Optimal Information Design in Sender-Receiver Cheap Talk Interactions

TL;DR

The paper investigates how restricting the sender’s information in sender–receiver cheap-talk games can influence equilibrium outcomes, revealing that under binary actions there exist scenarios where garbling information raises both players’ utilities. It develops an information-design framework with filtered transmissions and derives efficient algorithms: an O(k log k) method to compute a receiver-optimal filter for a single sender, and a linear-programming reduction for two senders, with extensions to many senders via mediator-based insights. A key insight is the structure of Pareto-optimal Nash equilibria, along with the reduction to binary filters and amortized-time incentive checks enabling scalable computation. The results provide practical tools for designing optimal disclosure policies in strategic communication settings and highlight Pareto gains from information design in both transmission and aggregation contexts.

Abstract

This paper considers the dynamics of cheap talk interactions between an oblivious receiver and a sender with different amounts of information. Even though it may seem that having additional information about the state of the game is always beneficial to the sender, we show that there are cases in which garbling the information of a fully informed sender can improve not only receiver's utility in equilibrium, but also that of the sender herself. We also provide efficient algorithms that output the optimal amount of information in sender-receiver scenarios with binary actions and extend some of these results to settings with multiple senders and one receiver.

Theorems & Definitions (20)

• Theorem 1
• Theorem 2
• Theorem 3
• Proposition 1
• Lemma 1
• Corollary 1
• proof : Proof of Lemma \ref{['lemma:char']}
• Proposition 2: Refinement of Proposition \ref{['prop:characterization1']}
• Proposition 3
• proof