Nessah, Rabia and Tian, Guoqiang (2008): Existence of Nash Equilibrium in Discontinuous Games.
This is the latest version of this item.
Preview 
PDF
MPRA_paper_57906.pdf Download (197kB)  Preview 
Abstract
This paper offers an equilibrium existence theorem in discontinuous games. We introduce a new notion of continuity, called quasiweak transfer continuity that guarantees the existence of pure strategy Nash equilibrium in compact and quasiconcave games. We also consider possible extensions and improvements of the main result. Our conditions are simple and easy to verify. We present applications to show that our conditions allow for economically meaningful payoff discontinuities.
Item Type:  MPRA Paper 

Original Title:  Existence of Nash Equilibrium in Discontinuous Games 
Language:  English 
Keywords:  Discontinuous games; quasiweak transfer continuity; various notions of transfer continuity; Nash equilibrium 
Subjects:  C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C70  General D  Microeconomics > D0  General > D00  General 
Item ID:  57906 
Depositing User:  Guoqiang Tian 
Date Deposited:  14 Aug 2014 12:01 
Last Modified:  05 Oct 2019 10:02 
References:  ALIPRANTIS, C.B., BORDER, K.C., 2006. Infinite Dimensional Analysis: A Hitchhiker’s Guide, Third Edition, Springer. BAGH, A., JOFRE, A., 2006. Reciprocal Upper Semicontinuity and Better Reply Secure Games: A Comment. Econometrica 74, 1715–1721. BARELLI, P., MENEGHEL, I., 2013. A Note on the Equilibrium Existence Problem in Discontinuous Games. Econometrica 81, 813–824. BAYE, M.R., TIAN, G., ZHOU, J., 1993. Characterizations of the Existence of Equilibria in Games with Discontinuous and NonQuasiconcave Payoffs. The Review of Economic Studies 60, 935–948. BERTRAND, J., 1883. Theorie Mathematique de la Richesse Sociale. Journal des Savants 67, 499–508. CARMONA, G., 2009. An Existence Result for Discontinuous Games. Journal of Economic Theory 144, 13331340. CARMONA, G., 2011. Understanding Some Recent Existence Results for Discontinuous Games. Economic Theory 39, 31–45. DASGUPTA, P., MASKIN, E., 1986. The Existence of Equilibrium in Discontinuous Economic Games, I: Theory. The Review of Economic Studies 53, 1–26. DEBREU, G., 1952. A Social Equilibrium Existence Theorem. Proceedings of the National Academy of Sciences of the U.S.A. 38. HOTELLING, H., 1929. Stability in Competition. Economic Journal 39, 41–57. JACKSON, M.O., 2009. NonExistence of Equilibrium in Vickrey, SecondPrice, and English Auctions. Review of Economic Design 13, 137–145. MCLENNAN, A., MONTEIRO, P. K., TOURKY, R., 2011. Games with Discontinuous Payoffs: a Strengthening of Reny’s Existence Theorem. Econometrica 79, 1643–1664. MCMANUS, M., 1964. Equilibrium, Numbers and Size in Cournot Oligopoly. Yorkshire Bulletin of Social and Economic Research 16, 68–75. MILGROM, P., ROBERTS, H., 1990. Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities. Econometrica 58, 1255–1277. MILGROM, P., WEBER, R., 1985. Distributional Strategies for Games with Incomplete Information. Mathematics of Operations Research 10, 619–632. MORGAN, J., SCALZO, V., 2007. Pseudocontinuous Functions and Existence of Nash Equilibria. Journal of Mathematical Economics 43, 174–183. NASH, J., 1950. Equilibrium Points in nPerson Games. Proceedings of the National Academy of Sciences 36, 48–49. NASH, J.F., 1951. Noncooperative Games. Annals of Mathematics 54, 286–295. NESSAH, R., 2011. Generalized Weak Transfer Continuity and Nash Equilibrium. Journal of Mathematical Economics 47, 659–662. NESSAH, R., TIAN, G., 2009. The Existence of Equilibria in Discontinuous Games, mimeo. NESSAH, R., TIAN, G., 2013. Existence of Solution of Minimax Inequalities, Equilibria in Games and Fixed Points without Convexity and Compactness Assumptions. Journal of Optimization Theory and Applications 157, 75–95. NISHIMURA, K., FRIEDMAN, J., 1981. Existence of Nash Equilibrium in nPerson Games without Quasi Concavity. International Economic Review 22, 637–648. PROKOPOVYCH, P., 2011. On Equilibrium Existence in Payoff Secure Games. Economic Theory 48, 5–16. PROKOPOVYCH, P. 2013. The Single Deviation Property in Games with Discontinuous Payoffs. Economic Theory 53, 383–402. RENY, P. J., 1999. On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games. Econometrica 67, 1029–1056. RENY, P. J., 2009. Further Results on the Existence of Nash Equilibria in Discontinuous Games, mimeo. ROBERTS, J., SONNENSCHEIN, H., 1977. On the Foundations of the Theory of Monopolistic Competition. Econometrica 45, 101–113. ROSEN, J.B., 1965. Existence and Uniqueness of Equilibrium Point for Concave nPerson Games. Econometrica 33, 520–534. ROTHSTEIN, P., 2007. Discontinuous Payoffs, Shared Resources, and Games of Fiscal Competition: Existence of Pure Strategy Nash Equilibrium. Journal of Public Economic Theory 9, 335–368. SIMON, L., 1987. Games with Discontinuous Payoffs. Review of Economic Studies 54, 569–597. SIMON, L., ZAME, W., 1990. Discontinuous Games and Endogenous Sharing Rules. Econometrica 58, 861–872. TIAN, G., 1992a. Generalizations of the FKKM Theorem and Ky Fan Minimax Inequality, with Applications to Maximal Elements, Price Equilibrium, and Complementarity. Journal of Mathematical Analysis and Applications 170, 457–471. TIAN, G., 1992b. Existence of Equilibrium in Abstract Economies with Discontinuous Payoffs and Non Compact Choice Spaces. Journal of Mathematical Economics 21, 379–388. TIAN, G., 1992c. On the Existence of Equilibria in Generalized Games. International Journal of Game Theory 20, 247–254. TIAN, G., 1993. Necessary and Sufficient Conditions for Maximization of a Class of Preference Relations. The Review of Economic Studies 60, 949–958. TIAN, G., 2009. Existence of Equilibria in Games with Arbitrary Strategy Spaces and Payoffs: A Full Characterization, mimeo. TIAN, G., ZHOU, J., 1992. The Maximum Theorem and the Existence of Nash Equilibrium of (Generalized) Games Without Lower Semicontinuities. Journal of Mathematical Analysis and Applications 166, 351364. TIAN, G., ZHOU, J., 1995. Transfer Continuities, Generalizations of the Weierstrass and Maximum Theorems: A Full Characterization. Journal of Mathematical Economics 24, 281–303. TOPKIS, D. M., 1979. Equilibrium Points in NonzeroSum nPerson Submodular Games. SIAM Journal on Control and Optimization 17, 773–787. VIVES, X., 1990. Nash Equilibrium with Strategic Complementarities. Journal of Mathematical Economics 19, 305–321. YANNELIS, N.C., PRABHAKAR, N.D. 1983. Existence of Maximal Elements and Equilibria in Linear Topological Spaces. Journal of Mathematical Economics 12, 233–245. YAO, J.C. 1992. Nash Equilibria in nPerson Games without Convexity. Applied Mathematics Letters 5, 67–69. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/57906 
Available Versions of this Item

Existence of Equilibria in Discontinuous Games. (deposited 12 Sep 2012 12:49)
 Existence of Nash Equilibrium in Discontinuous Games. (deposited 14 Aug 2014 12:01) [Currently Displayed]