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Existence of Equilibria in Games with Arbitrary Strategy Spaces and Payoffs: A Full Characterization

By Guoqiang Tian

Abstract

This paper provides a complete solution to the question of the existence of equilibria in games with general strategy spaces that may be discrete, continuum or non-convex and payoff functions that may be discontinuous and do not have any form of quasi-concavity. We establish a single condition, called recursive diagonal transfer continuity, which is both necessary and sufficient for the existence of pure strategy Nash in games with arbitrary compact strategy spaces and payoffs. As such, our result strictly generalizes all the existing results on the existence of pure strategy Nash equilibrium. Recursive diagonal transfer continuity also permits full characterization of symmetric, mixed strategy, and Bayesian Nash equilibria in games with general strategy spaces and payoffs. The method of proof adopted to obtain our main results is also new and elementary — a non-fixed-point-theorem approach

Topics: Existence of pure, symmetric, mixed strategy, and Bayesian Nash equilibrium, recursive diagonal transfer continuity, discontinuity, non-quasiconcavity
Year: 2009
OAI identifier: oai:CiteSeerX.psu:10.1.1.415.996
Provided by: CiteSeerX
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