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Nash and Limit Equilibria of Games with a Continuum of Players

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  • Guilherme Carmona

Abstract

We show that a strategy is a Nash equilibrium in a game with a continuum of players if and only if there exists a sequence of finite games such that its restriction is an $\varepsilon_n$-equilibria, with $\varepsilon_n$ converging to zero. In our characterization, the sequence of finite games approaches the continuum game in the sense that the set of players and the distribution of characteristics and actions in the finite games converge to those of the continuum game. These results render approximate equilibria of large finite economies as an alternative way of obtaining strategic insignificance. Also, they suggest defining a refinement of Nash equilibria for games with a continuum of agents as limit points of equilibria of finite games. This allows us to discard those Nash equilibria that are artifacts of the continuum model, making limit equilibrium a natural equilibrium concept for games with a continuum of players.

Suggested Citation

  • Guilherme Carmona, 2003. "Nash and Limit Equilibria of Games with a Continuum of Players," Game Theory and Information 0311004, University Library of Munich, Germany.
  • Handle: RePEc:wpa:wuwpga:0311004
    Note: Type of Document - pdf; prepared on win xp; to print on general; pages: 39; figures: 0. none
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    1. Hart, Sergiu & Hildenbrand, Werner & Kohlberg, Elon, 1974. "On equilibrium allocations as distributions on the commodity space," Journal of Mathematical Economics, Elsevier, vol. 1(2), pages 159-166, August.
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    4. Guilherme Carmona, 2003. "Symmetric Approximate Equilibrium Distributions with Finite Support," Game Theory and Information 0311006, University Library of Munich, Germany.
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    Citations

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    Cited by:

    1. Guilherme Carmona, 2003. "Symmetric Approximate Equilibrium Distributions with Finite Support," Game Theory and Information 0311006, University Library of Munich, Germany.
    2. Carmona, Guilherme, 2004. "On the Existence of Equilibrium Bank Runs in a Diamond-Dybvig Environment," FEUNL Working Paper Series wp448, Universidade Nova de Lisboa, Faculdade de Economia.
    3. Aaron Bodoh-Creed & Brent Hickman, 2016. "College Assignment as a Large Contest," Working Papers 2016-27, Becker Friedman Institute for Research In Economics.
    4. repec:eee:jetheo:v:176:y:2018:i:c:p:886-934 is not listed on IDEAS
    5. Bodoh-Creed, Aaron, 2013. "Efficiency and information aggregation in large uniform-price auctions," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2436-2466.
    6. Carmona, Guilherme, 2007. "Bank failures caused by Large withdrawals: An explanation based purely on liquidity," Journal of Mathematical Economics, Elsevier, vol. 43(7-8), pages 818-841, September.
    7. Yang, Jian, 2011. "Asymptotic interpretations for equilibria of nonatomic games," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 491-499.
    8. repec:eee:jetheo:v:175:y:2018:i:c:p:88-126 is not listed on IDEAS
    9. Robin Nicole & Peter Sollich, 2017. "Dynamical selection of Nash equilibria using Experience Weighted Attraction Learning: emergence of heterogeneous mixed equilibria," Papers 1706.09763, arXiv.org.

    More about this item

    Keywords

    Nash equilibrium; limit equilibrium; games with a continuum of players;

    JEL classification:

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

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