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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Equilibrium points of nonatomic games over a Banach space


Author: M. Ali Khan
Journal: Trans. Amer. Math. Soc. 293 (1986), 737-749
MSC: Primary 90A14; Secondary 28C20, 46N05, 90D10
MathSciNet review: 816322
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Abstract: Schmeidler's results on the equilibrium points of nonatomic games with strategy sets in Euclidean $ n$-space are generalized to nonatomic games with strategy sets in a Banach space. Our results also extend previous work of the author which assumed the Banach space to be separable and its dual to possess the Radon-Nikodým property. Our proofs use recent results in functional analysis.


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DOI: https://doi.org/10.1090/S0002-9947-1986-0816322-3
Keywords: Nonatomic game, Gel'fand integral, Diestel's theorem, approximate pure strategy equilibrium
Article copyright: © Copyright 1986 American Mathematical Society