Social Learning over Weakly-Connected Graphs

TL;DR

This paper investigates how asymmetric information flow in weakly-connected social networks impacts collective learning, revealing influence dynamics and potential for control over agents' beliefs.

Contribution

It introduces a theoretical framework for understanding influence in weakly-connected graphs and derives formulas to quantify and potentially control this influence.

Findings

Asymmetric information flow impairs learning in certain agents.

Influential agents can shape beliefs of others, leading to 'mind-control' scenarios.

Closed-form expressions quantify influence dynamics.

Abstract

In this paper, we study diffusion social learning over weakly-connected graphs. We show that the asymmetric flow of information hinders the learning abilities of certain agents regardless of their local observations. Under some circumstances that we clarify in this work, a scenario of total influence (or "mind-control") arises where a set of influential agents ends up shaping the beliefs of non-influential agents. We derive useful closed-form expressions that characterize this influence, and which can be used to motivate design problems to control it. We provide simulation examples to illustrate the results.