Dynamics in near-potential games |
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Institution: | 1. Institute for Energy Systems, School of Engineering, The University of Edinburgh, The King''s Buildings, Mayfield Road, Edinburgh EH9 2JL, UK;2. Department of Industrial and Systems Engineering, UC Energy Research Center, Pontificia Universidad Católica de Chile, Av. Vicuña Mackenna 4860, Macul, Santiago, Chile;3. The Alan Turing Institute, British Library, 96 Euston Road, London NW1 2DB, UK;1. VITO, Boeretang 200, Mol, Belgium;2. EnergyVille, Thorpark 8310, Genk 3600, Belgium |
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Abstract: | 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. |
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Keywords: | Dynamics in games Near-potential games Best response dynamics Logit response dynamics Fictitious play |
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