19,382 research outputs found
Kinetic models of collective decision-making in the presence of equality bias
We introduce and discuss kinetic models describing the influence of the
competence in the evolution of decisions in a multi-agent system. The original
exchange mechanism, which is based on the human tendency to compromise and
change opinion through self-thinking, is here modified to include the role of
the agents' competence. In particular, we take into account the agents'
tendency to behave in the same way as if they were as good, or as bad, as their
partner: the so-called equality bias. This occurred in a situation where a wide
gap separated the competence of group members. We discuss the main properties
of the kinetic models and numerically investigate some examples of collective
decision under the influence of the equality bias. The results confirm that the
equality bias leads the group to suboptimal decisions
Hydrodynamic models of preference formation in multi-agent societies
In this paper, we discuss the passage to hydrodynamic equations for kinetic
models of opinion formation. The considered kinetic models feature an opinion
density depending on an additional microscopic variable, identified with the
personal preference. This variable describes an opinion-driven polarisation
process, leading finally to a choice among some possible options, as it happens
e.g. in referendums or elections. Like in the kinetic theory of rarefied gases,
the derivation of hydrodynamic equations is essentially based on the
computation of the local equilibrium distribution of the opinions from the
underlying kinetic model. Several numerical examples validate the resulting
model, shedding light on the crucial role played by the distinction between
opinion and preference formation on the choice processes in multi-agent
societies.Comment: 30 pages, 15 figure
Kinetic models of opinion formation in the presence of personal conviction
We consider a nonlinear kinetic equation of Boltzmann type which takes into
account the influence of conviction during the formation of opinion in a system
of agents which interact through the binary exchanges introduced in [G.
Toscani, Commun. Math. Sci. 4, 481 (2006)]. The original exchange mechanism,
which is based on the human tendency to compromise and change of opinion
through self-thinking, is here modified in the parameters of the compromise and
diffusion terms, which now are assumed to depend on the personal degree of
conviction. The numerical simulations show that the presence of conviction has
the potential to break symmetry, and to produce clusters of opinions. The model
is partially inspired by the recent work [L. Pareschi, G. Toscani, Phil. Trans.
R. Soc. A 372, 20130396 (2014)], in which the role of knowledge in the
formation of wealth distribution has been investigated.Comment: arXiv admin note: text overlap with arXiv:1401.455
Kinetic description of optimal control problems and applications to opinion consensus
In this paper an optimal control problem for a large system of interacting
agents is considered using a kinetic perspective. As a prototype model we
analyze a microscopic model of opinion formation under constraints. For this
problem a Boltzmann-type equation based on a model predictive control
formulation is introduced and discussed. In particular, the receding horizon
strategy permits to embed the minimization of suitable cost functional into
binary particle interactions. The corresponding Fokker-Planck asymptotic limit
is also derived and explicit expressions of stationary solutions are given.
Several numerical results showing the robustness of the present approach are
finally reported.Comment: 25 pages, 18 figure
Reducing complexity of multiagent systems with symmetry breaking: an application to opinion dynamics with polls
In this paper we investigate the possibility of reducing the complexity of a
system composed of a large number of interacting agents, whose dynamics feature
a symmetry breaking. We consider first order stochastic differential equations
describing the behavior of the system at the particle (i.e., Lagrangian) level
and we get its continuous (i.e., Eulerian) counterpart via a kinetic
description. However, the resulting continuous model alone fails to describe
adequately the evolution of the system, due to the loss of granularity which
prevents it from reproducing the symmetry breaking of the particle system. By
suitably coupling the two models we are able to reduce considerably the
necessary number of particles while still keeping the symmetry breaking and
some of its large-scale statistical properties. We describe such a multiscale
technique in the context of opinion dynamics, where the symmetry breaking is
induced by the results of some opinion polls reported by the media
Boltzmann type control of opinion consensus through leaders
The study of formations and dynamics of opinions leading to the so called
opinion consensus is one of the most important areas in mathematical modeling
of social sciences. Following the Boltzmann type control recently introduced in
[G. Albi, M. Herty, L. Pareschi arXiv:1401.7798], we consider a group of
opinion leaders which modify their strategy accordingly to an objective
functional with the aim to achieve opinion consensus. The main feature of the
Boltzmann type control is that, thanks to an instantaneous binary control
formulation, it permits to embed the minimization of the cost functional into
the microscopic leaders interactions of the corresponding Boltzmann equation.
The related Fokker-Planck asymptotic limits are also derived which allow to
give explicit expressions of stationary solutions. The results demonstrate the
validity of the Boltzmann type control approach and the capability of the
leaders control to strategically lead the followers opinion
Price dynamics in financial markets: a kinetic approach
The use of kinetic modelling based on partial differential equations for the
dynamics of stock price formation in financial markets is briefly reviewed. The
importance of behavioral aspects in market booms and crashes and the role of
agents' heterogeneity in emerging power laws for price distributions is
emphasized and discussed
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
Boltzmann-type models with uncertain binary interactions
In this paper we study binary interaction schemes with uncertain parameters
for a general class of Boltzmann-type equations with applications in classical
gas and aggregation dynamics. We consider deterministic (i.e., a priori
averaged) and stochastic kinetic models, corresponding to different ways of
understanding the role of uncertainty in the system dynamics, and compare some
thermodynamic quantities of interest, such as the mean and the energy, which
characterise the asymptotic trends. Furthermore, via suitable scaling
techniques we derive the corresponding deterministic and stochastic
Fokker-Planck equations in order to gain more detailed insights into the
respective asymptotic distributions. We also provide numerical evidences of the
trends estimated theoretically by resorting to recently introduced structure
preserving uncertainty quantification methods
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