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Fixed-point theorems with applications to game theory

By Roger Maleski

Abstract

Nash's Theorem is an important game-theoretic result following from the fixed-point theorem of Kakutani, which is itself a generalization of Brouwer's Fixed-Point Theorem. This paper will present a detailed proof of Brouwer's Theorem, as well as an overview of the concepts of homology, homotopy, and degree which are necessary to the proof. Also included are discussion and less-detailed proofs of Kakutani's and Nash's theorems

Year: 2002
OAI identifier: oai:triceratops.brynmawr.edu:10066/681
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