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Monotone equilibria in Bayesian games of strategic complementarities

  • Van Zandt, Timothy
  • Vives, Xavier

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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Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 134 (2007)
Issue (Month): 1 (May)
Pages: 339-360

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Handle: RePEc:eee:jetheo:v:134:y:2007:i:1:p:339-360
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  1. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
  2. David McAdams, 2003. "Isotone Equilibrium in Games of Incomplete Information," Econometrica, Econometric Society, vol. 71(4), pages 1191-1214, 07.
  3. Athey, Susan, 2002. "Monotone Comparative Statics Under Uncertainty," Scholarly Articles 3372263, Harvard University Department of Economics.
  4. Paul Milgrom & Robert J. Weber, 1981. "A Theory of Auctions and Competitive Bidding," Discussion Papers 447R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  5. Athey, S., 1996. "Characterizing Properties of Stochastic Objective Functions," Working papers 96-1, Massachusetts Institute of Technology (MIT), Department of Economics.
  6. 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.
  7. Susan Athey, 2002. "Monotone Comparative Statics under Uncertainty," The Quarterly Journal of Economics, Oxford University Press, vol. 117(1), pages 187-223.
  8. Masahiro Okuno-Fujiwara & Andrew Postlewaite & Kotaro Suzumura, 1990. "Strategic Information Revelation," Review of Economic Studies, Oxford University Press, vol. 57(1), pages 25-47.
  9. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November.
  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, June.
  11. 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.
  12. Edlin, Aaron S. & Shannon, Chris, 1998. "Strict Monotonicity in Comparative Statics," Journal of Economic Theory, Elsevier, vol. 81(1), pages 201-219, July.
  13. Xavier Vives, 2001. "Oligopoly Pricing: Old Ideas and New Tools," MIT Press Books, The MIT Press, edition 1, volume 1, number 026272040x, June.
  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. Athey, Susan, 2001. "Single Crossing Properties and the Existence of Pure Strategy Equilibria in Games of Incomplete Information," Econometrica, Econometric Society, vol. 69(4), pages 861-89, July.
  16. McAdams, David, 2002. "Isotone Equilibrium in Games of Incomplete Information," Working papers 4248-02, Massachusetts Institute of Technology (MIT), Sloan School of Management.
  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. Eric Maskin & John Riley, 2000. "Equilibrium in Sealed High Bid Auctions," Review of Economic Studies, Oxford University Press, vol. 67(3), pages 439-454.
  19. Russell Cooper & Andrew John, 1988. "Coordinating Coordination Failures in Keynesian Models," The Quarterly Journal of Economics, Oxford University Press, vol. 103(3), pages 441-463.
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