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On the purification of Nash equilibria of large games

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  • Guilherme Carmona

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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  • Guilherme Carmona, 2003. "On the purification of Nash equilibria of large games," Nova SBE Working Paper Series wp436, Universidade Nova de Lisboa, Nova School of Business and Economics.
    • Handle: RePEc:unl:unlfep:wp436
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    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. 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.
    3. Rashid, Salim, 1983. "Equilibrium points of non-atomic games : Asymptotic results," Economics Letters, Elsevier, vol. 12(1), pages 7-10.
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    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. Guilherme Carmona, 2003. "Nash and Limit Equilibria of Games with a Continuum of Players," Game Theory and Information 0311004, University Library of Munich, Germany.
    3. Jara-Moroni, Pedro, 2018. "Rationalizability and mixed strategies in large games," Economics Letters, Elsevier, vol. 162(C), pages 153-156.
    4. Yaron Azrieli & Eran Shmaya, 2013. "Lipschitz Games," Mathematics of Operations Research, INFORMS, vol. 38(2), pages 350-357, May.
    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. Guilherme Carmona, 2006. "A unified approach to the purification of Nash equilibria in large games," Nova SBE Working Paper Series wp491, Universidade Nova de Lisboa, Nova School of Business and Economics.
    7. 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.
    8. 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.
    9. Carmona, Guilherme & Podczeck, Konrad, 2020. "Pure strategy Nash equilibria of large finite-player games and their relationship to non-atomic games," Journal of Economic Theory, Elsevier, vol. 187(C).
    10. 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.

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    JEL classification:

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

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