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We study "logit dynamics" [Blume, Games and Economic Behavior, 1993] forstrategic games. This dynamics works as follows: at every stage of the game aplayer is selected uniformly at random and she plays according to a "noisy"best-response where the noise level is tuned by a parameter $\beta$. Such adynamics defines a family of ergodic Markov chains, indexed by $\beta$, overthe set of strategy profiles. We believe that the stationary distribution ofthese Markov chains gives a meaningful description of the long-term behaviorfor systems whose agents are not completely rational.  Our aim is twofold: On the one hand, we are interested in evaluating theperformance of the game at equilibrium, i.e. the expected social welfare whenthe strategy profiles are random according to the stationary distribution. Onthe other hand, we want to estimate how long it takes, for a system starting atan arbitrary profile and running the logit dynamics, to get close to itsstationary distribution; i.e., the "mixing time" of the chain.  In this paper we study the stationary expected social welfare for the3-player CK game, for 2-player coordination games, and for two simple$n$-player games. For all these games, we also give almost tight upper andlower bounds on the mixing time of logit dynamics. Our results show twodifferent behaviors: in some games the mixing time depends exponentially on$\beta$, while for other games it can be upper bounded by a functionindependent of $\beta$.

Mixing Time and Stationary Expected Social Welfare of Logit Dynamics