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

Author

Listed:
  • Tian, Guoqiang
  • Zhou, Jianxin

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.

Suggested Citation

  • Tian, Guoqiang & Zhou, Jianxin, 1990. "The Maximum Theorem and the Existence of Nash Equilibrium of (Generalized) Games without Lower Semicontinuities," MPRA Paper 41300, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:41300
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    References listed on IDEAS

    as
    1. Khan, M. Ali & Vohra, Rajiv, 1984. "Equilibrium in abstract economies without ordered preferences and with a measure space of agents," Journal of Mathematical Economics, Elsevier, vol. 13(2), pages 133-142, October.
    2. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, I: Theory," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(1), pages 1-26.
    3. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, II: Applications," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(1), pages 27-41.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Maximum Theorem; Existence; Nash Equilibrium; Lower Semicontinuities;
    All these keywords.

    JEL classification:

    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General

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