in a simultaneous equations model. The case under study is that of a general limited information setup with n + 1 endogenous variables. The Jeffreys prior is shown to give rise to a marginal posterior density which has Cauchy-like tails similar to that exhibited by the exact finite sample distribution of the corresponding LIML estimator. A stronger correspondence is established in the special case of a just-identified orthonormal canonical model, where the posterior density under the Jeffreys prior is shown to have the same functional form as the density of the finite sample distribution of the LIML estimator. The work here generalizes that of Chao and Phillips (1997), which gives analogous results for the special case of two endogenous variables.

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  • Giuseppe Moscarini & Marco Ottaviani, 1998. "Price Competition for an Informed Buyer," Cowles Foundation Discussion Papers 1199, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1199
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    Cited by:

    1. Chia-Hui Chen & Junichiro Ishida, 2013. "Auctions Versus Negotiations: The Role of Price Discrimination," ISER Discussion Paper 0873, Institute of Social and Economic Research, Osaka University.
    2. Subir Bose & Gerhard Orosel & Marco Ottaviani & Lise Vesterlund, 2006. "Dynamic monopoly pricing and herding," RAND Journal of Economics, RAND Corporation, vol. 37(4), pages 910-928, December.
    3. Marco LiCalzi, 2005. "A sufficient condition for all-or-nothing information supply in price discrimination," Game Theory and Information 0510005, EconWPA.
    4. Marco Ottaviani & Andrea Prat, 2001. "The Value of Public Information in Monopoly," Econometrica, Econometric Society, vol. 69(6), pages 1673-1683, November.
    5. Moscarini, Giuseppe & Ottaviani, Marco, 2001. "Price Competition for an Informed Buyer," Journal of Economic Theory, Elsevier, vol. 101(2), pages 457-493, December.
    6. Forand, Jean Guillaume, 2013. "Competing through information provision," International Journal of Industrial Organization, Elsevier, vol. 31(5), pages 438-451.
    7. Maxim Ivanov, 2013. "Information revelation in competitive markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(1), pages 337-365, January.
    8. Juan-José Ganuza & José S. Penalva, 2005. "On Information and Competition in Private Value Auctions," Working Papers 158, Barcelona Graduate School of Economics.
    9. Juan-José Ganuza, 2003. "Ignorance Promotes Competition: an Auction Model with Endogenous Private Valuations," Working Papers 107, Barcelona Graduate School of Economics.
    10. Saak, Alexander E., 2006. "The optimal private information in single unit monopoly," Economics Letters, Elsevier, vol. 91(2), pages 267-272, May.
    11. LOVO, Stefano M. & CALCAGNO, R., 2001. "Market efficiency and Price Formation when Dealers are Asymmetrically Informed," Les Cahiers de Recherche 737, HEC Paris.
    12. Il-Horn Hann & Kai-Lung Hui & Sang-Yong Tom Lee & Ivan P.L. Png, 2005. "Sales and Promotions: A More General Model," Industrial Organization 0508014, EconWPA.
    13. Kean Siang Ch’Ng & Suet Leng Khoo, 2015. "Market Mechanisms To Allocate Heritage Conservation Fund: An Experimental Study," The Singapore Economic Review (SER), World Scientific Publishing Co. Pte. Ltd., vol. 60(05), pages 1-19, December.
    14. Janko Gorter, 2012. "Commission Bans and the Source and Quality of Financial Advice," DNB Working Papers 350, Netherlands Central Bank, Research Department.
    15. Heidrun Hoppe & Ulrich Lehmann-Grube, 2008. "Price competition in markets with customer testing: the captive customer effect," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 35(3), pages 497-521, June.
    16. Raphael Boleslavsky & Christopher Cotton, 2015. "Information and Extremism in Elections," American Economic Journal: Microeconomics, American Economic Association, vol. 7(1), pages 165-207, February.
    17. Roman Inderst & Marco Ottaviani, 2012. "Competition through Commissions and Kickbacks," American Economic Review, American Economic Association, vol. 102(2), pages 780-809, April.
    18. Meagher, Kieron J. & Zauner, Klaus G., 2004. "Product differentiation and location decisions under demand uncertainty," Journal of Economic Theory, Elsevier, vol. 117(2), pages 201-216, August.
    19. Giovanni Dell'Ariccia & Robert Marquez, 2008. "Can cost increases increase competition? Asymmetric information and equilibrium prices," RAND Journal of Economics, RAND Corporation, vol. 39(1), pages 144-162.
    20. Christopher Cotton & Cheng Li, 2016. "Clueless Politicians," Working Papers 1341, Queen's University, Department of Economics.
    21. Alexander E. Saak, 2011. "A Model of Labeling with Horizontal Differentiation and Cost Variability," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 93(4), pages 1131-1150.
    22. Krähmer, Daniel, 2002. "Entry and experimentation in oligopolistic markets for experience goods
      [Markteintritt und Experimentation in oligopolistischen Märkten für Erfahrungsgüter]
      ," Discussion Papers, Research Unit: Market Processes and Governance FS IV 02-13, Social Science Research Center Berlin (WZB).

    More about this item

    Keywords

    Cauchy tails; exact finite sample distributions; Jeffreys prior; just identification; limited information; posterior density; simultaneous equations model;

    JEL classification:

    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • L15 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Information and Product Quality

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