Interactive Communication in Bilateral Trade

TL;DR

This paper models interactive communication in bilateral trade, showing that agents either reach an efficient outcome in finitely many rounds or require infinitely many, with some settings achieving efficiency quickly.

Contribution

It introduces a new model of multi-round communication in bilateral trade and characterizes conditions for finite or infinite communication protocols to achieve efficiency.

Findings

Agents reach efficient outcomes in finitely many rounds in some settings

Optimal protocols may require infinitely many rounds in general

Certain trade settings allow efficient allocation with few communication rounds

Abstract

We define a model of interactive communication where two agents with private types can exchange information before a game is played. The model contains Bayesian persuasion as a special case of a one-round communication protocol. We define message complexity corresponding to the minimum number of interactive rounds necessary to achieve the best possible outcome. Our main result is that for bilateral trade, agents don't stop talking until they reach an efficient outcome: Either agents achieve an efficient allocation in finitely many rounds of communication; or the optimal communication protocol has infinite number of rounds. We show an important class of bilateral trade settings where efficient allocation is achievable with a small number of rounds of communication.