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Uniform payoff security and Nash equilibrium in metric games

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  • Paulo Klinger Monteiro

    (FGV-EPGE)

  • Frank H. Page Jr

    ()
    (Department of finance, University of Alabama)

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.

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Bibliographic Info

Paper provided by Université Panthéon-Sorbonne (Paris 1) in its series Cahiers de la Maison des Sciences Economiques with number b05086.

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Length: 13 pages
Date of creation: Dec 2005
Date of revision:
Handle: RePEc:mse:wpsorb:b05086

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Keywords: Uniform payoff security; Nash equilibrium; discontinuous games; mixed extension.;

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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. Baye, M.R. & Kovenock, D. & De Varies, C.G., 1990. "The All-Pay Auction With Complete Information," Papers 9051, Tilburg - Center for Economic Research.
  3. Simon, Leo K, 1987. "Games with Discontinuous Payoffs," Review of Economic Studies, Wiley Blackwell, vol. 54(4), pages 569-97, October.
  4. Carmona, Guilherme, 2003. "On the Existence of Equilibria in Discontinuous Games: Three Counterexamples," FEUNL Working Paper Series wp438, Universidade Nova de Lisboa, Faculdade de Economia.
  5. 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.
  6. Carbonell-Nicolau, Oriol & Ok, Efe A., 2007. "Voting over income taxation," Journal of Economic Theory, Elsevier, vol. 134(1), pages 249-286, May.
  7. Monteiro, Paulo Klinger & Moreira, Humberto, 2006. "First-price auctions without affiliation," Economics Letters, Elsevier, vol. 91(1), pages 1-7, April.
  8. Dasgupta, Partha & Maskin, Eric, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, I: Theory," Review of Economic Studies, Wiley Blackwell, vol. 53(1), pages 1-26, January.
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