The Perils of Overreaction

TL;DR

This paper explores how agents' overreaction or underreaction to information can be exploited by a malicious principal, revealing a fundamental dichotomy with significant implications for information processing and strategic manipulation.

Contribution

It introduces a novel analysis of the exploitation risks associated with overreaction versus underreaction in Bayesian updating within strategic settings.

Findings

Overreaction allows unbounded exploitation by the principal.

Underreaction prevents exploitation entirely.

A fundamental dichotomy exists between overreaction and underreaction in strategic information scenarios.

Abstract

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.