  We consider distributed learning problem in games with an unknown
cost-relevant parameter, and aim to find the Nash equilibrium while learning
the true parameter. Inspired by the social learning literature, we propose a
distributed non-Bayesian rule to learn the parameter (each agent maintains a
belief on the parameter and updates the belief according to the received noisy
cost), combined with best response dynamics for strategy update. The difficulty
of the analysis lies mainly in the fact that the parameter learning process and
strategy update process are coupled. We first prove that agents' beliefs
converge to a common belief and the strategy profiles converge to a Nash
equilibrium under this common belief. On this basis, we further show that the
beliefs eventually concentrate on the true parameter.
