AN APPLICATION OF A DISCRETE FIXED POINT THEOREM TO A GAME IN EXPANSIVE FORM

Hidefumi Kawasaki (), Akifumi Kira () and Shinpei Kira ()
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Hidefumi Kawasaki: Faculty of Mathematics, Kyushu University, Motooka 744, Nishi-ku, Fukuoka 819-0395, Japan
Akifumi Kira: Graduate School of Economics and Management, Tohoku University, 27-1 Kawauchi, Aoba-ku, Sendai, 980-8576, Japan
Shinpei Kira: The Dai-ichi Life Insurance Company Limited, 1-13-1 Yurakucho, Chiyoda-ku, Tokyo, 100-8411, Japan

Asia-Pacific Journal of Operational Research (APJOR), 2013, vol. 30, issue 03, 1-7

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.

Keywords: Discrete fixed point theorem; Nash equilibrium; contraction mapping (search for similar items in EconPapers)
Date: 2013
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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DOI: 10.1142/S0217595913400137

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