IDEAS home Printed from
   My bibliography  Save this paper

On the existence of pure strategy equilibria in large generalized games with atomic players


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


We consider a game with a continuum of players where only a finite number of them are atomic. Objective functions and admissible strategies may depend on the actions chosen by atomic players and on aggregate information about the actions chosen by non-atomic players. Only atomic players are required to have convex sets of admissible strategies and quasi-concave objective functions. We prove the existence of a pure strategy Nash equilibria. Thus, we extend to large generalized games with atomic players the results of equilibrium existence for non-atomic games of Schemeidler (1973) and Rath (1992). We do not obtain a pure strategy equilibrium by purification of mixed strategy equilibria. Thus, we have a direct proof of both Balder (1999, Theorem 2.1) and Balder (2002, Theorem 2.2.1), for the case where non-atomic players have a common non-empty set of strategies and integrable bounded codification of action profiles. Our main result is readily applicable to many interesting problems in general equilibrium. As an application, we extend Aumann (1966) result on the existence of equilibrium with a continuum of traders to a standard general equilibrium model with incomplete asset markets.

Suggested Citation

  • Riascos Villegas, Alvaro & Torres-Martínez, Juan Pablo, 2012. "On the existence of pure strategy equilibria in large generalized games with atomic players," MPRA Paper 36626, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:36626

    Download full text from publisher

    File URL:
    File Function: original version
    Download Restriction: no

    References listed on IDEAS

    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. 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.
    4. Aumann, Robert J., 1976. "An elementary proof that integration preserves uppersemicontinuity," Journal of Mathematical Economics, Elsevier, vol. 3(1), pages 15-18, March.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Correa, Sofía & Torres-Martínez, Juan Pablo, 2012. "Essential stability for large generalized games," MPRA Paper 36625, University Library of Munich, Germany.

    More about this item


    Generalized games; Non-convexities; Pure-strategy Nash equilibrium;

    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

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:36626. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Joachim Winter) or (Rebekah McClure). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.