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Uniform payoff security and Nash equilibrium in metric games

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Author Info
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 - CNRS : UMR8095 - Université Panthéon-Sorbonne - Paris I)

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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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Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00197491_v1.

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Date of creation: Dec 2005
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Handle: RePEc:hal:cesptp:halshs-00197491_v1

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

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  1. Simon, Leo K, 1987. "Games with Discontinuous Payoffs," Review of Economic Studies, Blackwell Publishing, vol. 54(4), pages 569-97, October. [Downloadable!] (restricted)
  2. Carbonell-Nicolau, Oriol & Ok, Efe A., 2007. "Voting over income taxation," Journal of Economic Theory, Elsevier, vol. 134(1), pages 249-286, May. [Downloadable!] (restricted)
  3. Dasgupta, Partha & Maskin, Eric, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, I: Theory," Review of Economic Studies, Blackwell Publishing, vol. 53(1), pages 1-26, January. [Downloadable!] (restricted)
  4. Monteiro, Paulo Klinger & Moreira, Humberto, 2006. "First-price auctions without affiliation," Economics Letters, Elsevier, vol. 91(1), pages 1-7, April. [Downloadable!] (restricted)
  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. Guilherme Carmona, 2005. "On the existence of equilibria in discontinuous games: three counterexamples," International Journal of Game Theory, Springer, vol. 33(2), pages 181-187, 06. [Downloadable!] (restricted)
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  7. Dan Kovenock & Michael R. Baye & Casper G. de Vries, 1996. "The all-pay auction with complete information (*)," Economic Theory, Springer, vol. 8(2), pages 291-305.
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  8. 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. [Downloadable!] (restricted)
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