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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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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DOI: https://doi.org/10.1007/978-3-662-48670-2_11
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