Reputation building with endogenous speed of learning

I study reputation models in which information about the long-run player's past behavior is dispersed among short-run players. I identify two challenges to reputation building when such information is aggregated via the short-run players' actions. First, when the long-run player's action can only affect short-run players' future behaviors, the informativeness of short-run players' actions decreases when the long-run player becomes more patient. This leads to equilibria in which both players receive low payoffs. Second, when each short-run player can also observe an informative signal about the long-run player's current period action, I propose a resistent to learning condition under which reputation fails. This is because the short-run player's action can be uninformative about the long-run player's type in periods where the latter receives a low payoff. When the environment is not resistent to learning, the patient long-run player can secure his commitment payoff in all equilibria.