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Zbl 1236.49014
Park, Sehie
The Fan minimax inequality implies the Nash equilibrium theorem. (English)
[J] Appl. Math. Lett. 24, No. 12, 2206-2210 (2011). ISSN 0893-9659

Summary: We show that in an abstract convex space $(E,D;\Gamma )$, the partial KKM principle implies the Ky Fan minimax inequality, from which we deduce a generalization of the Nash equilibrium theorem.

MSC 2000:: *49J35 Minimax problems (existence)
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces

Keywords: abstract convex space; KKM principle; Fan's minimax inequality; Nash equilibrium

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Zentralblatt MATH Berlin [Germany]