Sender-Receiver Games with Payment Commitments

Abstract

We study sender-receiver games in which players commit, before the state is drawn, to payments contingent on the subsequently verified state and the receiver's action. Payments may be transferred or burned, serving as contractual guarantees or promised tips. We analyze equilibrium guarantees, welfare, and computational complexity. For arbitrary finite action sets, we characterize pessimistic utility guarantees under unilateral commitments. Sender-only and sender-first commitments have worst-equilibrium welfare equal to the best constant-action welfare. Simultaneous commitments can instead reduce welfare below every equilibrium of the original game. Neither simultaneous nor sender-first commitments always admit an efficient equilibrium. Receiver-first commitments always admit an efficiently computable welfare-maximizing equilibrium, but can also reduce worst-equilibrium welfare. For binary actions, we characterize their entire equilibrium payoff region. With binary actions, optimal receiver commitments are computable in linear time, whereas optimizing deterministic sender commitments is NP-hard. Privately randomized sender commitments admit an exact $O(n\log n)$ algorithm, with an optimal lottery over at most two schemes differing at only one state. This yields an additive approximation by deterministic commitments. For arbitrary finite action sets, optimal privately randomized sender payoffs equal Bayesian persuasion values: ordinary persuasion with burning alone, and persuasion with nonnegative compliance payments when transfers are allowed. These equivalences yield polynomial-time algorithms with polynomial-size commitment lotteries.