The Perils of Overreaction

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, for some signal realization, the agent's updating rule produces a posterior that lies outside the convex hull of the Bayesian posteriors induced by the signal structure, she can be exploited by the principal without bound: Her ex ante expected loss can be made arbitrarily large. In contrast, an agent who underreacts—whose posterior after each signal realization lies between the prior and the corresponding Bayesian posterior—cannot be exploited at all. (JEL D82, D83)