Sharing Beliefs to Learn Nash Equilibria

We consider finite games where the agents only share their beliefs on the possible equilibrium configuration. Specifically, the agents experience the strategies of their opponents only as realized parameters, thereby updating and sharing beliefs on the possible configurations iteratively. We show that combining non-bayes updates with best-response dynamics allows the agents to learn the Nash equilibrium, i.e., the belief distribution over the set of parameters has a peak on the true configuration. Convergence results of the learning mechanism are provided in two cases: the agents learn the equilibrium configuration as a whole, or the agents learn those strategies of the opponents that constitute such an equilibrium.