An application of a discrete fixed point theorem to a game in expansive form

Hidefumi Kawasaki, Akifumi Kira, Shinpei Kira

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

In this paper, we first present a discrete fixed point theorem for contraction mappings from the product set of integer intervals into itself, which is an extension of Robert's discrete fixed point theorem. Next, we derive an existence theorem of a pure-strategy Nash equilibrium for a noncooperative n-person game from our fixed point theorem. Finally, we show that Kuhn's theorem for a game in expansive form can be explained by our existence theorem.

Original languageEnglish
Article number1340013
JournalAsia-Pacific Journal of Operational Research
Volume30
Issue number3
DOIs
Publication statusPublished - Jun 1 2013

Fingerprint

Fixed point theorem
Contraction mapping
Pure strategy Nash equilibrium
Integer

All Science Journal Classification (ASJC) codes

  • Management Science and Operations Research

Cite this

An application of a discrete fixed point theorem to a game in expansive form. / Kawasaki, Hidefumi; Kira, Akifumi; Kira, Shinpei.

In: Asia-Pacific Journal of Operational Research, Vol. 30, No. 3, 1340013, 01.06.2013.

Research output: Contribution to journalArticle

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