An Algorithm for Computing Stochastically Stable Distributions with Applications to Multiagent Learning in Repeated Games

One of the proposed solutions to the equi- librium selection problem for agents learning in repeated games is obtained via the notion of stochastic stability. Learning algorithms are perturbed so that the Markov chain un- derlying the learning dynamics is necessarily irreducible and yields a unique stable distri- bution. The stochastically stable distribution is the limit of these stable distributions as the perturbation rate tends to zero. We present the first exact algorithm for computing the stochastically stable distribution of a Markov chain. We use our algorithm to predict the long-term dynamics of simple learning algo- rithms in sample repeated games.