Metastability of Logit Dynamics for Coordination Games

Logit Dynamics [Blume, Games and Economic Behavior, 1993] is a randomized best response dynamics for strategic games: at every time step a player is selected uniformly at random and she chooses a new strategy according to a probability distribution biased toward strategies promising higher payoffs. This process defines an ergodic Markov chain, over the set of strategy profiles of the game, whose unique stationary distribution is the long-term equilibrium concept for the game. However, when the mixing time of the chain is large (e.g. exponential in the number of players), the stationary distribution loses its appeal as equilibrium concept, and the transient phase of the Markov chain becomes important. In several cases it happens that on a time-scale shorter than mixing time the chain is “quasi-stationary”, meaning that it stays close to some small set of the state space, while in a time-scale multiple of the mixing time it jumps from one quasi-stationary configuration to anothe...

• Type: Journal
• Year: 2011
• Where: CORR
• Authors: Vincenzo Auletta, Diodato Ferraioli, Francesco Pasquale, Giuseppe Persiano
• Keywords: Coordination Games, CORR 2011, Education, Logit Dynamics, Markov Chain