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On purification of equilibrium in Bayesian games and expost Nash equilibrium

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  • Edward Cartwright

    ()

  • Myrna Wooders

    ()

Abstract

We demonstrate that if any realization of a strategy for a Bayesiangame is, with high probability, an approximate Nash equilibrium of the induced game of complete information, then there is purification of that strategy that is an approximate equilibrium of the original Bayesian game. We also provide two examples demonstrating, amongst other things, that the bound we obtain on the distance of the purification from satisfying the requirements for 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. 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.
  3. Ehud Kalai, 2002. "Large Robust Games," Discussion Papers 1350, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  4. 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.
  5. Rui Pascoa, Mario, 1993. "Approximate equilibrium in pure strategies for non-atomic games," Journal of Mathematical Economics, Elsevier, vol. 22(3), pages 223-241.
  6. 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.
  7. 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 381, The Johns Hopkins University,Department of Economics, revised Feb 1997.
  8. Mas-Colell, Andreu, 1984. "On a theorem of Schmeidler," Journal of Mathematical Economics, Elsevier, vol. 13(3), pages 201-206, December.
  9. M Ali Khan & Yeneng Sun, 1996. "Non-Cooperative Games with Many Players," Economics Working Paper Archive 382, The Johns Hopkins University,Department of Economics.
  10. Richard McLean & Andrew Postlewaite, 2002. "Informational Size and Incentive Compatibility," Econometrica, Econometric Society, vol. 70(6), pages 2421-2453, November.
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Citations

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Cited by:
  1. Edward Cartwright & Myrna Wooders, 2003. "On Equilibrium in Pure Strategies in Games with Many Players," Working Papers 2003.122, Fondazione Eni Enrico Mattei.
  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. 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.
  4. 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.

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