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| Title: | | Refinements of Nash equilibrium in potential games  |
| 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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