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

Author

Listed:
  • 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.

Suggested Citation

  • 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.
    • Handle: RePEc:van:wpaper:0512
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    References listed on IDEAS

    as
    1. 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.
    2. Edward Cartwright & Myrna Wooders, 2009. "On equilibrium in pure strategies in games with many players," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(1), pages 137-153, March.
    3. SCHMEIDLER, David, 1973. "Equilibrium points of nonatomic games," LIDAM Reprints CORE 146, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Paul R. Milgrom & Robert J. Weber, 1985. "Distributional Strategies for Games with Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 10(4), pages 619-632, November.
    5. Richard McLean & Andrew Postlewaite, 2002. "Informational Size and Incentive Compatibility," Econometrica, Econometric Society, vol. 70(6), pages 2421-2453, November.
    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. Mas-Colell, Andreu, 1984. "On a theorem of Schmeidler," Journal of Mathematical Economics, Elsevier, vol. 13(3), pages 201-206, December.
    8. Rui Pascoa, Mario, 1993. "Approximate equilibrium in pure strategies for non-atomic games," Journal of Mathematical Economics, Elsevier, vol. 22(3), pages 223-241.
    9. Ehud Kalai, 2004. "Large Robust Games," Econometrica, Econometric Society, vol. 72(6), pages 1631-1665, November.
    10. 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 345-361, March.
    11. Mario Rui Pascoa, 1998. "Nash equilibrium and the law of large numbers," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(1), pages 83-92.
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    Citations

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    Cited by:

    1. , & , P. & , & ,, 2015. "Strategic uncertainty and the ex-post Nash property in large games," Theoretical Economics, Econometric Society, vol. 10(1), January.
    2. Edward Cartwright & Myrna Wooders, 2009. "On equilibrium in pure strategies in games with many players," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(1), pages 137-153, March.
    3. Khan, M. Ali & Rath, Kali P. & Sun, Yeneng & Yu, Haomiao, 2013. "Large games with a bio-social typology," Journal of Economic Theory, Elsevier, vol. 148(3), pages 1122-1149.
    4. Arsen Palestini & Ilaria Poggio, 2015. "A Bayesian potential game to illustrate heterogeneity in cost/benefit characteristics," International Review of Economics, Springer;Happiness Economics and Interpersonal Relations (HEIRS), vol. 62(1), pages 23-39, March.
    5. 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.
    6. Deb, Joyee & Kalai, Ehud, 2015. "Stability in large Bayesian games with heterogeneous players," Journal of Economic Theory, Elsevier, vol. 157(C), pages 1041-1055.

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    More about this item

    Keywords

    Ex-post Nash equilibrium; noncooperative games; incomplete information; purification; epsilon ex-post Nash equilibrium;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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