Learning in near-potential games
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Ozdaglar_Learning in near.pdf
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190.5 KB
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Author(s)
Candogan, Utku Ozan
Ozdaglar, Asuman E.
Parrilo, Pablo A.
Date Issued
December 2011
Journal
Proceedings on the 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC), 2011
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Candogan, Ozan, Asuman Ozdaglar, and Pablo A. Parrilo. “Learning in Near-potential Games.” 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC), 2011. 2428–2433.
Version
Author's final manuscript
Abstract
Except for special classes of games, there is no systematic framework for analyzing the dynamical properties of multi-agent strategic interactions. Potential games are one such special but restrictive class of games that allow for tractable dynamic analysis. Intuitively, games that are “close” to a potential game should share similar properties. In this paper, we formalize and develop this idea by quantifying to what extent the dynamic features of potential games extend to “near-potential” games. We first show that in an arbitrary finite game, the limiting behavior of better-response and best-response dynamics can be characterized by the approximate equilibrium set of a close potential game. Moreover, the size of this set is proportional to a closeness measure between the original game and the potential game. We then focus on logit response dynamics, which induce a Markov process on the set of strategy profiles of the game, and show that the stationary distribution of logit response dynamics can be approximated using the potential function of a close potential game, and its stochastically stable strategy profiles can be identified as the approximate maximizers of this function. Our approach presents a systematic framework for studying convergence behavior of adaptive learning dynamics in finite strategic form games.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
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Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1109/CDC.2011.6160867
