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Title:Refinements of Nash equilibrium in potential games PDF Logo
Authors:Carbonell-Nicolau, Oriol
McLean, Richard P.
Issue Date:2011
Series/Report no.:Working Papers, Department of Economics, Rutgers, the State University of New Jersey 2011,25
Abstract:We prove the existence of strategically stable sets of pure-strategy Nash equilibria (and hence the existence of pure-strategy trembling-hand perfect equilibria) in potential games that admit an upper semicontinuous potential, and we show that generic potential games possess pure-strategy strictly perfect and essential equilibria. In addition, we provide a link between upper semicontinuity of a potential and conditions defined directly on the payoff functions of a potential game. Finally, we show that stable sets and (strictly) perfect equilibria are related to the set of maximizers of a potential, which refines the set of Nash equilibria. Specifically, the set of maximizers of a potential contains a strategically stable set of pure-strategy Nash equilibria (and hence a pure-strategy trembling-hand perfect equilibrium) and, for generic games, any maximizer of a potential is a pure-strategy strictly perfect and essential equilibrium.
Subjects:discontinuous game
potential game
trembling-hand perfect equilibrium
stable set
essential equilibrium
JEL:C72
Document Type:Working Paper
Appears in Collections:Working Papers, Department of Economics, Rutgers University

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