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.
Date issued
2013-07Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science; Massachusetts Institute of Technology. Laboratory for Information and Decision SystemsJournal
Games and Economic Behavior
Publisher
Elsevier
Citation
Candogan, Ozan, Asuman Ozdaglar, and Pablo A. Parrilo. “Dynamics in near-Potential Games.” Games and Economic Behavior 82 (2013): 66–90.
Version: Original manuscript
ISSN
0899-8256