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On the Existence of Pure Strategy Nash Equilibria in Large Games

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Author Info
Guilherme Carmona (Universidade Nova de Lisboa)

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Abstract

We consider an asymptotic version of Mas-Colell's 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 epsilon - pure, epsilon - equilibrium for all epsilon greater than 0. We also show that our result is equivalent to Mas-Colell's existence theorem, implying that it can properly be considered as its asymptotic version.

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Paper provided by EconWPA in its series Game Theory and Information with number 0412008.

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Length: 24 pages
Date of creation: 21 Dec 2004
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Handle: RePEc:wpa:wuwpga:0412008

Note: Type of Document - pdf; pages: 24. none
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Web page: http://129.3.20.41

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Related research
Keywords: Nash Equilibrium; Asymptotic Results; Pure Strategies; Approximate equilibria; Equicontinuity; Purification;

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Find related papers by JEL classification:
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  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. [Downloadable!] (restricted)
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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!]
    Other versions:
  4. 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)
  5. Rashid, Salim, 1983. "Equilibrium points of non-atomic games : Asymptotic results," Economics Letters, Elsevier, vol. 12(1), pages 7-10. [Downloadable!] (restricted)
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  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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