The maximum Theorem and the existence of Nash equilibrium of (generalized) games without lower semicontinuities Academic Article

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 lower semicontinuous. 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 lower semicontinuous. Thus the existence theorems given in this paper generalize many existence theorems on Nash equilibrium and equilibrium for the generalized games in the literature. 1992.

authors

• Tian, Guoqiang
• Zhou, Jianxin

published proceedings

• Journal of Mathematical Analysis and Applications

author list (cited authors)

• Tian, G., & Zhou, J.

citation count

• 24

complete list of authors

• Tian, Guoqiang||Zhou, Jianxin

publication date

• January 1992

publisher

• Elsevier  Publisher

published in

• Journal of Mathematical Analysis and Applications  Journal

Digital Object Identifier (DOI)

• 10.1016/0022-247x(92)90302-t

start page

• 351

end page

• 364

volume

• 166

issue

• 2

URL

• http://dx.doi.org/10.1016/0022-247x(92)90302-t