Commitment and Randomization in Communication

Abstract

When does Sender, in a Sender-Receiver game, strictly value commitment? In a setting with finitely many actions and states, we establish that, generically, commitment has no value if and only if a partitional experiment is optimal. Moreover, if Sender's preferred cheap-talk equilibrium necessarily involves randomization, then Sender values commitment. Our results imply that if a school values commitment to a grading policy, then the school necessarily prefers to grade unfairly. We also ask: for what share of preference profiles does commitment have no value? For any state space, if there are $\left|A\right|$ actions, the share is at least $\frac{1}{\left|A\right|^{\left|A\right|}}$. As the number of states grows large, the share converges precisely to $\frac{1}{\left|A\right|^{\left|A\right|}}$.