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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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File URL: http://128.118.178.162/eps/game/papers/0311/0311007.pdf
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Bibliographic Info

Paper provided by EconWPA in its series Game Theory and Information with number 0311007.

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Length: 6 pages
Date of creation: 22 Nov 2003
Date of revision:
Handle: RePEc:wpa:wuwpga:0311007

Note: Type of Document - pdf; prepared on win xp; to print on general; pages: 6; figures: 0. none
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Web page: http://128.118.178.162

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Keywords: Nash Equilibrium; large games; purification;

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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. 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.
  2. 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.
  3. Carmona, Guilherme, 2004. "Nash and Limit Equilibria of Games with a Continuum of Players," FEUNL Working Paper Series wp442, Universidade Nova de Lisboa, Faculdade de Economia.
  4. Edward Cartwright & Myrna Wooders, 2003. "On Equilibrium in Pure Strategies in Games with Many Players," Working Papers 2003.122, Fondazione Eni Enrico Mattei.
  5. Carmona, Guilherme & Podczeckz, Konrad, 2008. "On the Existence of Pure-Strategy Equilibria in Large Games," FEUNL Working Paper Series wp531, Universidade Nova de Lisboa, Faculdade de Economia.

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