Belief Control Strategies for Interactions over Weakly-Connected Graphs

TL;DR

This paper investigates how influential agents can control beliefs in weakly-connected social networks, analyzing the extent of their influence and proposing mechanisms for belief steering despite structural limitations.

Contribution

It provides a detailed analysis of belief control limits and introduces mechanisms enabling influential agents to steer beliefs regardless of local observations.

Findings

Influential agents can significantly shape beliefs within network limits.

Structural constraints limit but do not entirely prevent belief control.

Proposed mechanisms enable belief steering despite network restrictions.

Abstract

In diffusion social learning over weakly-connected graphs, it has been shown recently that influential agents shape the beliefs of non-influential agents. This paper analyzes this mechanism more closely and addresses two main questions. First, the article examines how much freedom influential agents have in controlling the beliefs of the receiving agents, namely, whether receiving agents can be driven to arbitrary beliefs and whether the network structure limits the scope of control by the influential agents. Second, even if there is a limit to what influential agents can accomplish, this article develops mechanisms by which they can lead receiving agents to adopt certain beliefs. These questions raise interesting possibilities about belief control over networked agents. Once addressed, one ends up with design procedures that allow influential agents to drive other agents to endorse particular beliefs regardless of their local observations or convictions. The theoretical findings are illustrated by means of examples.