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On the Purification of Nash Equilibria of Large Games

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  • Carmona, Guilherme

Abstract

We consider Salim Rashids asymptotic version of David Schmeidlers 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 Rashids 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://fesrvsd.fe.unl.pt/WPFEUNL/WP2003/wp436.pdf
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Bibliographic Info

Paper provided by Universidade Nova de Lisboa, Faculdade de Economia in its series FEUNL Working Paper Series with number wp436.

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Length: 6 pages
Date of creation: 2003
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Handle: RePEc:unl:unlfep:wp436

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  1. Rashid, Salim, 1983. "Equilibrium points of non-atomic games : Asymptotic results," Economics Letters, Elsevier, Elsevier, vol. 12(1), pages 7-10.
  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, Elsevier, vol. 76(1), pages 13-46, September.
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Cited by:
  1. Cartwright, Edward & Wooders, Myrna, 2003. "On Equilibrium in Pure Stategies in Games with Many Players," The Warwick Economics Research Paper Series (TWERPS), University of Warwick, Department of Economics 686, University of Warwick, Department of Economics.
  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, The Johns Hopkins University,Department of Economics 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, Universidade Nova de Lisboa, Faculdade de Economia wp442, Universidade Nova de Lisboa, Faculdade de Economia.
  4. Carmona, Guilherme & Podczeckz, Konrad, 2008. "On the Existence of Pure-Strategy Equilibria in Large Games," FEUNL Working Paper Series, Universidade Nova de Lisboa, Faculdade de Economia wp531, Universidade Nova de Lisboa, Faculdade de Economia.
  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.

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