Refinements of Nash equilibrium in potential games

Oriol Carbonell-Nicolau and Richard McLean

Departmental Working Papers from Rutgers University, Department of Economics

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 payo ff 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.

Keywords: discontinuous game; potential game; trembling-hand perfect equilibrium; stable set; essential equilibrium (search for similar items in EconPapers)
JEL-codes: C72 (search for similar items in EconPapers)
Pages: 20 pages
Date: 2011-06-06
New Economics Papers: this item is included in nep-gth and nep-mic
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Journal Article: Refinements of Nash equilibrium in potential games (2014)
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Persistent link: https://EconPapers.repec.org/RePEc:rut:rutres:201125

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