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On the purification of Nash equilibria of large games

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  • Carmona, Guilherme

Abstract

We consider Salim Rashid's asymptotic version of David Schmeidler's theorem on the purification of Nash equilibria. We show that, in contrast to what is stated, players' payoff functions have to be selected from an equicontinuous family in order for Rashid's theorem to hold. That is, a bound on the diversity of payoffs is needed in order for such asymptotic result to be valid.
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Suggested Citation

  • Carmona, Guilherme, 2004. "On the purification of Nash equilibria of large games," Economics Letters, Elsevier, vol. 85(2), pages 215-219, November.
  • Handle: RePEc:eee:ecolet:v:85:y:2004:i:2:p:215-219
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    References listed on IDEAS

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    1. 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.
    2. Rashid, Salim, 1983. "Equilibrium points of non-atomic games : Asymptotic results," Economics Letters, Elsevier, vol. 12(1), pages 7-10.
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    Cited by:

    1. 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.
    2. Carmona, Guilherme, 2006. "A Uni¯ed Approach to the Puri¯cation of Nash Equilibria in Large Games," FEUNL Working Paper Series wp491, Universidade Nova de Lisboa, Faculdade de Economia.
    3. Carmona, Guilherme & Podczeck, Konrad, 2009. "On the existence of pure-strategy equilibria in large games," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1300-1319, May.
    4. repec:eee:ecolet:v:162:y:2018:i:c:p:153-156 is not listed on IDEAS
    5. 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.
    6. Guilherme Carmona, 2003. "Nash and Limit Equilibria of Games with a Continuum of Players," Game Theory and Information 0311004, EconWPA.
    7. Ennio Bilancini & Leonardo Boncinelli, 2016. "Strict Nash equilibria in non-atomic games with strict single crossing in players (or types) and actions," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(1), pages 95-109, April.
    8. 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.

    More about this item

    JEL classification:

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

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