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On the Existence of Pure Strategy Nash Equilibria in Large Games

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  • Carmona, Guilherme

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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Bibliographic Info

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
Date of revision:
Handle: RePEc:unl:unlfep:wp465

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  1. Ehud Kalai, 2001. "Ex-Post Stability in Large Games," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 1351, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  2. Carmona, Guilherme, 2004. "Nash Equilibria of Games with a Continuum of Players," FEUNL Working Paper Series, Universidade Nova de Lisboa, Faculdade de Economia wp466, Universidade Nova de Lisboa, Faculdade de Economia.
  3. 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, The Johns Hopkins University,Department of Economics 381, The Johns Hopkins University,Department of Economics, revised Feb 1997.
  4. Rashid, Salim, 1983. "Equilibrium points of non-atomic games : Asymptotic results," Economics Letters, Elsevier, Elsevier, vol. 12(1), pages 7-10.
  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.
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Cited by:
  1. Barlo, Mehmet & Carmona, Guilherme, 2011. "Strategic behavior in non-atomic games," MPRA Paper 35549, University Library of Munich, Germany.
  2. Guilherme Carmona, 2004. "Nash Equilibria of Games with a Continuum of Players," Game Theory and Information, EconWPA 0412009, EconWPA.
  3. Rabia Nessah, 2013. "Weakly Continuous Security in Discontinuous and Nonquasiconcave Games: Existence and Characterization," Working Papers, IESEG School of Management 2013-ECO-20, IESEG School of Management.
  4. Mallick, Indrajit, 2011. "On the existence of pure strategy Nash equilibria in two person discrete games," Economics Letters, Elsevier, Elsevier, vol. 111(2), pages 144-146, May.
  5. Noguchi, Mitsunori, 2010. "Large but finite games with asymmetric information," Journal of Mathematical Economics, Elsevier, vol. 46(2), pages 191-213, March.
  6. Carmona, Guilherme, 2006. "On a Theorem by Mas-Colell," FEUNL Working Paper Series, Universidade Nova de Lisboa, Faculdade de Economia wp485, Universidade Nova de Lisboa, Faculdade de Economia.

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