Search results for "Opinion Dynamics"

Distance-constrained data clustering by combined k-means algorithms and opinion dynamics filters

2014

Data clustering algorithms represent mechanisms for partitioning huge arrays of multidimensional data into groups with small in–group and large out–group distances. Most of the existing algorithms fail when a lower bound for the distance among cluster centroids is specified, while this type of constraint can be of help in obtaining a better clustering. Traditional approaches require that the desired number of clusters are specified a priori, which requires either a subjective decision or global meta–information knowledge that is not easily obtainable. In this paper, an extension of the standard data clustering problem is addressed, including additional constraints on the cluster centroid di…

Complex Networked Systems: Convergence Analysis, Dynamic Behaviour, and Security.

Complex networked systems are a modern reference framework through which very dierent systems from far disciplines, such as biology, computer science, physics, social science, and engineering, can be described. They arise in the great majority of modern technological applications. Examples of real complex networked systems include embedded systems, biological networks, large-scale systems such as power generation grids, transportation networks, water distribution systems, and social network. In the recent years, scientists and engineers have developed a variety of techniques, approaches, and models to better understand and predict the behaviour of these systems, even though several research…

Opinion dynamics, stubbornness and mean-field games

2014

This paper studies opinion dynamics and stubbornness using mean-field game theory. Assuming an initial exponential density function and affine control policies we analyze under what conditions the Fokker-Planck equation returns an exponential density function over the horizon. Consensus and clusters formation are also studied.

Opinion dynamics in coalitional games with transferable utilities

2014

This paper studies opinion dynamics in a large number of homogeneous coalitional games with transferable utilities (TU), where the characteristic function is a continuous-time stochastic process. For each game, which we can see as a “small world”, the players share opinions on how to allocate revenues based on the mean-field interactions with the other small worlds. As a result of such mean-field interactions among small worlds, in each game, a central planner allocates revenues based on the extra reward that a coalition has received up to the current time and the extra reward that the same coalition has received in the other games. The paper also studies the convergence and stability of op…

Opinion dynamics and stubbornness through mean-field games

2013

This paper provides a mean field game theoretic interpretation of opinion dynamics and stubbornness. The model describes a crowd-seeking homogeneous population of agents, under the influence of one stubborn agent. The game takes on the form of two partial differential equations, the Hamilton-Jacobi-Bellman equation and the Kolmogorov-Fokker-Planck equation for the individual optimal response and the population evolution, respectively. For the game of interest, we establish a mean field equilibrium where all agents reach epsilon-consensus in a neighborhood of the stubborn agent's opinion.

Opinion dynamics in social networks through mean field games

2016

Emulation, mimicry, and herding behaviors are phenomena that are observed when multiple social groups interact. To study such phenomena, we consider in this paper a large population of homogeneous social networks. Each such network is characterized by a vector state, a vector-valued controlled input, and a vector-valued exogenous disturbance. The controlled input of each network aims to align its state to the mean distribution of other networks' states in spite of the actions of the disturbance. One of the contributions of this paper is a detailed analysis of the resulting mean-field game for the cases of both polytopic and $mathcal L_2$ bounds on controls and disturbances. A second contrib…

Mean-Field Game Modeling the Bandwagon Effect with Activation Costs

2015

This paper provides a mean-field game theoretic model of the bandwagon effect in social networks. This effect can be observed whenever individuals tend to align their own opinions to a mainstream opinion. The contribution is threefold. First, we describe the opinion propagation as a mean-field game with local interactions. Second, we establish mean-field equilibrium strategies in the case where the mainstream opinion is constant. Such strategies are shown to have a threshold structure. Third, we extend the use of threshold strategies to the case of time-varying mainstream opinion and study the evolution of the macroscopic system.

Opinion Dynamics and Stubbornness via Multi-Population Mean-Field Games

2016

This paper studies opinion dynamics for a set of heterogeneous populations of individuals pursuing two conflicting goals: to seek consensus and to be coherent with their initial opinions. The multi-population game under investigation is characterized by (i) rational agents who behave strategically, (ii) heterogeneous populations, and (iii) opinions evolving in response to local interactions. The main contribution of this paper is to encompass all of these aspects under the unified framework of mean-field game theory. We show that, assuming initial Gaussian density functions and affine control policies, the Fokker---Planck---Kolmogorov equation preserves Gaussianity over time. This fact is t…