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On pure strategy equilibria in large generalized games

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  • Riascos Villegas, Alvaro
  • Torres-Martínez, Juan Pablo

Abstract

We consider a game with a continuum of players where at most a finite number of them are atomic. Objective functions are continuous and admissible strategies may depend on the actions chosen by atomic players and on aggregate information about the actions chosen by non-atomic players. When atomic players have convex sets of admissible strategies and quasi-concave objective functions, a pure strategy Nash equilibria always exists.

Suggested Citation

  • Riascos Villegas, Alvaro & Torres-Martínez, Juan Pablo, 2013. "On pure strategy equilibria in large generalized games," MPRA Paper 46840, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:46840
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    File URL: https://mpra.ub.uni-muenchen.de/46840/8/MPRA_paper_46840.pdf
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    References listed on IDEAS

    as
    1. Balder, Erik J., 1999. "On the existence of Cournot-Nash equilibria in continuum games," Journal of Mathematical Economics, Elsevier, vol. 32(2), pages 207-223, October.
    2. Rath, Kali P, 1992. "A Direct Proof of the Existence of Pure Strategy Equilibria in Games with a Continuum of Players," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(3), pages 427-433, July.
    3. Aumann, Robert J., 1976. "An elementary proof that integration preserves uppersemicontinuity," Journal of Mathematical Economics, Elsevier, vol. 3(1), pages 15-18, March.
    4. Balder, Erik J., 2002. "A Unifying Pair of Cournot-Nash Equilibrium Existence Results," Journal of Economic Theory, Elsevier, vol. 102(2), pages 437-470, February.
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    Cited by:

    1. Sofía Correa & Juan Torres-Martínez, 2014. "Essential equilibria of large generalized games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 57(3), pages 479-513, November.

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    More about this item

    Keywords

    Generalized games; Non-convexities; Pure-strategy Nash equilibrium;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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