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

  • Tian, Guoqiang
  • Zhou, Jianxin

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.

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File URL: https://mpra.ub.uni-muenchen.de/41300/1/MPRA_paper_41300.pdf
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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 41300.

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Date of creation: 17 Apr 1990
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Handle: RePEc:pra:mprapa:41300
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  1. Dasgupta, Partha & Maskin, Eric, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, II: Applications," Review of Economic Studies, Wiley Blackwell, vol. 53(1), pages 27-41, January.
  2. Dasgupta, Partha & Maskin, Eric, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, I: Theory," Review of Economic Studies, Wiley Blackwell, vol. 53(1), pages 1-26, January.
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