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Metastability of Asymptotically Well-Behaved Potential Games

(Extended Abstract)
  • Diodato Ferraioli
  • Carmine Ventre
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9235)

Abstract

One of the main criticisms to game theory concerns the assumption of full rationality. Logit dynamics is a decentralized algorithm in which a level of irrationality (a.k.a. “noise”) is introduced in players’ behavior. In this context, the solution concept of interest becomes the logit equilibrium, as opposed to Nash equilibria. Logit equilibria are distributions over strategy profiles that possess several nice properties, including existence and uniqueness. However, there are games in which their computation may take exponential time. We therefore look at an approximate version of logit equilibria, called metastable distributions, introduced by Auletta et al. [4]. These are distributions which remain stable (i.e., players do not go too far from it) for a large number of steps (rather than forever, as for logit equilibria). The hope is that these distributions exist and can be reached quickly by logit dynamics.

We identify a class of potential games, that we name asymptotically well-behaved, for which the behavior of the logit dynamics is not chaotic as the number of players increases, so to guarantee meaningful asymptotic results. We prove that any such game admits distributions which are metastable no matter the level of noise present in the system, and the starting profile of the dynamics. These distributions can be quickly reached if the rationality level is not too big when compared to the inverse of the maximum difference in potential. Our proofs build on results which may be of independent interest, including some spectral characterizations of the transition matrix defined by logit dynamics for generic games and the relationship among convergence measures for Markov chains.

Keywords

Markov Chain Nash Equilibrium Stationary Distribution Strategy Profile Coordination Game 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

This work is supported by PRIN 2010-2011 project ARS TechnoMedia and EPSRC grant EP/M018113/1. Authors wish to thank Paul W. Goldberg for many invaluable discussions related to a number of results discussed in this paper, and an anonymous reviewer for the enlightening comments on an earlier version of this work.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Dipartimento di InformaticaUniversità di SalernoSalernoItaly
  2. 2.School of ComputingTeesside UniversityMiddlesbroughUK

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