On the benefits of being constrained when receiving signals

TL;DR

This paper investigates how constraints on a receiver in a Bayesian persuasion setting can improve their utility, showing that constraints help in binary states but not necessarily in multi-state scenarios.

Contribution

It demonstrates that constraints can enhance receiver utility in binary state settings and explores the limitations of this benefit in multi-state environments.

Findings

Constraints improve utility in binary state cases

The benefit of constraints does not extend straightforwardly to multi-state cases

Explicit example shows limitations in multi-state scenarios

Abstract

We study a Bayesian persuasion setting in which the receiver is trying to match the (binary) state of the world. The sender's utility is partially aligned with the receiver's, in that conditioned on the receiver's action, the sender derives higher utility when the state of the world matches the action. Our focus is on whether, in such a setting, being constrained helps a receiver. Intuitively, if the receiver can only take the sender's preferred action with a smaller probability, the sender might have to reveal more information, so that the receiver can take the action more specifically when the sender prefers it. We show that with a binary state of the world, this intuition indeed carries through: under very mild non-degeneracy conditions, a more constrained receiver will always obtain (weakly) higher utility than a less constrained one. Unfortunately, without additional assumptions, the result does not hold when there are more than two states in the world, which we show with an explicit example.