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Non-Monotone Comparative Statics in Games of Incomplete Information

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  • Ed Hopkins

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  • 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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Bibliographic Info

Paper provided by Edinburgh School of Economics, University of Edinburgh in its series ESE Discussion Papers with number 122.

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Length: 21
Date of creation: Sep 2004
Date of revision:
Handle: RePEc:edn:esedps:122

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Keywords: Monotone likelihood ratio; monotone probability ratio; conditional stochastic dominance; generalized Lorenz order; comparative statics; games of incomplete information; first price auctions.;

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References

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  1. Susan Athey, 2002. "Monotone Comparative Statics Under Uncertainty," The Quarterly Journal of Economics, MIT Press, vol. 117(1), pages 187-223, February.
  2. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
  3. 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.
  4. Maskin, Eric & Riley, John, 2000. "Equilibrium in Sealed High Bid Auctions," Review of Economic Studies, Wiley Blackwell, vol. 67(3), pages 439-54, July.
  5. An, Mark Yuying, 1995. "Logconcavity versus Logconvexity: A Complete Characterization," Working Papers 95-03, Duke University, Department of Economics.
  6. 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.
  7. 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.
  8. Jacob K. Goeree & Theo Offerman, 2003. "Competitive Bidding in Auctions with Private and Common Values," Economic Journal, Royal Economic Society, vol. 113(489), pages 598-613, 07.
  9. 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.
  10. Bagwell, Kyle & Wolinsky, Asher, 2002. "Game theory and industrial organization," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 49, pages 1851-1895 Elsevier.
  11. Paul R. Milgrom, 1981. "Good News and Bad News: Representation Theorems and Applications," Bell Journal of Economics, The RAND Corporation, vol. 12(2), pages 380-391, Autumn.
  12. Spulber, Daniel F, 1995. "Bertrand Competition When Rivals' Costs Are Unknown," Journal of Industrial Economics, Wiley Blackwell, vol. 43(1), pages 1-11, March.
  13. 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.
  14. 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.
  15. Maskin, Eric S & Riley, John G, 1984. "Optimal Auctions with Risk Averse Buyers," Econometrica, Econometric Society, vol. 52(6), pages 1473-1518, November.
  16. Maskin, Eric & Riley, John, 2000. "Asymmetric Auctions," Review of Economic Studies, Wiley Blackwell, vol. 67(3), pages 413-38, July.
  17. Lebrun, Bernard, 1998. "Comparative Statics in First Price Auctions," Games and Economic Behavior, Elsevier, vol. 25(1), pages 97-110, October.
  18. Athey, Susan, 2002. "Monotone Comparative Statics Under Uncertainty," Scholarly Articles 3372263, Harvard University Department of Economics.
  19. Larry Samuelson, 2004. "Information-Based Relative Consumption Effects," Econometrica, Econometric Society, vol. 72(1), pages 93-118, 01.
  20. Varian, Hal R, 1980. "A Model of Sales," American Economic Review, American Economic Association, vol. 70(4), pages 651-59, September.
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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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