Asymptotic Learning on Bayesian Social Networks

TL;DR

This paper investigates how agents in social networks learn a binary state through repeated observations, identifying conditions that ensure asymptotic learning as the network size grows.

Contribution

It provides sufficient conditions for asymptotic learning on large social networks and constructs examples where learning fails without these conditions.

Findings

Sufficient conditions for asymptotic learning are identified.

Examples are constructed where learning does not occur without these conditions.

The study advances understanding of information aggregation in large networks.

Abstract

Understanding information exchange and aggregation on networks is a central problem in theoretical economics, probability and statistics. We study a standard model of economic agents on the nodes of a social network graph who learn a binary "state of the world" S, from initial signals, by repeatedly observing each other's best guesses. Asymptotic learning is said to occur on a family of graphs G_n = (V_n, E_n), with |V_n| tending to infinity, if with probability tending to 1 as n tends to infinity all agents in G_n eventually estimate S correctly. We identify sufficient conditions for asymptotic learning and contruct examples where learning does not occur when the conditions do not hold.