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On the existence of pure strategy nash equilibria in large games

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  • Guilherme Carmona

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.

Suggested Citation

  • Guilherme Carmona, 2006. "On the existence of pure strategy nash equilibria in large games," Nova SBE Working Paper Series wp487, Universidade Nova de Lisboa, Nova School of Business and Economics.
    • Handle: RePEc:unl:unlfep:wp487
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    1. Edward Cartwright & Myrna Wooders, 2009. "On equilibrium in pure strategies in games with many players," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(1), pages 137-153, March.
    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. 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. Mas-Colell, Andreu, 1984. "On a theorem of Schmeidler," Journal of Mathematical Economics, Elsevier, vol. 13(3), pages 201-206, December.
    5. SCHMEIDLER, David, 1973. "Equilibrium points of nonatomic games," LIDAM Reprints CORE 146, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Ehud Kalai, 2001. "Ex-Post Stability in Large Games," Discussion Papers 1351, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    7. Guilherme Carmona, 2004. "Nash equilibria of games with a continuum of players," Nova SBE Working Paper Series wp466, Universidade Nova de Lisboa, Nova School of Business and Economics.
    8. Rashid, Salim, 1983. "Equilibrium points of non-atomic games : Asymptotic results," Economics Letters, Elsevier, vol. 12(1), pages 7-10.
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    Cited by:

    1. Barlo, Mehmet & Carmona, Guilherme, 2015. "Strategic behavior in non-atomic games," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 134-144.
    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. Noguchi, Mitsunori, 2010. "Large but finite games with asymmetric information," Journal of Mathematical Economics, Elsevier, vol. 46(2), pages 191-213, March.
    4. 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.
    5. Guilherme Carmona, 2004. "Nash equilibria of games with a continuum of players," Nova SBE Working Paper Series wp466, Universidade Nova de Lisboa, Nova School of Business and Economics.
    6. Guilherme Carmona, 2006. "On a theorem by Mas-Colell," Nova SBE Working Paper Series wp485, Universidade Nova de Lisboa, Nova School of Business and Economics.

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    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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