In this paper, I construct players' prior beliefs and show that these prior beliefs lead the players to learn to play an approximate Nash equilibrium uniformly in any infinitely repeated slightly perturbed game with discounting and perfect monitoring. That is, given any ε > 0, there exists a (single) profile of players' prior beliefs that leads play to almost surely converge to an ε-Nash equilibrium uniformly for any (finite normal form) stage game with slight payoff perturbation and any discount factor less than 1.