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On the Existence of Pure Strategy Nash Equilibria in Large Games

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  • Guilherme Carmona

    (Universidade Nova de Lisboa)

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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File URL: http://128.118.178.162/eps/game/papers/0412/0412008.pdf
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Bibliographic Info

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
Date of revision:
Handle: RePEc:wpa:wuwpga:0412008

Note: Type of Document - pdf; pages: 24. none
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Web page: http://128.118.178.162

Related research

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

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References

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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.
  2. Khan, M. Ali & Yeneng, Sun, 1995. "Pure strategies in games with private information," Journal of Mathematical Economics, Elsevier, vol. 24(7), pages 633-653.
  3. Rashid, Salim, 1983. "Equilibrium points of non-atomic games : Asymptotic results," Economics Letters, Elsevier, vol. 12(1), pages 7-10.
  4. Carmona, Guilherme, 2004. "Nash Equilibria of Games with a Continuum of Players," FEUNL Working Paper Series wp466, Universidade Nova de Lisboa, Faculdade de Economia.
  5. Ehud Kalai, 2001. "Ex-Post Stability in Large Games," Discussion Papers 1351, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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Cited by:
  1. Carmona, Guilherme, 2004. "Nash Equilibria of Games with a Continuum of Players," FEUNL Working Paper Series wp466, Universidade Nova de Lisboa, Faculdade de Economia.
  2. Rabia Nessah, 2013. "Weakly Continuous Security in Discontinuous and Nonquasiconcave Games: Existence and Characterization," Working Papers 2013-ECO-20, IESEG School of Management.
  3. Mallick, Indrajit, 2011. "On the existence of pure strategy Nash equilibria in two person discrete games," Economics Letters, Elsevier, vol. 111(2), pages 144-146, May.
  4. Noguchi, Mitsunori, 2010. "Large but finite games with asymmetric information," Journal of Mathematical Economics, Elsevier, vol. 46(2), pages 191-213, March.
  5. Carmona, Guilherme, 2006. "On a Theorem by Mas-Colell," FEUNL Working Paper Series wp485, Universidade Nova de Lisboa, Faculdade de Economia.
  6. Barlo, Mehmet & Carmona, Guilherme, 2011. "Strategic behavior in non-atomic games," MPRA Paper 35549, University Library of Munich, Germany.

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