Some extensions of discrete fixed point theorems and their applications to the game theory

Hidefumi Kawasaki

doi:10.1063/1.3241640

Some extensions of discrete fixed point theorems and their applications to the game theory

Hidefumi Kawasaki

Department of Mathematical Sciences

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

As is well-known in the game theory, fixed point theorems are useful to show the existence of Nash equilibrium. Since they are mathematical tools in continuous variables, it is expected that discrete fixed point theorems also useful to guarantee the existence of pure-strategy Nash equilibrium. In this talk, we review three types of discrete fixed point theorems, give some extensions, and apply them to non-cooperative games.

Original language	English
Title of host publication	Numerical Analysis and Applied Mathematics - International Conference on Numerical Analysis and Applied Mathematics 2009, ICNAAM-2009
Pages	941-944
Number of pages	4
Volume	1168
DOIs	https://doi.org/10.1063/1.3241640
Publication status	Published - Nov 26 2009
Event	International Conference on Numerical Analysis and Applied Mathematics 2009, ICNAAM-2009 - Rethymno, Crete, Greece Duration: Sep 18 2009 → Sep 22 2009

Other

Other	International Conference on Numerical Analysis and Applied Mathematics 2009, ICNAAM-2009
Country/Territory	Greece
City	Rethymno, Crete
Period	9/18/09 → 9/22/09

All Science Journal Classification (ASJC) codes

Physics and Astronomy(all)

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10.1063/1.3241640

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Kawasaki, H 2009, Some extensions of discrete fixed point theorems and their applications to the game theory. in Numerical Analysis and Applied Mathematics - International Conference on Numerical Analysis and Applied Mathematics 2009, ICNAAM-2009. vol. 1168, pp. 941-944, International Conference on Numerical Analysis and Applied Mathematics 2009, ICNAAM-2009, Rethymno, Crete, Greece, 9/18/09. https://doi.org/10.1063/1.3241640

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abstract = "As is well-known in the game theory, fixed point theorems are useful to show the existence of Nash equilibrium. Since they are mathematical tools in continuous variables, it is expected that discrete fixed point theorems also useful to guarantee the existence of pure-strategy Nash equilibrium. In this talk, we review three types of discrete fixed point theorems, give some extensions, and apply them to non-cooperative games.",

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Some extensions of discrete fixed point theorems and their applications to the game theory

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