Existence of Nash equilibria in large games
AbstractPodczeck [Podczeck, K., 1997. Markets with infinitely many commodities and a continuum of agents with non-convex preferences. Economic Theory 9, 385-426] provided a mathematical formulation of the notion of "many economic agents of almost every type" and utilized this formulation as a sufficient condition for the existence of Walras equilibria in an exchange economy with a continuum of agents and an infinite dimensional commodity space. The primary objective of this article is to demonstrate that a variant of Podczeck's condition provides a sufficient condition for the existence of pure-strategy Nash equilibria in a large non-anonymous game G when defined on an atomless probability space not necessary rich, and equipped with a common uncountable compact metric space of actions A. We also investigate to see whether the condition can be applied as well to the broader context of Bayesian equilibria and prove an analogue of Yannelis's results [Yannelis, N.C., in press. Debreu's social equilibrium theorem with asymmetric information and a continuum of agents. Economic Theory] on Debreu's social equilibrium theorem with asymmetric information and a continuum of agents.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Mathematical Economics.
Volume (Year): 45 (2009)
Issue (Month): 1-2 (January)
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Web page: http://www.elsevier.com/locate/jmateco
Large non-anonymous game Pure-strategy Nash equilibrium Large anonymous game Cornot-Nash equilibrium distribution Loeb space Rich probability space Bayesian games;
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