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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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


Author: Won Kyu Kim
Journal: Proc. Amer. Math. Soc. 116 (1992), 797-807
MSC: Primary 90D06; Secondary 47H99, 90A14
DOI: https://doi.org/10.1090/S0002-9939-1992-1123657-4
MathSciNet review: 1123657
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1992-1123657-4
Keywords: Maximal element, equilibrium, N-person game, $ {L_S}$-majorized correspondence, class $ L$, upper semicontinuous
Article copyright: © Copyright 1992 American Mathematical Society