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Monotone Equilibria in Bayesian Games of Strategic Complementarities

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  • Van Zandt, Timothy
  • Vives, Xavier

Abstract

For Bayesian games of strategic complementarities, we provide a constructive proof of the existence of a greatest and a least Bayes-Nash equilibrium - each one in strategies monotone in type - if the payoff to a player displays increasing differences in own action and the profile of types, and if the posteriors are increasing in type with respect to first-order stochastic dominance (e.g. if types are affiliated). The result holds for multidimensional action and type spaces and also for continuous and discrete type distributions. It uses an intermediate result on monotone comparative statics under uncertainty, which implies that the extremal equilibria increase when there is a first-order stochastic dominant shift in beliefs. We provide an application to strategic information revelation in games of voluntary disclosure.

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Bibliographic Info

Paper provided by C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number 4103.

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Date of creation: Nov 2003
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Handle: RePEc:cpr:ceprdp:4103

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Related research

Keywords: Cournot tatônnement; first-order stochastic dominance; incomplete information; monotone comparative statics; supermodular games; voluntary disclosure;

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References

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  1. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
  2. Xavier Vives, 2001. "Oligopoly Pricing: Old Ideas and New Tools," MIT Press Books, The MIT Press, edition 1, volume 1, number 026272040x, December.
  3. Athey, S., 1997. "Sigle Crossing Properties and the Existence of Pure Strategy Equilibria in Games of Incomplete Information," Working papers 97-11, Massachusetts Institute of Technology (MIT), Department of Economics.
  4. Frankel, David M. & Morris, Stephen & Pauzner, Ady, 2003. "Equilibrium selection in global games with strategic complementarities," Journal of Economic Theory, Elsevier, vol. 108(1), pages 1-44, January.
  5. Aaron S. Edlin and Chris Shannon., 1995. "Strict Monotonicity in Comparative Statics," Economics Working Papers 95-238, University of California at Berkeley.
  6. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
  7. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November.
  8. Susan Athey, 2002. "Monotone Comparative Statics Under Uncertainty," The Quarterly Journal of Economics, MIT Press, vol. 117(1), pages 187-223, February.
  9. David McAdams, 2003. "Isotone Equilibrium in Games of Incomplete Information," Econometrica, Econometric Society, vol. 71(4), pages 1191-1214, 07.
  10. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, December.
  11. Cooper, Russell & John, Andrew, 1988. "Coordinating Coordination Failures in Keynesian Models," The Quarterly Journal of Economics, MIT Press, vol. 103(3), pages 441-63, August.
  12. Paul Milgrom & Robert Weber, 1981. "Distributional Strategies for Games with Incomplete Information," Discussion Papers 428R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  13. Athey, S., 1996. "Characterizing Properties of Stochastic Objective Functions," Working papers 96-1, Massachusetts Institute of Technology (MIT), Department of Economics.
  14. Grossman, Sanford J, 1981. "The Informational Role of Warranties and Private Disclosure about Product Quality," Journal of Law and Economics, University of Chicago Press, vol. 24(3), pages 461-83, December.
  15. McAdams, David, 2002. "Isotone Equilibrium in Games of Incomplete Information," Working papers 4248-02, Massachusetts Institute of Technology (MIT), Sloan School of Management.
  16. Okuno-Fujiwara, Masahiro & Postlewaite, Andrew & Suzumura, Kotaro, 1990. "Strategic Information Revelation," Review of Economic Studies, Wiley Blackwell, vol. 57(1), pages 25-47, January.
  17. M Ali Khan & Yeneng Sun, 1996. "Non-Atomic Games on Loeb Spaces," Economics Working Paper Archive 374, The Johns Hopkins University,Department of Economics, revised Aug 1996.
  18. Maskin, Eric & Riley, John, 2000. "Equilibrium in Sealed High Bid Auctions," Review of Economic Studies, Wiley Blackwell, vol. 67(3), pages 439-54, July.
  19. Athey, Susan, 2002. "Monotone Comparative Statics Under Uncertainty," Scholarly Articles 3372263, Harvard University Department of Economics.
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