Dynamics in near-potential games
Author(s)Candogan, Utku Ozan; Koksal, Asuman E.; Parrilo, Pablo A
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We consider discrete-time learning dynamics in finite strategic form games, and show that games that are close to a potential game inherit many of the dynamical properties of potential games. We first study the evolution of the sequence of pure strategy profiles under better/best response dynamics. We show that this sequence converges to a (pure) approximate equilibrium set whose size is a function of the “distance” to a given nearby potential game. We then focus on logit response dynamics, and provide a characterization of the limiting outcome in terms of the distance of the game to a given potential game and the corresponding potential function. Finally, we turn attention to fictitious play, and establish that in near-potential games the sequence of empirical frequencies of player actions converges to a neighborhood of (mixed) equilibria, where the size of the neighborhood increases according to the distance to the set of potential games.
DepartmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science; Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
Games and Economic Behavior
Candogan, Ozan, Asuman Ozdaglar, and Pablo A. Parrilo. “Dynamics in near-Potential Games.” Games and Economic Behavior 82 (2013): 66–90.