A Game Approach to Multi-dimensional Opinion Dynamics in Social Networks with Stubborn Strategist Agents

TL;DR

This paper models multi-dimensional opinion dynamics in social networks using a differential game approach, deriving equilibrium strategies for strategist agents and comparing them with social optimality.

Contribution

It introduces a novel differential game model for multi-topic opinion formation with strategist agents and provides a distributed method for computing equilibrium strategies.

Findings

Unique Nash/worst-case equilibrium solutions derived.

Distributed implementation of strategies proposed.

Comparison between strategic and social optimality opinions conducted.

Abstract

In a social network, individuals express their opinions on several interdependent topics, and therefore the evolution of their opinions on these topics is also mutually dependent. In this work, we propose a differential game model for the multi-dimensional opinion formation of a social network whose population of agents interacts according to a communication graph. Each individual's opinion evolves according to an aggregation of disagreements between the agent's opinions and its graph neighbors on multiple interdependent topics exposed to an unknown extraneous disturbance. For a social network with strategist agents the opinions evolve over time with respect to the minimization of a quadratic cost function that solely represents each individual's motives against the disturbance. We find the unique Nash/worst-case equilibrium solution for the proposed differential game model of coupled multi-dimensional opinions under an open-loop information structure. Moreover, we propose a distributed implementation of the Nash/worst-case equilibrium solution. We examine the non-distributed and proposed distributed open-loop Nash/worst-case strategies on a small social network with strategist agents in a two-dimensional opinion space. Then we compare the opinions evolved based on the Nash/worst-case strategy with the opinions corresponding to social optimality actions for non-strategist agents.