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On Purification of Equilibrium in Bayesian Games and Ex-Post Nash Equilibrium

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  • Edward Cartwright

    ()
    (Department of Economics, Keynes College, University of Kent)

  • Myrna Wooders

    ()
    (Department of Economics, Vanderbilt University)

Abstract

Kalai (2002) demonstrates that in semi anonymous Bayesian games with sufficiently many players any Bayesian equilibrium is approximately ex-post Nash. In this paper we demonstrate that the existence of an approximate expost Nash property implies a purification result of the standard sort for the original Bayesian game. We also provide an example showing that the bound we obtain on the distance of a purified approximate equilibrium from an exact equilibrium is tight.

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File URL: http://www.accessecon.com/pubs/VUECON/vu05-w12.pdf
File Function: First version, 2005
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Bibliographic Info

Paper provided by Vanderbilt University Department of Economics in its series Vanderbilt University Department of Economics Working Papers with number 0512.

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Date of creation: Apr 2005
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Handle: RePEc:van:wpaper:0512

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Web page: http://www.vanderbilt.edu/econ/wparchive/index.html

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Keywords: Ex-post Nash equilibrium; noncooperative games; incomplete information; purification; epsilon ex-post Nash equilibrium;

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References

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  1. M Ali Khan & Kali P Rath & Yeneng Sun, 1994. "On the Existence of Pure Strategy Equilibria in Games with a Continuum of Players," Economics Working Paper Archive, The Johns Hopkins University,Department of Economics 381, The Johns Hopkins University,Department of Economics, revised Feb 1997.
  2. Mas-Colell, Andreu, 1984. "On a theorem of Schmeidler," Journal of Mathematical Economics, Elsevier, vol. 13(3), pages 201-206, December.
  3. Rui Pascoa, Mario, 1993. "Approximate equilibrium in pure strategies for non-atomic games," Journal of Mathematical Economics, Elsevier, vol. 22(3), pages 223-241.
  4. Ehud Kalai, 2002. "Large Robust Games," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 1350, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  5. Edward Cartwright & Myrna Wooders, 2005. "On Equilibrium in Pure Strategies in Games with Many Players," Vanderbilt University Department of Economics Working Papers, Vanderbilt University Department of Economics 0511, Vanderbilt University Department of Economics.
  6. Richard McLean & Andrew Postlewaite, . "Informational Size and Incentive Compatibility," CARESS Working Papres, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences 99-14, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
  7. Khan, M. Ali & Sun, Yeneng, 2002. "Non-cooperative games with many players," 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 46, pages 1761-1808 Elsevier.
  8. Cremer, Jacques & McLean, Richard P, 1985. "Optimal Selling Strategies under Uncertainty for a Discriminating Monopolist When Demands Are Interdependent," Econometrica, Econometric Society, Econometric Society, vol. 53(2), pages 345-61, March.
  9. Green, Jerry R & Laffont, Jean-Jacques, 1987. "Posterior Implementability in a Two-Person Decision Problem," Econometrica, Econometric Society, Econometric Society, vol. 55(1), pages 69-94, January.
  10. Mario Rui Pascoa, 1998. "Nash equilibrium and the law of large numbers," International Journal of Game Theory, Springer, Springer, vol. 27(1), pages 83-92.
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Cited by:
  1. Cartwright, Edward & Wooders, Myrna, 2003. "On Equilibrium in Pure Stategies in Games with Many Players," The Warwick Economics Research Paper Series (TWERPS), University of Warwick, Department of Economics 686, University of Warwick, Department of Economics.
  2. Carmona, Guilherme, 2008. "Purification of Bayesian-Nash equilibria in large games with compact type and action spaces," Journal of Mathematical Economics, Elsevier, vol. 44(12), pages 1302-1311, December.
  3. Yu, Haomiao & Khan, M. Ali & Rath, Kali P. & Sun, Yeneng, 0. "Strategic uncertainty and the ex-post Nash property in large games," Theoretical Economics, Econometric Society, Econometric Society.
  4. M. Ali Khan & Kali P. Rath & Yeneng Sun & Haomiao Yu, 2011. "On Large Games with a Bio-Social Typology," Economics Working Paper Archive, The Johns Hopkins University,Department of Economics 585, The Johns Hopkins University,Department of Economics.

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