Refinements of Nash equilibrium in potential games - Oriol Carbonell-Nicolau; Richard P. McLean (Rutgers University, Department of Economics, 2011)
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.
Keywords: C72; 330; discontinuous game; potential game; trembling-hand perfect equilibrium; stable set; essential equilibrium; Kooperatives Spiel; Nash-Gleichgewicht; Theorie