Optimal control of the convergence time in the Hegselmann--Krause dynamics

TL;DR

This paper investigates how strategic agents can optimally influence the opinion dynamics in the Hegselmann--Krause model to minimize convergence time, providing bounds and highlighting potential for faster consensus.

Contribution

It introduces a controlled extension of the Hegselmann--Krause model with strategic agents and derives bounds on convergence time under their influence.

Findings

Strategic agents can significantly reduce convergence time.

Provided lower and upper bounds for convergence with strategic influence.

Identified gaps for future research in optimal control strategies.

Abstract

We study the optimal control problem of minimizing the convergence time in the discrete Hegselmann--Krause model of opinion dynamics. The underlying model is extended with a set of strategic agents that can freely place their opinion at every time step. Indeed, if suitably coordinated, the strategic agents can significantly lower the convergence time of an instance of the Hegselmann--Krause model. We give several lower and upper worst-case bounds for the convergence time of a Hegselmann--Krause system with a given number of strategic agents, while still leaving some gaps for future research.