Directed graphical structure,Nash equilibrium,and potential games |
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Authors: | Shuige Liu |
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Affiliation: | Faculty of Political Science and Economics, Waseda University, 1-6-1 Nishi-Waseda, Shinjuku-Ku, 169-8050, Tokyo, Japan |
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Abstract: | This paper considers the directed graphical structure of a game, called influence structure, where a directed edge from player to player indicates that player may be able to affect ’s payoff via his unilateral change of strategies. We give a necessary and sufficient condition for the existence of pure-strategy Nash equilibrium of games having a directed graph in terms of the structure of that graph. We also discuss the relationship between the structure of graphs and potential games. |
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Keywords: | Directed graphical games Pure-strategy Nash equilibrium Potential games |
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