The Maximum Theorem and the Existence of Nash Equilibrium of (Generalized) Games without Lower Semicontinuities

Guoqiang Tian and Jianxin Zhou

MPRA Paper from University Library of Munich, Germany

Abstract: In this paper we generalize Berge's Maximum Theorem to the case where the payoff (utility) functions and the feasible action correspondences are not lowersemicontinuous. The condition we introduced is called the Feasible Path Transfer Lower Semicontinuity (in short, FPT l.s.c.). By applying our Maximum Theorem to game theory and economics, we are able to prove the existence of equilibrium for the generalized games (the so-called abstract economics) and Nash equilibrium for games where the payoff functions and the feasible strategy correspondences are not lowersemicontinuous. Thus the existence theorems given in this paper generalize many existence theorems on Nash equilibrium and equilibrium for the generalized games in the literature.

Keywords: Maximum Theorem; Existence; Nash Equilibrium; Lower Semicontinuities (search for similar items in EconPapers)
JEL-codes: D50 (search for similar items in EconPapers)
Date: 1990-04-17
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