Price Competition for an Informed Buyer
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.
|Date of creation:||Oct 1998|
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|Publication status:||Published in Journal of Economic Theory (December 2001), 101(2): 457-493|
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- Jean J. Gabszewicz & Isabel Grilo, 1992.
"Price Competition When Consumersare Uncertain About Which Firm Sells Which Quality,"
Journal of Economics & Management Strategy,
Wiley Blackwell, vol. 1(4), pages 629-650, December.
- Gabszewicz, Jean J & Grilo, Isabel, 1992. "Price Competition When Consumers Are Uncertain about Which Firm Sells Which Quality," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 1(4), pages 629-50, Winter.
- GABSZEWICZ, Jean J. & GRILO, Isabel, . "Price competition when consumers are uncertain about which firm sells which quality," CORE Discussion Papers RP -1055, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- d'ASPREMONT, Claude & GABSZEWICZ, Jean J. & THISSE, Jacques-François, .
"On Hotelling's "Stability in competition","
CORE Discussion Papers RP
-385, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Dasgupta, Partha & Maskin, Eric, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, I: Theory," Review of Economic Studies, Wiley Blackwell, vol. 53(1), pages 1-26, January.
- Butters, Gerard R, 1977. "Equilibrium Distributions of Sales and Advertising Prices," Review of Economic Studies, Wiley Blackwell, vol. 44(3), pages 465-91, October.
- Lewis, Tracy R & Sappington, David E M, 1994. "Supplying Information to Facilitate Price Discrimination," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(2), pages 309-27, May.
- Leo K. Simon and William R. Zame., 1987.
"Discontinuous Games and Endogenous Sharing Rules,"
Economics Working Papers
8756, University of California at Berkeley.
- Manelli, Alejandro M & Vincent, Daniel R, 1995.
"Optimal Procurement Mechanisms,"
Econometric Society, vol. 63(3), pages 591-620, May.
- Dirk Bergemann & Juuso Valimaki, 1996. "Market Experimentation and Pricing," Cowles Foundation Discussion Papers 1122, Cowles Foundation for Research in Economics, Yale University.
- Harrington Jr. , Joseph E., 1995. "Experimentation and Learning in a Differentiated-Products Duopoly," Journal of Economic Theory, Elsevier, vol. 66(1), pages 275-288, June.
- Dirk Bergemann & Juuso Valimaki, 1996.
"Experimentation in Markets,"
1220, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Cremer, J. & Khalil, F. & Rochet, J-C., 1997.
"Contracts and Productive Information Gathering,"
97.468, Toulouse - GREMAQ.
- Khalil, F & Rochet, J-C, 1997. "Contracts and Productive Information Gathering," Discussion Papers in Economics at the University of Washington 97-16, Department of Economics at the University of Washington.
- Cremer, J. & Khalil, F. & Rochet, J-C., 1997. "Contracts and productive information gathering," Discussion Paper Series In Economics And Econometrics 9707, Economics Division, School of Social Sciences, University of Southampton.
- Khalil, F & Rochet, J-C, 1997. "Contracts and Productive Information Gathering," Working Papers 97-16, University of Washington, Department of Economics.
- Milgrom, Paul R & Weber, Robert J, 1982.
"A Theory of Auctions and Competitive Bidding,"
Econometric Society, vol. 50(5), pages 1089-1122, September.
- Bikhchandani, Sushil & Hirshleifer, David & Welch, Ivo, 1992.
"A Theory of Fads, Fashion, Custom, and Cultural Change in Informational Cascades,"
Journal of Political Economy,
University of Chicago Press, vol. 100(5), pages 992-1026, October.
- Sushil Bikhchandani & David Hirshleifer & Ivo Welch, 2010. "A theory of Fads, Fashion, Custom and cultural change as informational Cascades," Levine's Working Paper Archive 1193, David K. Levine.
- Shaked, Avner & Sutton, John, 1982. "Relaxing Price Competition through Product Differentiation," Review of Economic Studies, Wiley Blackwell, vol. 49(1), pages 3-13, January.
- Bergemann, Dirk & Valimaki, Juuso, 1996.
"Learning and Strategic Pricing,"
Econometric Society, vol. 64(5), pages 1125-49, September.
- Edward E. Schlee, 1996. "The Value of Information About Product Quality," RAND Journal of Economics, The RAND Corporation, vol. 27(4), pages 803-815, Winter.
- Marco Ottaviani, 2000.
"The Value of Public Information in Monopoly,"
Econometric Society World Congress 2000 Contributed Papers
1479, Econometric Society.
- Varian, Hal R, 1980. "A Model of Sales," American Economic Review, American Economic Association, vol. 70(4), pages 651-59, September.
- Stole, Lars A, 1995. "Nonlinear Pricing and Oligopoly," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 4(4), pages 529-62, Winter.
- Riley, John & Zeckhauser, Richard, 1983. "Optimal Selling Strategies: When to Haggle, When to Hold Firm," The Quarterly Journal of Economics, MIT Press, vol. 98(2), pages 267-89, May.
- McAfee, R Preston, 1993. "Mechanism Design by Competing Sellers," Econometrica, Econometric Society, vol. 61(6), pages 1281-1312, November.
- Moscarini, Giuseppe & Ottaviani, Marco, 2001.
"Price Competition for an Informed Buyer,"
Journal of Economic Theory,
Elsevier, vol. 101(2), pages 457-493, December.
- Martin J Osborne & Carolyn Pitchik, 1985.
"Equilibrium in Hotelling's Model of Spatial Competition,"
Department of Economics Working Papers
1985-02, McMaster University.
- Osborne, Martin J & Pitchik, Carolyn, 1987. "Equilibrium in Hotelling's Model of Spatial Competition," Econometrica, Econometric Society, vol. 55(4), pages 911-22, July.
- Borgers, Tilman, 1992. "Iterated Elimination of Dominated Strategies in a Bertrand-Edgeworth Model," Review of Economic Studies, Wiley Blackwell, vol. 59(1), pages 163-76, January.
- Epstein, Larry G. & Peters, Michael, 1999.
"A Revelation Principle for Competing Mechanisms,"
Journal of Economic Theory,
Elsevier, vol. 88(1), pages 119-160, September.
- Motty Perry & Philip J. Reny, 1999. "On The Failure of the Linkage Principle in Multi-Unit Auctions," Econometrica, Econometric Society, vol. 67(4), pages 895-900, July.
- Rosenthal, Robert W & Weiss, Andrew, 1984. "Mixed-Strategy Equilibrium in a Market with Asymmetric Information," Review of Economic Studies, Wiley Blackwell, vol. 51(2), pages 333-42, April.
- Ramon Caminal & Xavier Vives, 1996. "Why Market Shares Matter: An Information-Based Theory," RAND Journal of Economics, The RAND Corporation, vol. 27(2), pages 221-239, Summer.
- Felli, Leonardo & Harris, Christopher, 1996. "Learning, Wage Dynamics, and Firm-Specific Human Capital," Journal of Political Economy, University of Chicago Press, vol. 104(4), pages 838-68, August.
- Broecker, Thorsten, 1990. "Credit-Worthiness Tests and Interbank Competition," Econometrica, Econometric Society, vol. 58(2), pages 429-52, March.
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