Bayesian Conversations

TL;DR

This paper introduces Bayesian conversations as a model for strategic interactive communication without a mediator, analyzing their structure, optimal protocols, and differences from mediated communication in two-player games.

Contribution

It characterizes the structure of optimal Bayesian conversation protocols, demonstrates the potential necessity of infinite rounds, and compares their capabilities to mediated protocols.

Findings

Optimal protocols can require infinitely many rounds.

In binary settings, optimal protocols are either finite with at most 6 rounds or infinite.

Bayesian conversations can achieve outcomes beyond mediated protocols.

Abstract

We initiate the study of Bayesian conversations, which model interactive communication between two strategic agents without a mediator. We compare this to communication through a mediator and investigate the settings in which a mediation can expand the range of implementable outcomes. We look into the eventual outcome of two-player games after interactive communication. We focus on games where only one agent has a non-trivial action and examine the performance of communication protocols that are individually rational (IR) for both parties. We characterize the structure of the social-welfare optimal protocol of a given number of rounds and thus show a separation between Bayesian conversation and mediated protocols. We demonstrate an example where the optimal conversation protocol requires infinitely many rounds of communication, and further show that for settings with binary actions and binary types, any optimal protocol either is finite (with at most 6 rounds) or requires infinitely many rounds of communication.