Reputation Effects: Robustness and Fragility

Reputation building depends on how evidence is parsed. I revisit the canonical reputation framework in which a long-lived player, either strategic or committed to a fixed action distribution, faces a sequence of short-lived players. I ask whether reputation effects are robust to short-lived players' slight misspecification of the signal process under commitment. I show that the relevant robustness test is not finite-sample correctness, but entropy-rate control of likelihoods along arbitrarily long reputation-building histories. If a misspecification satisfies this control, reputation effects survive. If it fails, they can collapse even when the misspecification is invisible on every fixed finite horizon.