We study a communication game between an informed sender and an uninformed receiver with repeated interactions and voluntary transfers. Transfers motivate the receiver's decision‐making and signal the sender's information. Although full separation can always be supported in equilibrium,...

We present a unified duality approach to Bayesian persuasion. The optimal dual variable, interpreted as a price function on the state space, is shown to be a supergradient of the concave closure of the objective function at the prior belief. Strong duality holds when the objective function is...

We offer a simple analysis of the problem of choosing a statistical experiment to optimize the induced distribution of posterior medians or, more generally, q-quantiles for any q ∈ (0,1). We show that a single experiment-the q-quantile matching experiment-implements all implementable...

We consider a Bayesian persuasion problem where a sender's utility depends only on the expected state. We show that upper censorship that pools the states above a cutoff and reveals the states below the cutoff is optimal for all prior distributions of the state if and only if the sender's...

Using data on essentially every U.S. Supreme Court decision since 1946, we estimate a model of peer effects on the Court. We estimate the impact of justice ideology and justice votes on the votes of their peers. To identify the peer effects, we use two instruments that generate plausibly...