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Uniform payoff security and Nash equilibrium in metric games

Author

Listed:
  • Paulo Klinger Monteiro

    (FGV-EPGE - Universidad de Brazil)

  • Frank H. Page Jr.

    (University of Alabama - Department of Finance, CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

We introduce a condition, uniform payoff security, for games with separable metric strategy spaces and payoffs bounded and measurable in players' strategies. We show that if any such metric game G is uniformly payoff secure, then its mixed extension G is payoff secure. We also establish that if a uniformly payoff secure metric game G has compact strategy spaces, and if its mixed extension G has reciprocally upper semicontinuous payoffs, then G has a Nash equilibrium in mixed strategies. We provide several economic examples of metric games satisfying uniform payoff security.

Suggested Citation

  • Paulo Klinger Monteiro & Frank H. Page Jr., 2005. "Uniform payoff security and Nash equilibrium in metric games," Post-Print halshs-00197491, HAL.
    • Handle: RePEc:hal:journl:halshs-00197491
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00197491
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    References listed on IDEAS

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    1. Page, Frank Jr. & Monteiro, Paulo K., 2003. "Three principles of competitive nonlinear pricing," Journal of Mathematical Economics, Elsevier, vol. 39(1-2), pages 63-109, February.
    2. Michael R. Baye & Dan Kovenock & Casper G. Vries, 1996. "The all-pay auction with complete information," Springer Books, in: Roger D. Congleton & Arye L. Hillman & Kai A. Konrad (ed.), 40 Years of Research on Rent Seeking 1, pages 209-223, Springer.
    3. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, I: Theory," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(1), pages 1-26.
    4. Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September.
    5. Leo K. Simon, 1987. "Games with Discontinuous Payoffs," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(4), pages 569-597.
    6. Monteiro, Paulo Klinger & Moreira, Humberto, 2006. "First-price auctions without affiliation," Economics Letters, Elsevier, vol. 91(1), pages 1-7, April.
    7. Guilherme Carmona, 2005. "On the existence of equilibria in discontinuous games: three counterexamples," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(2), pages 181-187, June.
    8. Carbonell-Nicolau, Oriol & Ok, Efe A., 2007. "Voting over income taxation," Journal of Economic Theory, Elsevier, vol. 134(1), pages 249-286, May.
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    More about this item

    Keywords

    Uniform payoff security; Nash equilibrium; discontinuous games; mixed extension; Sécurisation uniforme des paiements; équilibre de Nash; jeux discontinus; extension mixte;
    All these keywords.

    JEL classification:

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

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