Misinformation and Optimal Time to Detect

We study a continuous-time reputation game in which an informed player bene ts from persistent private information while an uninformed player suffers from it. Observing noisy signals of the informed player's actions, the uninformed player chooses when to reveal the informed player's private information, but revelation is costly. We characterize the sequential equilibrium in Markov strategies, provide comparative statistics of equilibrium, and study the probability that the uninformed player reveals the informed player's private information. In addition, we contrast our model with Kyletype models in terms of informativeness of signals and analyze the extended model in which observation is costly