Stochastic stability of perturbed Learning automata in positive-utility games

Autoren Georgios C. Chasparis
Editoren
Titel Stochastic stability of perturbed Learning automata in positive-utility games
Typ sonst
Ort LEG2019 - Learning, Evolution & Games Conference, Tel Aviv, Israel, June 24-26, 2019.
Monat June
Jahr 2019
SCCH ID# 19005
Abstract

This paper considers a class of reinforcement-based learning (namely, perturbed learning automata) and provides a stochastic-stability analysis in repeatedly-played, positiveutility,finite strategic-form games. Prior work in this class of learning dynamics primarily analyzes asymptotic convergence through stochastic approximations, where convergence can be associated with the limit points of an ordinary-differential equation (ODE). However, analyzing global convergence through an ODE-approximation requires the existence of a Lyapunov or a potential function, which naturally restricts the analysis to a fine class of games. To overcome these limitations, this paper introduces an alternative framework for analyzing asymptotic convergence that is based upon an explicit characterization of the invariant probability measure of the induced Markov chain. We further provide a methodology for computing the invariant probability measure in positive-utility games, together with an illustration in the context of coordination games.