Refinements of Nash equilibrium in potential games
AbstractWe 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.
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Bibliographic InfoPaper provided by Rutgers University, Department of Economics in its series Departmental Working Papers with number 201125.
Length: 20 pages
Date of creation: 06 Jun 2011
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discontinuous game; potential game; trembling-hand perfect equilibrium; stable set; essential equilibrium;
Other versions of this item:
- Carbonell-Nicolau, Oriol & McLean, Richard P., 0. "Refinements of Nash equilibrium in potential games," Theoretical Economics, Econometric Society.
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-12-13 (All new papers)
- NEP-GTH-2011-12-13 (Game Theory)
- NEP-MIC-2011-12-13 (Microeconomics)
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