Correa, Sofía and TorresMartínez, Juan Pablo (2012): Essential stability for large generalized games.
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Abstract
We address the essential stability of CournotNash equilibria for generalized games with a continuum of players, where only a finite number of them are atomic. Given any set of generalized games continuously parameterized by a complete metric space, we analyze the robustness of equilibria to perturbations on parameters.
Item Type:  MPRA Paper 

Original Title:  Essential stability for large generalized games 
Language:  English 
Keywords:  Essential equilibria; Essential sets and components; Generalized games 
Subjects:  C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C72  Noncooperative Games C  Mathematical and Quantitative Methods > C6  Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C62  Existence and Stability Conditions of Equilibrium 
Item ID:  36625 
Depositing User:  Juan Pablo TorresMartínez 
Date Deposited:  13. Feb 2012 16:58 
Last Modified:  16. Feb 2013 05:26 
References:  Aubin, J.P. (1982): Mathematical Methods of Games and Economic Theory, NorthHolland, Amsterdam. Aliprantis, C. and K. Border (1999): Infinite Dimensional Analysis, SpringerVerlag, Berlin, Heidelberg. AlNajjar, N. (1995): "Strategically stable equilibria in games with infinitely many pure strategies," Mathematical Social Sciences, volume 29, pages 151164. Balder, E.J. (1999): "On the existence of CournotNash equilibria in continuum games," Journal of Mathematical Economics 32, pages 207223. Balder, E.J. (2002): "A unifying pair of CournotNash equilibrium existence results," Journal of Economic Theory, volume 102, pages 437470. CarbonellNicolau, O. (2010): "Essential equilibria in normalform games," Journal of Economic Theory, volume 145, pages 421431. Fort, M.K. (1949): "A unified theory of semicontinuity," Duke Mathematical Journal, volume 16, pages 237246. Fort, M.K. (1950): "Essential and nonessential fixed points," American Journal of Mathematics, volume 72, pages 315322. Hildenbrand, W. (1974): Core and Equilibria in a Large Economy, Princeton University Press, Princeton, New Jersey. Hillas, J. (1990): "On the definition of the strategic stability of equilibria," Econometrica, volume 58, pages 13651390. JiaHe, J. (1962): "Essential fixed points of the multivalued mappings," Scientia Sinica, volume XI. pages 293298. JiaHe, J. (1963): "Essential components of the set of fixed points of the multivalued mappings and its application to the theory of games," Scientia Sinica, volume XII. pages 951964. Kinoshita, S. (1952): "On essential components of the set of fixed points," Osaka Mathematical Journal, volume 4, pages 1922. Kohlberg, E. and J.F. Mertens (1986): "On the strategic stability of equilibrium point," Econometrica, volume 54, pages 10031037. Ok, E. (2005): Real Analysis with Economic Applications, Princeton University Press, Princeton, USA. Rath, K.P. (1992): "A direct proof of the existence of pure strategy equilibria in games with a continuum of players", Economic Theory, Volume 2, pages 427433. Riascos, A.J. and J.P. TorresMartínez(2012):"On the existence of pure strategy equilibria in large generalized games with atomic players," working paper, Department of Economics, University of Chile. Available at http://www.econ.uchile.cl/cha/jutorres. Schmeidler, D. (1973): "Equilibrium points of nonatomic games," Journal of Statistical Physics, volume 17, 295300. Yu, J. (1999): "Essential equilibrium of nperson noncooperative games," Journal of Mathematical Economics, volume 31, pages 361372. Yu, J., and H. Yang (2004): "Essential components of the set of equilibrium points for setvalued maps," Journal of Mathematical Analysis and Applications, volume 300, pages 334342. Yu, J., H. Yang, and S. Xiang (2005): "Unified approach to existence and stability of essential components," Nonlinear Analysis, volume 63, pages 24152425. Yu, X. (2009): "Essential components of the set of equilibrium points for generalized games in the uniform topological space of best reply correspondences," International Journal of Pure and Applied Mathematics, volume 55, pages 349357. Zhou, Y., J.Yu, and S.Xiang (2007): "Essential stability in games with infinitely many pure strategies," International Journal of Game Theory, volume 35, pages 493503. Wu, W., and J. JiaHe (1962): "Essential equilibrium points of nperson noncooperative games," Scientia Sinica, volume XI, pages 13071322. 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/36625 
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