In a companion paper [`Learning to play equilibrium', Northwestern University, Evanston (1990)], the authors show that utility maximizing players, holding subjective beliefs about their opponents' strategies in an infinitely repeated game, must converge to a subjective equilibrium. At such an equilibrium, players' forecasts on the actual future play of the game are accurate, even if their conjectures regarding opponents' overall strategies are not. The current paper shows that a subjective equilibrium, even if perturbed, plays like (induces the same distribution on play paths) a Nash equilibrium. Thus, convergence to a Nash equilibrium is assured.