  This paper considers a class of reinforcement-based learning (namely,
perturbed learning automata) and provides a stochastic-stability analysis in
repeatedly-played, positive-utility, 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.
