Related papers: The Hegselmann-Krause dynamics for continuous agen…
This paper introduces a new multidimensional extension of the Hegselmann-Krause (HK) opinion dynamics model, where opinion proximity is not determined by a norm or metric. Instead, each agent trusts opinions within the Minkowski sum…
Models of continuous opinion dynamics under bounded confidence show a sharp transition between a consensus and a polarization phase at a critical global bound of confidence. In this paper, heterogeneous bounds of confidence are studied. The…
Recently, significant attention has been dedicated to the models of opinion dynamics in which opinions are described by real numbers, and agents update their opinions synchronously by averaging their neighbors' opinions. The neighbors of…
We consider the Hegselmann-Krause model for opinion dynamics and study the evolution of the system under various settings. We first analyze the termination time of the synchronous Hegselmann-Krause dynamics in arbitrary finite dimensions…
This paper focuses on the opinion dynamics under the influence of manipulative agents. This type of agents is characterized by the fact that their opinions follow a trajectory that does not respond to the dynamics of the model, although it…
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…
Hegselmann--Krause models are localized, distributed averaging dynamics on spatial data. A key aspect of these dynamics is that they lead to cluster formation, which has important applications in geographic information systems, dynamic…
We study the consensus formation for an agents based model, generalizing that originally proposed by Krause \cite{Kr}, by allowing the communication channels between any couple of agents to be switched on or off randomly, at each time step,…
We consider the Hegselmann-Krause bounded confidence dynamics for n equally spaced opinions on the real line, with gaps equal to the confidence bound r, which we take to be 1. We prove rigorous results on the evolution of this…
In the consensus model of Krause-Hegselmann, opinions are real numbers between 0 and 1 and two agents are compatible if the difference of their opinions is smaller than the confidence bound parameter \epsilon. A randomly chosen agent takes…
This paper presents a theoretical convergence analysis for an opinion-action coevolution model that integrates the opinion updating rule of the Hegselmann-Krause model with a utility-based decision-making mechanism. The model is…
The Hegselmann-Krause (HK) model allows one to characterize the continuous change of agents' opinions with the bounded confidence threshold $\varepsilon$. To consider the heterogeneity of agents in characteristics, we study the HK model on…
We study generalizations of the Hegselmann-Krause (HK) model for opinion dynamics, incorporating features and parameters that are natural components of observed social systems. The first generalization is one where the strength of influence…
The Hegselmann-Krause (HK) model of opinion dynamics describes how opinions held by individuals in a community change over time in response to the opinions of others and their access to the true value, T, to which these opinions relate.…
We present a model of opinion dynamics in which agents adjust continuous opinions as a result of random binary encounters whenever their difference in opinion is below a given threshold. High thresholds yield convergence of opinions towards…
We consider a variant of the Hegselmann-Krause model of consensus formation where information between agents propagates with a finite speed $\mathfrak{c}$. This leads to a system of ordinary differential equations (ODE) with state-dependent…
Motivated by various random variations of Hegselmann-Krause model for opinion dynamics and gossip algorithm in an endogenously changing environment, we propose a general framework for the study of endogenously varying random averaging…
Opinion dynamics of random-walking agents on finite two-dimensional lattices is studied. In the model, the opinion is continuous, and both the lattice and the opinion can be either periodic or non-periodic. At each time step, all agents…
We give an elementary proof of a conjecture by Hegselmann and Krause in opinion dynamics, concerning a symmetric bounded confidence interval model: If there is a truth and all individuals take each other seriously by a positive amount…
The dynamics of the model of agents with limited confidence introduced by Hegselmann and Krause exhibits multiple well-separated regimes characterised by the number of distinct clusters in the stationary state. We present indications that…