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On Characterization of Nash Equilibrium Strategy in Bi-Matrix Games with Set Payoffs

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Set Optimization and Applications - The State of the Art

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 151))

Abstract

In this paper, we consider set-valued payoff bi-matrix games where each player’s payoffs are given by non-empty sets in n-dimensional Euclidean spaces \( \mathbb {R}^{n} \). First, we define several types of set-orderings on the set of all non-empty subsets in \(\mathbb {R}^{n}\). Second, by using these orderings, we define four kinds of concepts of Nash equilibrium strategies to the games and investigate their properties. Finally, we give sufficient conditions for which there exists these types of Nash equilibrium strategy.

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Authors and Affiliations

  1. Faculty of Economics, Kanazawa University, Kakuma–machi, Kanazawa, Ishikawa, 920–1192, Japan

    Takashi Maeda

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  1. Takashi Maeda
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Correspondence to Takashi Maeda .

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Editors and Affiliations

  1. Free University Bozen-Bolzano, Bozen-Bolzano, Italy

    Andreas H Hamel

  2. Freiberg, University of Technology Bergakademie, Freiberg, Germany

    Frank Heyde

  3. Friedrich-Schiller-University Jena, Jena, Germany

    Andreas Löhne

  4. and Business, Vienna University of Economics, Vienna, Austria

    Birgit Rudloff

  5. Free University Bozen-Bolzano, Bozen-Bolzano, Italy

    Carola Schrage

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Maeda, T. (2015). On Characterization of Nash Equilibrium Strategy in Bi-Matrix Games with Set Payoffs. In: Hamel, A., Heyde, F., Löhne, A., Rudloff, B., Schrage, C. (eds) Set Optimization and Applications - The State of the Art. Springer Proceedings in Mathematics & Statistics, vol 151. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48670-2_11

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