Almost-Rational Learning of Nash Equilibrium without Absolute Continuity

If players learn to play an infinitely repeated game using Bayesian learning, it is known that their strategies eventually approximate Nash equilibria of the repeated game under an absolute-continuity assumption on their prior beliefs.  We suppose here that Bayesian learners do not start with such a "grain of truth", but with arbitrarily low probability they revise beliefs that are performing badly.  We show that this process converges in probability to a Nash equilibrium of the repeated game.