On the Existence of Equilibria in Discontinuous Games: Three Counterexamples
AbstractWe study whether we can weaken the conditions given in Reny  and still obtain existence of pure strategy Nash equilibria in quasiconcave normal form games, or, at least, existence of pure strategy "!equilibria for all " > 0. We show by examples that there are: 1. quasiconcave, payoff secure games without pure strategy "!equilibria for small enough " > 0 (and hence, without pure strategy Nash equilibria), 2. quasiconcave, reciprocally upper semicontinuous games without pure strategy "!equilibria for small enough " > 0, and 3. payoff secure games whose mixed extension is not payoff secure. The last example, due to Sion and Wolfe , also shows that nonquasiconcave games that are payoff secure and reciprocally upper semicontinuous may fail to have mixed strategy equilibria.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Universidade Nova de Lisboa, Faculdade de Economia in its series FEUNL Working Paper Series with number wp438.
Length: 11 pages
Date of creation: 2003
Date of revision:
Other versions of this item:
- 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.
- Guilherme Carmona, 2004. "On the Existence of Equilibria in Discontinuous Games: Three Counterexamples," Game Theory and Information 0402001, EconWPA.
- C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Simon, Leo K, 1987. "Games with Discontinuous Payoffs," Review of Economic Studies, Wiley Blackwell, vol. 54(4), pages 569-97, October.
- 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.
- 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.
- Baye, Michael R & Tian, Guoqiang & Zhou, Jianxin, 1993. "Characterizations of the Existence of Equilibria in Games with Discontinuous and Non-quasiconcave Payoffs," Review of Economic Studies, Wiley Blackwell, vol. 60(4), pages 935-48, October.
- Luciano Castro, 2011. "Equilibrium existence and approximation of regular discontinuous games," Economic Theory, Springer, vol. 48(1), pages 67-85, September.
- Capraro, Valerio & Scarsini, Marco, 2013. "Existence of equilibria in countable games: An algebraic approach," Games and Economic Behavior, Elsevier, vol. 79(C), pages 163-180.
- Paulo Klinger Monteiro & Frank H. Page Jr, 2005.
"Uniform payoff security and Nash equilibrium in metric games,"
Cahiers de la Maison des Sciences Economiques
b05086, Université Panthéon-Sorbonne (Paris 1).
- Pavlo Prokopovych, 2011. "On equilibrium existence in payoff secure games," Economic Theory, Springer, vol. 48(1), pages 5-16, September.
- Carmona, Guilherme, 2006. "Polyhedral Convexity and the Existence of Approximate Equilibria in Discontinuous Games," FEUNL Working Paper Series wp488, Universidade Nova de Lisboa, Faculdade de Economia.
- Pavlo Prokopovych & Nicholas C. Yannelis, 2012. "On Uniform Conditions for the Existence of Mixed Strategy Equilibria," Discussion Papers 48, Kyiv School of Economics.
- Nessah, Rabia & Tian, Guoqiang, 2008. "Existence of Equilibria in Discontinuous Games," MPRA Paper 41206, University Library of Munich, Germany, revised Mar 2010.
- 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.
- Rabia Nessah & Guoqiang Tian, 2009. "Existence of Equilibria in Discontinuous and Nonconvex Games," Levine's Working Paper Archive 814577000000000206, David K. Levine.
- Rabia Nessah & Guoqiang Tian, 2008. "The Existence of Equilibria in Discontinuous and Nonconvex Games," Working Papers 2008-ECO-14, IESEG School of Management, revised Mar 2010.
- Oriol Carbonell-Nicolau, 2011. "The Existence of Perfect Equilibrium in Discontinuous Games," Games, MDPI, Open Access Journal, vol. 2(3), pages 235-256, July.
- Pavlo Prokopovych & Nicholas C.Yannelis, 2013. "On the Existence of Mixed Strategy Nash equilibria," Discussion Papers 50, Kyiv School of Economics.
- Luciano I. de Castro, 2008. "Equilibria Existence in Regular Discontinuous Games," Discussion Papers 1463, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- repec:hal:journl:halshs-00197491 is not listed on IDEAS
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sean Story).
If references are entirely missing, you can add them using this form.