Price Competition for an Informed Buyer
AbstractWe 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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Bibliographic InfoPaper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1199.
Length: 37 pages
Date of creation: Oct 1998
Date of revision:
Publication status: Published in Journal of Economic Theory (December 2001), 101(2): 457-493
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA
Other versions of this item:
- D43 - Microeconomics - - Market Structure and Pricing - - - Oligopoly and Other Forms of Market Imperfection
- D44 - Microeconomics - - Market Structure and Pricing - - - 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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- 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.
- Giuseppe Moscarini & Marco Ottaviani, 1998.
"Price Competition for an Informed Buyer,"
Cowles Foundation Discussion Papers
1199, Cowles Foundation for Research in Economics, Yale University.
- Larry Epstein & Michael Peters, 1996.
"A Revelation Principle For Competing Mechanisms,"
peters-96-02, University of Toronto, Department of Economics.
- Marco Ottaviani, 2000.
"The Value of Public Information in Monopoly,"
Econometric Society World Congress 2000 Contributed Papers
1479, Econometric Society.
- 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.
- 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, . "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).
- Stole, Lars A, 1995. "Nonlinear Pricing and Oligopoly," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 4(4), pages 529-62, Winter.
- 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.
- Butters, Gerard R, 1977. "Equilibrium Distributions of Sales and Advertising Prices," Review of Economic Studies, Wiley Blackwell, vol. 44(3), pages 465-91, October.
- 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.
- Shaked, Avner & Sutton, John, 1982. "Relaxing Price Competition through Product Differentiation," Review of Economic Studies, Wiley Blackwell, vol. 49(1), pages 3-13, January.
- Broecker, Thorsten, 1990. "Credit-Worthiness Tests and Interbank Competition," Econometrica, Econometric Society, vol. 58(2), pages 429-52, March.
- 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.
- Khalil, F & Rochet, J-C, 1997. "Contracts and Productive Information Gathering," Working Papers 97-16, University of Washington, Department of Economics.
- 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.
- Cremer, J. & Khalil, F. & Rochet, J-C., 1997. "Contracts and Productive Information Gathering," Papers 97.468, Toulouse - GREMAQ.
- Varian, Hal R, 1980. "A Model of Sales," American Economic Review, American Economic Association, vol. 70(4), pages 651-59, September.
- Bergemann, Dirk & Valimaki, Juuso, 1996.
"Learning and Strategic Pricing,"
Econometric Society, vol. 64(5), pages 1125-49, September.
- Dirk Bergemann & Juuso Valimaki, 1999.
"Experimentation in Markets,"
Cowles Foundation Discussion Papers
1214, Cowles Foundation for Research in Economics, Yale University.
- Simon, Leo K. & Zame, William R., 1987.
"Discontinous Games and Endogenous Sharing Rules,"
Department of Economics, Working Paper Series
qt8n46v2wv, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
- 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.
- 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.
- McAfee, R Preston, 1993. "Mechanism Design by Competing Sellers," Econometrica, Econometric Society, vol. 61(6), pages 1281-1312, November.
- Dirk Bergemann & Juuso Valimaki, 1996. "Market Experimentation and Pricing," Cowles Foundation Discussion Papers 1122, Cowles Foundation for Research in Economics, Yale University.
- 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.
- Manelli, Alejandro M & Vincent, Daniel R, 1995.
"Optimal Procurement Mechanisms,"
Econometric Society, vol. 63(3), pages 591-620, May.
- Paul Milgrom & Robert J. Weber, 1981.
"A Theory of Auctions and Competitive Bidding,"
447R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- 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.
- 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).
- 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.
- 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.
- 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.
- Osborne, Martin J & Pitchik, Carolyn, 1987.
"Equilibrium in Hotelling's Model of Spatial Competition,"
Econometric Society, vol. 55(4), pages 911-22, July.
- Martin J Osborne & Carolyn Pitchik, 1985. "Equilibrium in Hotelling's Model of Spatial Competition," Department of Economics Working Papers 1985-02, McMaster University.
- 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.
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