Related papers: Fixed points in models of continuous opinion dynam…
We study the dynamics of opinion formation in the situation where changing opinion involves a cost for the agents. To do so we couple the dynamics of a heterogeneous bounded confidence Hegselmann-Krause model with that of the resources that…
In this paper, we propose a new model for continuous time opinion dynamics on an evolving network. As opposed to existing models, in which the network typically evolves by discretely adding or removing edges, we instead propose a model for…
Krause's model of opinion dynamics has recently been the object of several studies, partly because it is one of the simplest multi-agent systems involving position-dependent changing topologies. In this model, agents have an opinion…
We perform a detailed study of the Hegselmann-Krause bounded confidence opinion dynamics model with heterogeneous confidence $\varepsilon_i$ drawn from uniform distributions in different intervals $[\varepsilon_l, \varepsilon_u]$. The phase…
We study convergence of the following discrete-time non-linear dynamical system: n agents are located in R^d and at every time step, each moves synchronously to the average location of all agents within a unit distance of it. This popularly…
The study of opinions $-$ e.g., their formation and change, and their effects on our society $-$ by means of theoretical and numerical models has been one of the main goals of sociophysics until now, but it is one of the defining topics…
In the consensus model with bounded confidence, studied by Deffuant et al. (2000), two randomly selected people who differ not too much in their opinion both shift their opinions towards each other. Now we restrict this exchange of…
The weighted median mechanism provides a robust alternative to weighted averaging in opinion dynamics. Existing models, however, are predominantly formulated on pairwise interaction graphs, which limits their ability to represent…
We study the Hegselmann-Krause model of opinion dynamics on sparse, unbiased networks generated via Wilson's algorithm, unveiling how network connectivity and confidence bounds jointly determine collective behavior. By systematically…
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…
Recently the theory of noise-induced synchronization of Hegselmann-Krause (HK) dynamics has been well developed. As a typical opinion dynamics of bounded confidence, the HK model obeys a synchronous updating rule, i.e., \emph{all} agents…
Three conjectures from [R. Hegselmann, The Journal of Artificial Societies and Social Simulations 26(4), 11 (2023)] about the Hegselmann-Krause opinion dynamics and the structure of $\epsilon$-switches are proved. The first conjecture…
Individuals who interact with each other in social networks often exchange ideas and influence each other's opinions. A popular approach to study the spread of opinions on networks is by examining bounded-confidence models (BCMs), in which…
When it comes to the mathematical modelling of social interaction patterns, a number of different models have emerged and been studied over the last decade, in which individuals randomly interact on the basis of an underlying graph…
The bounded confidence model represents a widely adopted framework for modeling opinion dynamics wherein actors have a continuous-valued opinion and interact and approach their positions in the opinion space only if their opinions are…
Mean-field equations have been developed recently to approximate the dynamics of the Deffuant model of opinion formation. These equations can describe both fully-mixed populations and the case where individuals interact only along edges of…
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 a tractable opinion dynamics model that generates long-run disagreements and persistent opinion fluctuations. Our model involves an inhomogeneous stochastic gossip process of continuous opinion dynamics in a society consisting of…
Mechanistic and tractable mathematical models play a key role in understanding how social influence shapes public opinions. Recently, a weighted-median mechanism has been proposed as a new micro-foundation of opinion dynamics and validated…
In the compromise model of continuous opinions proposed by Deffuant et al, the states of two agents in a network can start to converge if they are neighbors and if their opinions are sufficiently close to each other, below a given threshold…