  We study learning dynamics induced by strategic agents who repeatedly play a
game with an unknown payoff-relevant parameter. In this dynamics, a belief
estimate of the parameter is repeatedly updated given players' strategies and
realized payoffs using Bayes's rule. Players adjust their strategies by
accounting for best response strategies given the belief. We show that, with
probability 1, beliefs and strategies converge to a fixed point, where the
belief consistently estimates the payoff distribution for the strategy, and the
strategy is an equilibrium corresponding to the belief. However, learning may
not always identify the unknown parameter because the belief estimate relies on
the game outcomes that are endogenously generated by players' strategies. We
obtain sufficient and necessary conditions, under which learning leads to a
globally stable fixed point that is a complete information Nash equilibrium. We
also provide sufficient conditions that guarantee local stability of fixed
point beliefs and strategies.
