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Contributions to Game Theory and Management, 2011, Volume 4, Pages 347–360 (Mi cgtm199)  
The Fixed Point Method Versus the KKM Method

Sehie Parkab

a Department of Mathematical Sciences, Seoul National University, Seoul 151–747, Korea
b The National Academy of Sciences, Republic of Korea, Seoul 137–044
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Abstract: In this survey, we compare the fixed point method and the KKM method in nonlinear analysis. Especially, we consider two methods in the proofs of the following important theorems in the chronological order: (1) The von Neumann minimax theorem, (2) The von Neumann intersection lemma, (3) The Nash equilibrium theorem, (4) The social equilibrium existence theorem of Debreu, (5) The Gale-Nikaido-Debreu theorem, (6) The Fan-Browder fixed point theorem, (7) Generalized Fan minimax inequality, and (8) The Himmelberg fixed point theorem.
Keywords: KKM type theorems; Fixed point; Minimax theorem; Nash equilibria.
Document Type: Article
Language: English
Citation: Sehie Park, “The Fixed Point Method Versus the KKM Method”, Contributions to Game Theory and Management, 4 (2011), 347–360
Citation in format AMSBIB
\Bibitem{Par11}
\by Sehie~Park
\paper The Fixed Point Method Versus the KKM Method
\jour Contributions to Game Theory and Management
\yr 2011
\vol 4
\pages 347--360
\mathnet{http://mi.mathnet.ru/cgtm199}
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