  We study "logit dynamics" [Blume, Games and Economic Behavior, 1993] for
strategic games. This dynamics works as follows: at every stage of the game a
player 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 a
dynamics defines a family of ergodic Markov chains, indexed by $\beta$, over
the set of strategy profiles. We believe that the stationary distribution of
these Markov chains gives a meaningful description of the long-term behavior
for systems whose agents are not completely rational.
  Our aim is twofold: On the one hand, we are interested in evaluating the
performance of the game at equilibrium, i.e. the expected social welfare when
the strategy profiles are random according to the stationary distribution. On
the other hand, we want to estimate how long it takes, for a system starting at
an arbitrary profile and running the logit dynamics, to get close to its
stationary distribution; i.e., the "mixing time" of the chain.
  In this paper we study the stationary expected social welfare for the
3-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 and
lower bounds on the mixing time of logit dynamics. Our results show two
different behaviors: in some games the mixing time depends exponentially on
$\beta$, while for other games it can be upper bounded by a function
independent of $\beta$.
