We consider large systems composed of stategic players and look at ways of describing their long term behaviour. We give evidence that the notion of a Nash equilibrium is not a completely satisfactory answer to this question and propose to look at the stationary equilibrium induced by the logit dynamics . Here at every stage of the game a player is selected uniformly at random and she plays according to a noisy best-response dynamics where the noise level is tuned by a parameter β. Such a dynamics defines a family of ergodic Markov chains, indexed by β, over the set of strategy profiles. Being ergodic, the induced Markov chain admits a unique stationary distribution and, for any possible initial state, the chain approaches the stationary distribution. For games for which the mixing time is polynomial in the number of players, the stationary distribution can be taken as descriptive of the behaviour of system (having to discount only the short transient initial period). We show that for ptential games, the mixing time is related to properties of the potential landscape. For games for which the mixing time is super-polynomial, the system will spend to much time out of equilibrium and thus we look at metastable distributions for such systems. Joint work with: Vincenzo Auletta, Diodato Ferraioli, Francesco Pasquale and Paolo Penna [2,1,3]. © 2012 Springer-Verlag Berlin Heidelberg.
|Titolo:||Stability and metastability of the logit dynamics of strategic games|
|Data di pubblicazione:||2012|
|Appare nelle tipologie:||4.1 Contributi in Atti di convegno|