### 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 |
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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 | |

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 |
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Country | Greece |

City | Rethymno, Crete |

Period | 9/18/09 → 9/22/09 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

### Cite this

*Numerical Analysis and Applied Mathematics - International Conference on Numerical Analysis and Applied Mathematics 2009, ICNAAM-2009*(Vol. 1168, pp. 941-944) https://doi.org/10.1063/1.3241640

**Some extensions of discrete fixed point theorems and their applications to the game theory.** / Kawasaki, Hidefumi.

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

*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

}

TY - GEN

T1 - Some extensions of discrete fixed point theorems and their applications to the game theory

AU - Kawasaki, Hidefumi

PY - 2009/11/26

Y1 - 2009/11/26

N2 - 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.

AB - 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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U2 - 10.1063/1.3241640

DO - 10.1063/1.3241640

M3 - Conference contribution

AN - SCOPUS:70450185870

SN - 9780735407091

VL - 1168

SP - 941

EP - 944

BT - Numerical Analysis and Applied Mathematics - International Conference on Numerical Analysis and Applied Mathematics 2009, ICNAAM-2009

ER -