IDEAS home Printed from https://ideas.repec.org/p/udc/wpaper/wp311.html
   My bibliography  Save this paper

A direct proof of the existence of pure strategy equilibria in large generalized games with atomic players

Author

Listed:
  • Alvaro Riascos V.
  • Juan Pablo Torres-Martínez

Abstract

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. In this context, we prove the existence of pure strategy Nash equilibria, a result that extends Rath (1992, Theorem 2) to generalized games and gives a direct proof of a special case of Balder (1999, Theorem 2.1). Our proof has the merit of being simple, based only on standard fixed point arguments and finite dimensional real analysis.

Suggested Citation

  • Alvaro Riascos V. & Juan Pablo Torres-Martínez, 2010. "A direct proof of the existence of pure strategy equilibria in large generalized games with atomic players," Working Papers wp311, University of Chile, Department of Economics.
    • Handle: RePEc:udc:wpaper:wp311
    as

    Download full text from publisher

    File URL: http://www.econ.uchile.cl/uploads/publicacion/445e6352650e98928fdc6c17134cb5cb8698aafe.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

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

    Citations

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


    Cited by:

    1. Rubén Poblete-Cazenave & Juan Torres-Martínez, 2013. "Equilibrium with limited-recourse collateralized loans," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 53(1), pages 181-211, May.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Riascos Villegas, Alvaro & Torres-Martínez, Juan Pablo, 2013. "On pure strategy equilibria in large generalized games," MPRA Paper 46840, University Library of Munich, Germany.
    2. 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.
    3. Camacho, Carmen & Kamihigashi, Takashi & Sağlam, Çağrı, 2018. "Robust comparative statics for non-monotone shocks in large aggregative games," Journal of Economic Theory, Elsevier, vol. 174(C), pages 288-299.
    4. Lorenzo Rocco, 2007. "Anonymity in nonatomic games," International Review of Economics, Springer;Happiness Economics and Interpersonal Relations (HEIRS), vol. 54(2), pages 225-247, June.
    5. Jara-Moroni, Pedro, 2012. "Rationalizability in games with a continuum of players," Games and Economic Behavior, Elsevier, vol. 75(2), pages 668-684.
    6. Filipe Martins-da-Rocha, V. & Topuzu, Mihaela, 2008. "Cournot-Nash equilibria in continuum games with non-ordered preferences," Journal of Economic Theory, Elsevier, vol. 140(1), pages 314-327, May.
    7. Youcef Askoura, 2019. "On the core of normal form games with a continuum of players : a correction," Papers 1903.09819, arXiv.org.
    8. 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.
    9. Sofía Correa & Juan Pablo Torres-Martínez, 2012. "Essential Stability for Large Generalized Games," Working Papers wp362, University of Chile, Department of Economics.
    10. Jacquot, Paulin & Wan, Cheng, 2022. "Nonatomic aggregative games with infinitely many types," European Journal of Operational Research, Elsevier, vol. 301(3), pages 1149-1165.
    11. Correa, Sofía & Torres-Martínez, Juan Pablo, 2012. "Essential stability for large generalized games," MPRA Paper 36625, University Library of Munich, Germany.
    12. Jian Yang, 2023. "Nonatomic game with general preferences over returns," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(3), pages 861-889, September.
    13. Khan, M. Ali & Yeneng, Sun, 1995. "Pure strategies in games with private information," Journal of Mathematical Economics, Elsevier, vol. 24(7), pages 633-653.
    14. Erhan Bayraktar & Alexander Munk, 2016. "High-Roller Impact: A Large Generalized Game Model of Parimutuel Wagering," Papers 1605.03653, arXiv.org, revised Mar 2017.
    15. Askoura, Y., 2017. "On the core of normal form games with a continuum of players," Mathematical Social Sciences, Elsevier, vol. 89(C), pages 32-42.
    16. 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.
    17. 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.
    18. Lorenzo Rocco, 2001. "Nonatomic Games with Limited Anonymity," Working Papers 39, University of Milano-Bicocca, Department of Economics, revised Nov 2001.
    19. Siemroth, Christoph, 2014. "Why prediction markets work : The role of information acquisition and endogenous weighting," Working Papers 14-02, University of Mannheim, Department of Economics.
    20. Lorenzo Rocco, 2002. "Pricing of an Endogenous Peak-Load," Working Papers 54, University of Milano-Bicocca, Department of Economics, revised Aug 2002.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    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:udc:wpaper:wp311. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Mohit Karnani (email available below). General contact details of provider: https://edirc.repec.org/data/deuclcl.html .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.