This paper investigates a class of multi-player discrete games where each player aims to maximize its own utility function. Each player does not know the other players' action sets, their deployed actions or the structures of its own or the others' utility functions. Instead, each player only knows its own deployed actions and its received utility values in recent history. We propose a reinforcement learning algorithm which converges to the set of action profiles which have maximal stochastic potential with probability one. Furthermore, an upper bound on the convergence rate is derived and is minimized when the exploration rates are restricted to p-series. The algorithm performance is verified using a case study in the smart grid. (C) 2019 Elsevier Ltd. All rights reserved.