Gaussian Learning-Without-Recall in a Dynamic Social Network

TL;DR

This paper studies how rational, memoryless agents in a dynamic social network learn the true state of the world through noisy signals, showing they reach truthful consensus under certain conditions with polynomial convergence.

Contribution

It demonstrates that Gaussian priors and bounded truth signals lead to almost sure truthful consensus with polynomial convergence, highlighting the impact of network structure.

Findings

Agents reach truthful consensus almost surely.

High outdegree can slow down learning.

Bounded truth-hearing frequency is essential for convergence.

Abstract

We analyze the dynamics of the Learning-Without-Recall model with Gaussian priors in a dynamic social network. Agents seeking to learn the state of the world, the "truth", exchange signals about their current beliefs across a changing network and update them accordingly. The agents are assumed memoryless and rational, meaning that they Bayes-update their beliefs based on current states and signals, with no other information from the past. The other assumption is that each agent hears a noisy signal from the truth at a frequency bounded away from zero. Under these conditions, we show that the system reaches truthful consensus almost surely with a convergence rate that is polynomial in expectation. Somewhat paradoxically, high outdegree can slow down the learning process. The lower-bound assumption on the truth-hearing frequency is necessary: even infinitely frequent access to the truth offers no guarantee of truthful consensus in the limit.