Related papers: Hegselmann--Krause model with environmental noise
In the Hegselmann-Krause model, an agent updates its opinion by averaging with others whose opinions differ by at most a given confidence threshold. With agents' initial opinions uniformly distributed on the unit interval, we provide a…
The small mass limit is derived for a McKean-Vlasov equation subject to environmental noise with state-dependent friction. By applying the averaging approach to a non-autonomous stochastic slow-fast system with the microscopic and…
A noncooperative differential (dynamic) game model of opinion dynamics is proposed. In this game, the agents' motives are shaped by their expectations of the nature of others' opinions as well as how susceptible they are to get influenced…
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…
We investigate the regularizing effect of certain perturbations by noise in singular interacting particle systems under the mean field scaling. In particular, we show that the addition of a suitably irregular path can regularise these…
Information-communication technology promotes collaborative environments like Wikipedia where, however, controversiality and conflicts can appear. To describe the rise, persistence, and resolution of such conflicts we devise an extended…
Influence of mesoscopic channel noise on excitable dynamics of living cells became a hot subject within the last decade, and the traditional biophysical models of neuronal dynamics such as Hodgkin-Huxley model have been generalized to…
We study the convergence properties of Social Hegselmann-Krause dynamics, a {variant} of the Hegselmann-Krause (HK) model of opinion dynamics where a physical connectivity graph that accounts for the extrinsic factors that could prevent…
Spatially structured neural networks driven by jump diffusion noise with monotone coefficients, fully path dependent delay and with a disorder parameter are considered. Well-posedness for the associated McKean-Vlasov equation and a…
We present a stochastic version of the Cucker-Smale flocking dynamics based on a markovian $N$-particle system of pair interactions with unbounded and, in general, non-Lipschitz continuous interaction potential. We establish the infinite…
In this paper, we present a scalable deep learning approach to solve opinion dynamics stochastic optimal control problems with mean field term coupling in the dynamics and cost function. Our approach relies on the probabilistic…
In many stochastic games stemming from financial models, the environment evolves with latent factors and there may be common noise across agents' states. Two classic examples are: (i) multi-agent trading on electronic exchanges, and (ii)…
A kinetic inhomogeneous Boltzmann-type equation is proposed to model the dynamics of the number of agents in a large market depending on the estimated value of an asset and the rationality of the agents. The interaction rules take into…
We analyze a continuous time multidimensional opinion model where agents have heterogeneous but symmetric and compactly supported interaction functions. We consider Filippov solutions of the resulting dynamics and show strong Lyapunov…
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…
In several real \emph{Multi-Agent Systems} (MAS), it has been observed that only weaker forms of\emph{metastable consensus} are achieved, in which a large majority of agents agree on some opinion while other opinions continue to be…
We consider the problem of parameter estimation for a stochastic McKean-Vlasov equation, and the associated system of weakly interacting particles. We study two cases: one in which we observe multiple independent trajectories of the…
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…
In this paper, we present a numerical approach to solve the McKean-Vlasov equations, which are distribution-dependent stochastic differential equations, under some non-globally Lipschitz conditions for both the drift and diffusion…
Networked multi-agent dynamical systems have been used to model how individual opinions evolve over time due to the opinions of other agents in the network. Particularly, such a model has been used to study how a planning agent can be used…