Dynamics in near-potential games
AbstractWe 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.
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Bibliographic InfoArticle provided by Elsevier in its journal Games and Economic Behavior.
Volume (Year): 82 (2013)
Issue (Month): C ()
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Web page: http://www.elsevier.com/locate/inca/622836
Dynamics in games; Near-potential games; Best response dynamics; Logit response dynamics; Fictitious play;
Find related papers by JEL classification:
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
- D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search, Learning, and Information
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