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In this paper we consider the modeling of opinion dynamics over time dependent large scale networks. A kinetic description of the agents' distribution over the evolving network is considered which combines an opinion update based on binary…

Numerical Analysis · Mathematics 2016-04-05 Giacomo Albi , Lorenzo Pareschi , Mattia Zanella

In this paper, we investigate the interaction of two populations with a large number of indistinguishable agents. The problem consists in two levels: the interaction between agents of a same population, and the interaction between the two…

Optimization and Control · Mathematics 2018-10-30 Alain Bensoussan , Tao Huang , Mathieu Laurière

We introduce a 2-state opinion dynamics model where agents evolve by majority rule. In each update, a group of agents is specified whose members then all adopt the local majority state. In the mean-field limit, where a group consists of…

Statistical Mechanics · Physics 2009-11-10 P. L. Krapivsky , S. Redner

We investigate a dynamical model of opinion formation in which an individual's opinion is influenced by interactions with a group of other agents. We introduce a bias towards one of the opinions in a manner not considered earlier to the…

Physics and Society · Physics 2024-09-17 Pratik Mullick , Parongama Sen

We present an opinion dynamics model framework discarding two common assumptions in the literature: (a) that there is direct influence between beliefs of neighbouring agents, and (b) that agent belief is static in the absence of social…

Physics and Society · Physics 2023-05-17 Benedikt V. Meylahn , Christa Searle

We study discrete-time, finite-state mean-field games (MFGs) under model uncertainty, where agents face ambiguity about the state transition probabilities. Each agent maximizes its expected payoff against the worst-case transitions within…

Optimization and Control · Mathematics 2026-01-21 Zongxia Liang , Zhou Zhou , Yaqi Zhuang , Bin Zou

Modelling efforts in opinion dynamics have to a large extent ignored that opinion exchange between individuals can also have an effect on how willing they are to express their opinion publicly. Here, we introduce a model of public opinion…

Physics and Society · Physics 2020-10-14 Felix Gaisbauer , Eckehard Olbrich , Sven Banisch

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…

Analysis of PDEs · Mathematics 2026-03-31 Young-Pil Choi , Chiara Cicolani , Cristina Pignotti

This paper focuses on the role of a government of a large population of interacting agents as a mean field optimal control problem derived from deterministic finite agent dynamics. The control problems are constrained by a PDE of…

Analysis of PDEs · Mathematics 2020-11-17 Massimo Fornasier , Stefano Lisini , Carlo Orrieri , Giuseppe Savaré

We consider two-opinion voter models on dense dynamic random graphs. Our goal is to understand and describe the occurrence of consensus versus polarisation over long periods of time. The former means that all vertices have the same opinion,…

Probability · Mathematics 2024-10-29 Simone Baldassarri , Peter Braunsteins , Frank den Hollander , Michel Mandjes

In this work, we systematically investigate mean field games and mean field type control problems with multiple populations using a coupled system of forward-backward stochastic differential equations of McKean-Vlasov type stemming from…

Probability · Mathematics 2020-11-03 Masaaki Fujii

We investigate the effects of external and autonomous global interaction fields on an adaptive network of social agents with an opinion formation dynamics based on a simple imitation rule. We study the competition between global fields and…

Physics and Society · Physics 2022-09-07 Mario G. Cosenza , José L. Herrera-Diestra

The statement of the mean field approximation theorem in the mean field theory of Markov processes particularly targets the behaviour of population processes with an unbounded number of agents. However, in most real-world engineering…

Probability · Mathematics 2017-05-11 Mahmoud Talebi , Jan Friso Groote , Jean-Paul Linnartz

The spread of an epidemic disease and the population's collective behavioural response are deeply intertwined, influencing each other's evolution. Such a co-evolution typically has been overlooked in mathematical models, limiting their…

Dynamical Systems · Mathematics 2024-10-24 Kathinka Frieswijk , Lorenzo Zino , Mengbin Ye , Alessandro Rizzo , Ming Cao

A broad range of dynamical systems involve multi-body interactions, or group interactions, which may not be encoded in traditional graphical structures. In this work, we focus on a canonical example from opinion dynamics, the Majority Rule,…

Physics and Society · Physics 2021-09-01 James Noonan , Renaud Lambiotte

We consider mean-field control problems in discrete time with discounted reward, infinite time horizon and compact state and action space. The existence of optimal policies is shown and the limiting mean-field problem is derived when the…

Optimization and Control · Mathematics 2025-10-16 Nicole Bäuerle

This paper is concerned with developing mean-field game models for the evolution of epidemics. Specifically, an agent's decision -- to be socially active in the midst of an epidemic -- is modeled as a mean-field game with health-related…

Optimization and Control · Mathematics 2021-11-23 S. Yagiz Olmez , Shubham Aggarwal , Jin Won Kim , Erik Miehling , Tamer Başar , Matthew West , Prashant G. Mehta

The mean-field limit in a weakly interacting stochastic many-particle system for multiple population species in the whole space is proved. The limiting system consists of cross-diffusion equations, modeling the segregation of populations.…

Analysis of PDEs · Mathematics 2019-09-04 Li Chen , Esther S. Daus , Ansgar Jüngel

The formation of opinions in a large population is governed by endogenous (human interactions) and exogenous (media influence) factors. In the analysis of opinion evolution in a large population, decision making rules can be approximated…

Dynamical Systems · Mathematics 2012-05-08 Anahita Mirtabatabaei , Peng Jia , Francesco Bullo

Empirically derived continuum models of collective behavior among large populations of dynamic agents are a subject of intense study in several fields, including biology, engineering and finance. We formulate and study a mean-field game…

Adaptation and Self-Organizing Systems · Physics 2018-06-22 Piyush Grover , Kaivalya Bakshi , Evangelos A. Theodorou