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Purification of Bayesian-Nash equilibria in large games with compact type and action spaces

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Author Info

  • Carmona, Guilherme

Abstract

We present a purification result for incomplete information games with a large but finite number of players that allows compact metric spaces for both actions and types. We then compare our framework and findings to the early purification theorems of Rashid (1983. Equilibrium points of non-atomic games: asymptotic results. Economics Letters 12, 7-10), Cartwright and Wooders (2002 On equilibrium in pure strategies in games with many players. University of Warwick Working Paper 686 (revised 2005)), Kalai (2004. Large robust games. Econometrica 72, 1631-1665) and Wooders, Cartwright and Selten (2006. Behavioral conformity in games with many players. Games and Economic Behavior 57, 347-360). Our proofs are elementary and rely on the Shapley-Folkman theorem.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 44 (2008)
Issue (Month): 12 (December)
Pages: 1302-1311

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Handle: RePEc:eee:mateco:v:44:y:2008:i:12:p:1302-1311

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Web page: http://www.elsevier.com/locate/jmateco

Related research

Keywords: Bayesian games Bayesian-Nash equilibrium Pure strategies Purification;

References

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  1. Carmona, Guilherme, 2004. "On the purification of Nash equilibria of large games," Economics Letters, Elsevier, vol. 85(2), pages 215-219, November.
  2. Edward Cartwright & Myrna Wooders, 2005. "On Purification of Equilibrium in Bayesian Games and Ex-Post Nash Equilibrium," Vanderbilt University Department of Economics Working Papers 0512, Vanderbilt University Department of Economics.
  3. P. D., 1988. "Introduction," Journal of Post Keynesian Economics, M.E. Sharpe, Inc., vol. 10(4), pages 527, July.
  4. Ehud Kalai, 2002. "Large Robust Games," Discussion Papers 1350, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  5. Rashid, Salim, 1983. "Equilibrium points of non-atomic games : Asymptotic results," Economics Letters, Elsevier, vol. 12(1), pages 7-10.
  6. Wooders, Myrna & Cartwright, Edward & Selten, Reinhard, 2006. "Behavioral conformity in games with many players," Games and Economic Behavior, Elsevier, vol. 57(2), pages 347-360, November.
  7. Starr, Ross M, 1969. "Quasi-Equilibria in Markets with Non-Convex Preferences," Econometrica, Econometric Society, vol. 37(1), pages 25-38, January.
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Citations

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Cited by:
  1. M. Ali Khan & Kali P. Rath, 2011. "The Shapley-Folkman Theorem and the Range of a Bounded Measure: An Elementary and Unified Treatment," Economics Working Paper Archive 586, The Johns Hopkins University,Department of Economics.
  2. Gradwohl, Ronen & Reingold, Omer, 2010. "Partial exposure in large games," Games and Economic Behavior, Elsevier, vol. 68(2), pages 602-613, March.
  3. Noguchi, Mitsunori, 2010. "Large but finite games with asymmetric information," Journal of Mathematical Economics, Elsevier, vol. 46(2), pages 191-213, March.
  4. Carmona, Guilherme & Podczeck, Konrad, 2012. "Ex-post stability of Bayes–Nash equilibria of large games," Games and Economic Behavior, Elsevier, vol. 74(1), pages 418-430.

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