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Carbonell-Nicolau, Oriol
McLean, Richard P.
Year of Publication: 
Series/Report no.: 
Working Papers, Department of Economics, Rutgers, the State University of New Jersey 2011,25
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.
discontinuous game
potential game
trembling-hand perfect equilibrium
stable set
essential equilibrium
Document Type: 
Working Paper

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