Mediated Cheap Talk Design (with proofs)

TL;DR

This paper investigates an information design framework with uncommitted senders and a mediator, characterizing equilibrium outcomes and providing efficient algorithms for optimal strategies for both senders and the receiver.

Contribution

It introduces a novel model of mediated cheap talk with uncommitted senders, characterizes implementable distributions, and offers efficient computation methods for optimal equilibria.

Findings

Characterization of implementable action distributions in equilibrium.

An $O(n ext{log} n)$ algorithm for computing optimal sender equilibria.

A simple revelation mechanism achieves the receiver's optimal equilibrium.

Abstract

We study an information design problem with two informed senders and a receiver in which, in contrast to traditional Bayesian persuasion settings, senders do not have commitment power. In our setting, a trusted mediator/platform gathers data from the senders and recommends the receiver which action to play. We characterize the set of implementable action distributions that can be obtained in equilibrium, and provide an $O(n \log n)$ algorithm (where $n$ is the number of states) that computes the optimal equilibrium for the senders. Additionally, we show that the optimal equilibrium for the receiver can be obtained by a simple revelation mechanism.