Learning to Collude : A Partial Folk Theorem for Smooth Fictitious Play

We propose an extension to smooth fictitious play and prove that play converges to an ε-Markov perfect equilibrium with probability one in a class of stochastic games known as Markov potential games. We then prove a partial Folk theorem for repeated games under one-period perfect monitoring. We show that through repeated interactions, decentralized learning algorithms can learn to both define the terms of a collusive arrangement and to implement that arrangement