Information Percolation

TL;DR

This paper models how information spreads among many agents who are randomly matched over time, providing explicit dynamics and showing exponential convergence of beliefs independent of group size.

Contribution

It offers an explicit solution for the belief distribution dynamics and demonstrates that convergence rate depends only on individual matching frequency.

Findings

Belief distribution converges exponentially to a common posterior.

Convergence rate is independent of group size.

Rate equals the mean individual matching rate.

Abstract

For a setting in which a large number of asymmetrically informed agents are randomly matched into groups over time, exchanging their information with each other when matched, we provide an explicit solution for the dynamics of the cross-sectional distribution of posterior beliefs. We also show that convergence of the cross-sectional distribution of beliefs to a common posterior is exponential and that the rate of convergence does not depend on the size of the groups of agents that meet. The rate of convergence is merely the mean rate at which an individual agent is matched.