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Non-Monotone Comparative Statics in Games of Incomplete Information

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  • Ed Hopkins
  • Tatiana Kornienko

Abstract

This paper analyses comparative statics for two classes of n-player games of incomplete information with continuous action spaces. The two classes are defined by differences in the payoff and behaviour of the weakest type: the lowest value bidder or highest cost firm. We show that in ``weakly competitive games'', including all-pay auctions and some oligopoly models, weak types will respond to a stochastically higher distribution of types by playing less aggressively. In ``strongly competitive'' games, all types play more aggressively. Furthermore, we show that a decrease in dispersion of types, in the sense of a refinement of second order stochastic dominance, although also associated with an increase in competitiveness, may in addition result in less aggressive play by strong types in both strongly and weakly competitive games.

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Paper provided by UCLA Department of Economics in its series Levine's Bibliography with number 122247000000000662.

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Date of creation: 06 Nov 2004
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Handle: RePEc:cla:levrem:122247000000000662

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  1. Jacob K. Goeree & Theo Offerman, 2000. "Competitive Bidding in Auctions with Private and Common Values," Tinbergen Institute Discussion Papers 00-044/1, Tinbergen Institute.
  2. Maskin, Eric S & Riley, John G, 1984. "Optimal Auctions with Risk Averse Buyers," Econometrica, Econometric Society, Econometric Society, vol. 52(6), pages 1473-1518, November.
  3. Ed Hopkins & Tatiana Kornienko, 2004. "Running to Keep in the Same Place: Consumer Choice as a Game of Status," ESE Discussion Papers 92, Edinburgh School of Economics, University of Edinburgh.
  4. Maskin, Eric & Riley, John, 2003. "Uniqueness of equilibrium in sealed high-bid auctions," Games and Economic Behavior, Elsevier, vol. 45(2), pages 395-409, November.
  5. Krishna, Vijay & Morgan, John, 1997. "An Analysis of the War of Attrition and the All-Pay Auction," Journal of Economic Theory, Elsevier, vol. 72(2), pages 343-362, February.
  6. Benny Moldovanu & Aner Sela, 2001. "The Optimal Allocation of Prizes in Contests," American Economic Review, American Economic Association, vol. 91(3), pages 542-558, June.
  7. Lebrun, Bernard, 1998. "Comparative Statics in First Price Auctions," Games and Economic Behavior, Elsevier, vol. 25(1), pages 97-110, October.
  8. Larry Samuelson, 2004. "Information-Based Relative Consumption Effects," Econometrica, Econometric Society, Econometric Society, vol. 72(1), pages 93-118, 01.
  9. Spulber, Daniel F, 1995. "Bertrand Competition When Rivals' Costs Are Unknown," Journal of Industrial Economics, Wiley Blackwell, vol. 43(1), pages 1-11, March.
  10. Athey, Susan, 2002. "Monotone Comparative Statics Under Uncertainty," Scholarly Articles 3372263, Harvard University Department of Economics.
  11. Bagwell, Kyle & Wolinsky, Asher, 2002. "Game theory and industrial organization," Handbook of Game Theory with Economic Applications, Elsevier, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 49, pages 1851-1895 Elsevier.
  12. Maskin, Eric & Riley, John, 2000. "Asymmetric Auctions," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 67(3), pages 413-38, July.
  13. John H. Kagel & Colin M. Campbell & Dan Levin, 1999. "The Winner's Curse and Public Information in Common Value Auctions: Reply," American Economic Review, American Economic Association, vol. 89(1), pages 325-334, March.
  14. Maskin, Eric & Riley, John, 2000. "Equilibrium in Sealed High Bid Auctions," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 67(3), pages 439-54, July.
  15. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
  16. Paul R. Milgrom, 1979. "Good Nevs and Bad News: Representation Theorems and Applications," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 407R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  17. An, Mark Yuying, 1995. "Logconcavity versus Logconvexity: A Complete Characterization," Working Papers, Duke University, Department of Economics 95-03, Duke University, Department of Economics.
  18. Ramos, Hector M. & Ollero, Jorge & Sordo, Miguel A., 2000. "A Sufficient Condition for Generalized Lorenz Order," Journal of Economic Theory, Elsevier, vol. 90(2), pages 286-292, February.
  19. Varian, Hal R, 1980. "A Model of Sales," American Economic Review, American Economic Association, vol. 70(4), pages 651-59, September.
  20. Susan Athey, 2002. "Monotone Comparative Statics Under Uncertainty," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 117(1), pages 187-223, February.
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Cited by:
  1. Ed Hopkins & Tatiana Kornienko, 2006. "Which Inequality? The Inequality of Resources Versus the Inequality of Rewards," Levine's Bibliography 784828000000000621, UCLA Department of Economics.

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