Nonconvergence to saddle boundary points under perturbed reinforcement learning

For several classes of reinforcement learning schemes, convergence to action profiles that are not Nash equilibria may occur with positive probability under certain conditions on the payoff function. In this paper, we explore how an alternative reinforcement learning scheme, where the strategy of each agent is also perturbed by a strategy-dependent perturbation (or mutations) function, may exclude convergence to non-Nash pure strategy profiles. This approach extends prior analysis on reinforcement learning in games that addresses the issue of convergence to saddle boundary points. It further provides a framework under which the effect of mutations can be analyzed in the context of reinforcement learning. JEL classifications: C72, C73, D83