Boltzmann games in heterogeneous consensus dynamics

TL;DR

This paper models hierarchical opinion dynamics with competing leaders using Boltzmann-type control, analyzing strategies and asymptotic behavior in heterogeneous follower populations with varying knowledge levels.

Contribution

It introduces a Boltzmann control framework for leader competition in opinion dynamics and explores the impact of knowledge heterogeneity on outcomes.

Findings

Leads to a Fokker-Planck model for asymptotic analysis.

Shows how knowledge heterogeneity affects leader credibility.

Provides insights into strategic behavior in opinion formation.

Abstract

We consider a constrained hierarchical opinion dynamics in the case of leaders' competition and with complete information among leaders. Each leaders' group tries to drive the followers' opinion towards a desired state accordingly to a specific strategy. By using the Boltzmann-type control approach we analyze the best-reply strategy for each leaders' population. Derivation of the corresponding Fokker-Planck model permits to investigate the asymptotic behaviour of the solution. Heterogeneous followers populations are then considered where the effect of knowledge impacts the leaders' credibility and modifies the outcome of the leaders' competition.