Existence of Equilibria in Discontinuous Games
AbstractThis paper investigates the existence of pure strategy, dominant strategy, and mixed strategy Nash equilibria in discontinuous games. We introduce a new notion of weak continuity, called weak transfer quasi-continuity, which is weaker than most known weak notions of continuity, including diagonal transfer continuity in Baye et al (1993) and better-reply security in Reny (1999), and holds in a large class of discontinuous games. We show that it, together with strong diagonal transfer quasiconcavity introduced in the paper, is enough to guarantee the existence of Nash equilibria in compact and convex normal form games. We provide sufficient conditions for weak transfer quasi-continuity by introducing notions of weak transfer continuity, weak transfer upper continuity, and weak transfer lower continuity. Moreover, an analogous analysis is applied to show the existence of dominant strategy and mixed strategy Nash equilibria in discontinuous games.
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 41206.
Date of creation: Nov 2008
Date of revision: Mar 2010
Discontinuous games; weak transfer quasi-continuity; pure strategy; mixed strategy; dominant strategy; Nash equilibrium; existence;
Find related papers by JEL classification:
- C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
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- Vives, X., 1988.
"Nash Equilibrium With Strategic Complementarities,"
UFAE and IAE Working Papers
107-88, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
- Morgan, Jacqueline & Scalzo, Vincenzo, 2007. "Pseudocontinuous functions and existence of Nash equilibria," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 174-183, February.
- Tian, Guoqiang, 1992. "On the Existence of Equilibria in Generalized Games," International Journal of Game Theory, Springer, vol. 20(3), pages 247-54.
- Robson, A.J., 1990.
"An "Informationally Robust Equilibrium" For Two-Person Nonzero-Sum Games,"
9039, Tilburg - Center for Economic Research.
- Robson~ Arthur J., 1994. "An Informationally Robust Equilibrium for Two-Person Nonzero-Sum Games," Games and Economic Behavior, Elsevier, vol. 7(2), pages 233-245, September.
- Robson, A.J., 1990. "An "informationally robust equilibrium" for two-person nonzero-sum games," Discussion Paper 1990-39, Tilburg University, Center for Economic Research.
- Adib Bagh & Alejandro Jofre, 2006. "Reciprocal Upper Semicontinuity and Better Reply Secure Games: A Comment," Econometrica, Econometric Society, vol. 74(6), pages 1715-1721, November.
- 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.
- 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.
- Guilherme Carmona, 2004. "On the Existence of Equilibria in Discontinuous Games: Three Counterexamples," Game Theory and Information 0402001, EconWPA.
- 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.
- Monteiro, Paulo Klinger & Page Jr, Frank H., 2007. "Uniform payoff security and Nash equilibrium in compact games," Journal of Economic Theory, Elsevier, vol. 134(1), pages 566-575, May.
- Simon, Leo K, 1987. "Games with Discontinuous Payoffs," Review of Economic Studies, Wiley Blackwell, vol. 54(4), pages 569-97, October.
- Paul Rothstein, 2007. "Discontinuous Payoffs, Shared Resources, and Games of Fiscal Competition: Existence of Pure Strategy Nash Equilibrium," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 9(2), pages 335-368, 04.
- Andrew McLennan & Paulo K. Monteiro & Rabee Tourky, 2011. "Games With Discontinuous Payoffs: A Strengthening of Reny's Existence Theorem," Econometrica, Econometric Society, vol. 79(5), pages 1643-1664, 09.
- 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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