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We introduce a new, and quite general variational model for opinion dynamics based on pairwise interaction potentials and a range of opinion evolution protocols ranging from random interactions to global synchronous flows in the opinion…
In this era of fast and large-scale opinion formation, a mathematical understanding of opinion evolution, a.k.a. opinion dynamics, is especially important. Linear graph-based dynamics and bounded confidence dynamics are the two most popular…
In recent years, numerous studies have focused on the mathematical modeling of social dynamics, with self-organization, i.e., the autonomous pattern formation, as the main driving concept. Usually, first or second order models are employed…
The problem of consensus in the presence of adversarially behaving agents has been studied extensively in the literature. The proposed algorithms typically guarantee that the consensus value lies within the convex hull of initial normal…
In this chapter we look at one of the canonical driving examples for multi-agent systems: average consensus. In this scenario, a group of agents seek to agree on the average of their initial states. Depending on the particular application,…
We introduce multi-population opinion dynamics models linked to the bounded confidence model, aiming to explore how interactions between individuals contribute to the emergence of consensus, polarization, or fragmentation. Existing models…
Interest is growing in social learning models where users share opinions and adjust their beliefs in response to others. This paper introduces generalized-bias opinion models, an extension of the DeGroot model, that captures a broader range…
We review in details some recently proposed kinetic models of opinion dynamics. We discuss the several variants including a generalised model. We provide mean field estimates for the critical points, which are numerically supported with…
We investigate how the concepts of optimal control of measurables of a system with a time dependent Hamiltonian may be mixed with the level set technique to keep the desired entity invariant. We derive sets of equations for this purpose and…
The effects of interpersonal interactions on individual's agreements result in a social aggregation process which is reflected in the formation of collective states, as for instance, groups of individuals with a similar opinion about a…
We study a time-delayed variant of the Hegselmann-Krause opinion formation model featuring a small group of leaders and a large group of non-leaders. In this model, leaders influence all agents but only interact among themselves. At the…
We consider stochastic model predictive control of a multi-agent systems with constraints on the probabilities of inter-agent collisions. We first study a sample-based approximation of the collision probabilities and use this approximation…
We study how the opinions of a group of individuals determine their spatial distribution and connectivity, through an agent-based model. The interaction between agents is described by a Potts-like Hamiltonian in which agents are allowed to…
Recently, social phenomena have received a lot of attention not only from social scientists, but also from physicists, mathematicians and computer scientists, in the emerging interdisciplinary field of complex system science. Opinion…
In this paper we model the role of a government of a large population as a mean field optimal control problem. Such control problems are constrainted by a PDE of continuity-type, governing the dynamics of the probability distribution of the…
The study of density-dependent stochastic population processes is important from a historical perspective as well as from the perspective of a number of existing and emerging applications today. In more recent applications of these…
The study of population dynamics originated with early sociological works but has since extended into many fields, including biology, epidemiology, evolutionary game theory, and economics. Most studies on population dynamics focus on the…
We consider the plurality consensus problem among $n$ agents. Initially, each agent has one of $k$ different opinions. Agents choose random interaction partners and revise their state according to a fixed transition function, depending on…
Learning-based control methods typically assume stationary system dynamics, an assumption often violated in real-world systems due to drift, wear, or changing operating conditions. We study reinforcement learning for control under…
Simple yet predictive mathematical models are essential for mechanistic understanding of opinion evolution in social groups. The weighted-median mechanism has recently been proposed as a well-founded alternative to conventional DeGroot-type…