Boltzmann type control of opinion consensus through leaders

Abstract

The study of formations and dynamics of opinions leading to the so called opinion consensus is one of the most important areas in mathematical modeling of social sciences. Following the Boltzmann type control recently introduced in [G. Albi, M. Herty, L. Pareschi arXiv:1401.7798], we consider a group of opinion leaders which modify their strategy accordingly to an objective functional with the aim to achieve opinion consensus. The main feature of the Boltzmann type control is that, thanks to an instantaneous binary control formulation, it permits to embed the minimization of the cost functional into the microscopic leaders interactions of the corresponding Boltzmann equation. The related Fokker-Planck asymptotic limits are also derived which allow to give explicit expressions of stationary solutions. The results demonstrate the validity of the Boltzmann type control approach and the capability of the leaders control to strategically lead the followers opinion.

References in corpus (5)

• Multiscale modeling of granular flows with application to crowd dynamics
• Bifurcations and Patterns in Compromise Processes
• Persuasion dynamics
• Freezing and Slow Evolution in a Constrained Opinion Dynamics Model
• Opinion dynamics: rise and fall of political parties

Cited by in corpus (22)

• Invisible control of self-organizing agents leaving unknown environments
• Opinion modeling on social media and marketing aspects
• Opinion dynamics: inhomogeneous Boltzmann-type equations modelling opinion leadership and political segregation
• Kinetic models for optimal control of wealth inequalities
• Kinetic models of collective decision-making in the presence of equality bias
• Kinetic-controlled hydrodynamics for traffic models with driver-assist vehicles
• Model-based assessment of the impact of driver-assist vehicles using kinetic theory
• Kinetic modelling of epidemic dynamics: social contacts, control with uncertain data, and multiscale spatial dynamics
• Uncertainty damping in kinetic traffic models by driver-assist controls
• Mathematical models and methods for crowd dynamics control
• Reducing complexity of multiagent systems with symmetry breaking: an application to opinion dynamics with polls
• Breaking Consensus in Kinetic Opinion Formation Models on Graphons
• Distributed Real-Time Non-Linear Receding Horizon Control Methodology for Multi-Agent Consensus Problems
• Boltzmann and Fokker-Planck equations modelling the Elo rating system with learning effects
• Opinion polarization in human communities can emerge as a natural consequence of beliefs being interrelated
• Control strategies for road risk mitigation in kinetic traffic modelling
• Microscopic modeling and analysis of collective decision making: equality bias leads suboptimal solutions
• A Macroscopic Portfolio Model: From Rational Agents to Bounded Rationality
• Uncertainty quantification and control of kinetic models of tumour growth under clinical uncertainties
• PDE-constrained optimal control of a leader-follower opinion formation model
• A Pontryagin Maximum Principle for agent-based models with convex state space
• Optimal control of a kinetic model describing social interactions on a graph