The Perils of Overreaction

In order to study updating rules, we consider the problem of a malevolent principal screening an imperfectly Bayesian agent. We uncover a fundamental dichotomy between underreaction and overreaction to information. If an agent’s posterior is farther away from the prior than it should be under Bayes’ law, she can always be exploited by the principal to an unfettered degree: the agent’s ex ante expected loss can be made arbitrarily large. In stark contrast, an agent who underreacts (whose posterior is closer to the prior than the Bayesian posterior) cannot be exploited at all.