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On the Existence of Pure Strategy Nash Equilibria in Large Games

  • Carmona, Guilherme

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
Date of revision:
Handle: RePEc:unl:unlfep:wp465
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  1. Khan, M. Ali & Yeneng, Sun, 1995. "Pure strategies in games with private information," Journal of Mathematical Economics, Elsevier, vol. 24(7), pages 633-653.
  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, vol. 76(1), pages 13-46, September.
  3. Ehud Kalai, 2001. "Ex-Post Stability in Large Games," Discussion Papers 1351, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  4. Guilherme Carmona, 2004. "Nash Equilibria of Games with a Continuum of Players," Game Theory and Information 0412009, EconWPA.
  5. Rashid, Salim, 1983. "Equilibrium points of non-atomic games : Asymptotic results," Economics Letters, Elsevier, vol. 12(1), pages 7-10.
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