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On the Existence of Pure Strategy Nash Equilibria in Large Games

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Carmona, Guilherme

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Abstract

We consider an asymptotic version of Mas-Colells theorem on the existence of pure strategy Nash equilibria in large games. Our result states that, if players payoff functions are selected from an equicontinuous family, then all sufficiently large games have an "  pure, "  equilibrium for all " > 0. We also show that our result is equivalent to Mas-Colells existence theorem, implying that it can properly be considered as its asymptotic version.

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Paper provided by Universidade Nova de Lisboa, Faculdade de Economia in its series FEUNL Working Paper Series with number wp465.

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Length: 24 pages
Date of creation: 2004
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Handle: RePEc:unl:unlfep:wp465

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  1. M Ali Khan & Kali P Rath & Yeneng Sun, 1994. "On the Existence of Pure Strategy Equilibria in Games with a Continuum of Players," Economics Working Paper Archive 381, The Johns Hopkins University,Department of Economics, revised Feb 1997.
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  2. Ehud Kalai, 2001. "Ex-Post Stability in Large Games," Discussion Papers 1351, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
  3. Guilherme Carmona, 2004. "Nash Equilibria of Games with a Continuum of Players," Game Theory and Information 0412009, EconWPA. [Downloadable!]
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  4. Rashid, Salim, 1983. "Equilibrium points of non-atomic games : Asymptotic results," Economics Letters, Elsevier, vol. 12(1), pages 7-10. [Downloadable!] (restricted)
  5. Khan, M. Ali & Yeneng, Sun, 1995. "Pure strategies in games with private information," Journal of Mathematical Economics, Elsevier, vol. 24(7), pages 633-653. [Downloadable!] (restricted)
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  1. Carmona, Guilherme, 2006. "On a Theorem by Mas-Colell," FEUNL Working Paper Series wp485, Universidade Nova de Lisboa, Faculdade de Economia. [Downloadable!]
  2. Guilherme Carmona, 2004. "Nash Equilibria of Games with a Continuum of Players," Game Theory and Information 0412009, EconWPA. [Downloadable!]
    Other versions:
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