Disinformation in the Wald Model

With X. Shi
Working paper (July 2024)

In the classical sequential sampling model of Wald (1945), a decision maker (Alice) learns a binary state from a noisy signal. We study the effects of disinformation by introducing an adversary (Bob) who can pay a cost to distort the signal. Both players are Bayesian, ex-ante symmetrically informed, and share a common prior about the state. Alice wants to choose an action that matches the state, while Bob prefers her to choose a high action regardless of the state. We show that disinformation invariably reduces Alice’s welfare and decision accuracy. Although Bob has an incentive to engage in distortion, it may backfire on him in equilibrium. We also analyze how the distribution of Bob’s distortion cost affects the equilibrium strategies and outcomes of both players. The basis for our results are novel insights into the classic sequential sampling problem with more than two states.