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On the Existence of Pure Strategy Nash Equilibria in Large Games

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  • Carmona, Guilherme

Abstract

Over the years, several formalizations of games with a continuum of players have been given. These include those of Schmeidler (1973), Mas-Colell (1984) and Khan and Sun (1999). Unlike the others, Khan and Sun (1999) also addressed the equilibrium problem of large ¯- nite games, establishing the existence of a pure strategy approximate equilibrium in su±ciently large games. This ability for their formal- ization to yield asymptotic results led them to argue for it as the right approach to games with a continuum of players. We challenge this view by establishing an equivalent asymptotic theorem based only on Mas-Colell's formalization. Furthermore, we show that it is equivalent to Mas-Colell's existence theorem. Thus, in contrast to Khan and Sun (1999), we conclude that Mas-Colell's for- malization is as good as theirs for the development of the equilibrium theory of large ¯nite games.

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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 wp487.

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Length: 48 pages
Date of creation: 2006
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Handle: RePEc:unl:unlfep:wp487

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  1. 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.
  2. 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.
  3. Khan, M. Ali & Yeneng, Sun, 1995. "Pure strategies in games with private information," Journal of Mathematical Economics, Elsevier, vol. 24(7), pages 633-653.
  4. 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, Elsevier, vol. 76(1), pages 13-46, September.
  5. Rashid, Salim, 1983. "Equilibrium points of non-atomic games : Asymptotic results," Economics Letters, Elsevier, Elsevier, vol. 12(1), pages 7-10.
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Cited by:
  1. 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.
  2. 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.
  3. 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.
  4. Noguchi, Mitsunori, 2010. "Large but finite games with asymmetric information," Journal of Mathematical Economics, Elsevier, vol. 46(2), pages 191-213, March.
  5. 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.
  6. Barlo, Mehmet & Carmona, Guilherme, 2011. "Strategic behavior in non-atomic games," MPRA Paper 35549, University Library of Munich, Germany.

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