Existence of maximal element and equilibrium for a nonparacompact 𝑁-person game

Kim, Won Kyu

doi:10.1090/S0002-9939-1992-1123657-4

Existence of maximal element and equilibrium for a nonparacompact $N$-person game
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Proc. Amer. Math. Soc. 116 (1992), 797-807 Request permission

Abstract:

In this paper, we will introduce the concept of ${L_S}$-majorized correspondence and prove a new maximal element existence theorem on nonparacompact sets. As applications, we prove a new existence theorem of equilibrium for a nonparacompact $1$-person game with ${L_S}$-majorized preference correspondences, and then we prove that a nonparacompact N-person game with preference correspondences of class $L$ can be reduced to a $1$-person game with ${L_S}$-majorized preference correspondences.

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