17,581 research outputs found
On symmetric continuum opinion dynamics
This paper investigates the asymptotic behavior of some common opinion
dynamic models in a continuum of agents. We show that as long as the
interactions among the agents are symmetric, the distribution of the agents'
opinion converges. We also investigate whether convergence occurs in a stronger
sense than merely in distribution, namely, whether the opinion of almost every
agent converges. We show that while this is not the case in general, it becomes
true under plausible assumptions on inter-agent interactions, namely that
agents with similar opinions exert a non-negligible pull on each other, or that
the interactions are entirely determined by their opinions via a smooth
function.Comment: 28 pages, 2 figures, 3 file
Can a few fanatics influence the opinion of a large segment of a society?
Models that provide insight into how extreme positions regarding any social
phenomenon may spread in a society or at the global scale are of great current
interest. A realistic model must account for the fact that globalization and
internet have given rise to scale-free networks of interactions between people.
We propose a novel model which takes into account the nature of the
interactions network, and provides some key insights into this phenomenon,
including: (1) There is a fundamental difference between a hierarchical network
whereby people are influenced by those that are higher on the hierarchy but not
by those below them, and a symmetrical network where person-on-person influence
works mutually. (2) A few "fanatics" can influence a large fraction of the
population either temporarily (in the hierarchical networks) or permanently (in
symmetrical networks). Even if the "fanatics" disappear, the population may
still remain susceptible to the positions advocated by them. The model is,
however, general and applicable to any phenomenon for which there is a degree
of enthusiasm or susceptibility to in the population.Comment: Enlarged to 28 pages including 15 figure
Compromise and Synchronization in Opinion Dynamics
We discuss two models of opinion dynamics. First wepresent a brief review of
the Hegselmann and Krause (HK) compromise model in two dimensions, showing that
it is possible to simulate the dynamics in the limit of an infinite number of
agents by solving numerically a rate equation for a continuum distribution of
opinions. Then, we discuss the Opinion Changing Rate (OCR) model, which allows
to study under which conditions a group of agents with a different natural
tendency (rate) to change opinion can find the agreement. In the context of the
this model, consensus is viewed as a synchronization process.Comment: Talk presented at the international conference Next05 Sigma Phi,
13-18 august 2005, Kolymbari, Crete. EPJ B (2006) in press. Typos corrected,
refs adde
Spontaneous Symmetry Breaking in Fermion-Gauge Systems- A Non Standard Approach
We propose a new method for the study of the chiral properties of the ground
state in QFT's based on the computation of the probability distribution
function of the chiral condensate. It can be applied directly in the chiral
limit and therefore no mass extrapolations are needed. Furthermore this
approach allows to write up equations relating the chiral condensate with
quantities computable by standard numerical methods, the functional form of
these relations depending on the broken symmetry group. As a check, we report
some results for the compact Schwinger model.Comment: Latex file, 11 pages plus two figure
Reality Inspired Voter Models: A Mini-Review
This mini-review presents extensions of the voter model that incorporate
various plausible features of real decision-making processes by individuals.
Although these generalizations are not calibrated by empirical data, the
resulting dynamics are suggestive of realistic collective social behaviors.Comment: 13 pages, 16 figures. Version 2 contains various proofreading
improvements. V3: fixed one trivial typ
Continuous-time average-preserving opinion dynamics with opinion-dependent communications
We study a simple continuous-time multi-agent system related to Krause's
model of opinion dynamics: each agent holds a real value, and this value is
continuously attracted by every other value differing from it by less than 1,
with an intensity proportional to the difference.
We prove convergence to a set of clusters, with the agents in each cluster
sharing a common value, and provide a lower bound on the distance between
clusters at a stable equilibrium, under a suitable notion of multi-agent system
stability.
To better understand the behavior of the system for a large number of agents,
we introduce a variant involving a continuum of agents. We prove, under some
conditions, the existence of a solution to the system dynamics, convergence to
clusters, and a non-trivial lower bound on the distance between clusters.
Finally, we establish that the continuum model accurately represents the
asymptotic behavior of a system with a finite but large number of agents.Comment: 25 pages, 2 figures, 11 tex files and 2 eps file
Mean-Field-Type Games in Engineering
A mean-field-type game is a game in which the instantaneous payoffs and/or
the state dynamics functions involve not only the state and the action profile
but also the joint distributions of state-action pairs. This article presents
some engineering applications of mean-field-type games including road traffic
networks, multi-level building evacuation, millimeter wave wireless
communications, distributed power networks, virus spread over networks, virtual
machine resource management in cloud networks, synchronization of oscillators,
energy-efficient buildings, online meeting and mobile crowdsensing.Comment: 84 pages, 24 figures, 183 references. to appear in AIMS 201
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