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An Application Of A Discrete Fixed Point Theorem To A Game In Expansive Form

Author

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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)

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.

Suggested Citation

  • Hidefumi Kawasaki & Akifumi Kira & Shinpei Kira, 2013. "An Application Of A Discrete Fixed Point Theorem To A Game In Expansive Form," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 30(03), pages 1-7.
    • Handle: RePEc:wsi:apjorx:v:30:y:2013:i:03:n:s0217595913400137
    DOI: 10.1142/S0217595913400137
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    Cited by:

    1. Wang, Hua & Meng, Qiang & Zhang, Xiaoning, 2014. "Game-theoretical models for competition analysis in a new emerging liner container shipping market," Transportation Research Part B: Methodological, Elsevier, vol. 70(C), pages 201-227.
    2. Kazuo Murota, 2016. "Discrete convex analysis: A tool for economics and game theory," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 1(1), pages 151-273, December.

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