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On purification of equilibrium in Bayesian games and expost Nash equilibrium

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  • Edward Cartwright

    ()

  • Myrna Wooders

    ()

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://hdl.handle.net/10.1007/s00182-008-0149-y
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Bibliographic Info

Article provided by Springer in its journal International Journal of Game Theory.

Volume (Year): 38 (2009)
Issue (Month): 1 (March)
Pages: 127-136

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Handle: RePEc:spr:jogath:v:38:y:2009:i:1:p:127-136

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Related research

Keywords: Semi-anonymous games; Purification; Expost Nash; Bayesian equilibrium;

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References

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  1. Mario Rui Pascoa, 1998. "Nash equilibrium and the law of large numbers," International Journal of Game Theory, Springer, vol. 27(1), pages 83-92.
  2. Khan, A. & Sun, Y., 2000. "Non-Cooperative Games with Many Players," Papiers d'Economie Mathématique et Applications 2000.80, Université Panthéon-Sorbonne (Paris 1).
  3. Richard McLean & Andrew Postlewaite, 2002. "Informational Size and Incentive Compatibility," Econometrica, Econometric Society, vol. 70(6), pages 2421-2453, November.
  4. Green, Jerry R & Laffont, Jean-Jacques, 1987. "Posterior Implementability in a Two-Person Decision Problem," Econometrica, Econometric Society, vol. 55(1), pages 69-94, January.
  5. Mas-Colell, Andreu, 1984. "On a theorem of Schmeidler," Journal of Mathematical Economics, Elsevier, vol. 13(3), pages 201-206, December.
  6. Khan, M. Ali & Rath, Kali P. & Sun, Yeneng, 1997. "On the Existence of Pure Strategy Equilibria in Games with a Continuum of Players," Journal of Economic Theory, Elsevier, vol. 76(1), pages 13-46, September.
  7. Edward Cartwright & Myrna Wooders, 2009. "On equilibrium in pure strategies in games with many players," International Journal of Game Theory, Springer, vol. 38(1), pages 137-153, March.
  8. Ehud Kalai, 2004. "Large Robust Games," Econometrica, Econometric Society, vol. 72(6), pages 1631-1665, November.
  9. Cremer, Jacques & McLean, Richard P, 1985. "Optimal Selling Strategies under Uncertainty for a Discriminating Monopolist When Demands Are Interdependent," Econometrica, Econometric Society, vol. 53(2), pages 345-61, March.
  10. Rui Pascoa, Mario, 1993. "Approximate equilibrium in pure strategies for non-atomic games," Journal of Mathematical Economics, Elsevier, vol. 22(3), pages 223-241.
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Citations

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Cited by:
  1. 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.
  2. M. Ali Khan & Kali P. Rath & Yeneng Sun & Haomiao Yu, 2011. "On Large Games with a Bio-Social Typology," Economics Working Paper Archive 585, The Johns Hopkins University,Department of Economics.
  3. Edward Cartwright & Myrna Wooders, 2005. "On Equilibrium in Pure Strategies in Games with Many Players," Vanderbilt University Department of Economics Working Papers 0511, Vanderbilt University Department of Economics.
  4. 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.

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