Learning to agree over large state spaces

TL;DR

This paper investigates how consensus emerges in large, complex state spaces through rational dialogues among agents with private signals, emphasizing the importance of communication structure and dialogue length.

Contribution

It generalizes classical models by removing assumptions on state space size and introduces conditions under which consensus always occurs in large, asymmetric information settings.

Findings

Consensus is guaranteed if communication is complete and reciprocal.

Transfinite dialogues are essential for reaching agreement.

The model extends classical rational dialogue frameworks to larger state spaces.

Abstract

We study how a consensus emerges in a finite population of like-minded individuals who are asymmetrically informed about the realization of the true state of the world. Agents observe a private signal about the state and then start exchanging messages. Generalizing the classical model of rational dialogues of Geanakoplos and Polemarchakis (1982) and its subsequent extensions, we dispense with the standard assumption that the state space is a probability space and we do not put any bound on the cardinality of the state space itself or the information partitions. We show that a class of rational dialogues can be found that always lead to consensus provided that three main conditions are met. First, everybody must be able to send messages to everybody else, either directly or indirectly. Second, communication must be reciprocal. Finally, agents need to have the opportunity to engage in dialogues of transfinite length.