RESUMEN
Fake news spreading, with the aim of manipulating individuals' perceptions of facts, is now recognized as a major problem in many democratic societies. Yet, to date, little has been understood about how fake news spreads on social networks, what the influence of the education level of individuals is, when fake news is effective in influencing public opinion, and what interventions might be successful in mitigating their effect. In this paper, starting from the recently introduced kinetic multi-agent model with competence by the first two authors, we propose to derive reduced-order models through the notion of social closure in the mean-field approximation that has its roots in the classical hydrodynamic closure of kinetic theory. This approach allows to obtain simplified models in which the competence and learning of the agents maintain their role in the dynamics and, at the same time, the structure of such models is more suitable to be interfaced with data-driven applications. Examples of different Twitter-based test cases are described and discussed.
RESUMEN
We introduce and discuss a nonlinear kinetic equation of Boltzmann type that describes the influence of knowledge in the evolution of wealth in a system of agents that interact through the binary trades, an equation first introduced by Cordier et al. (2005 J. Stat. Phys. 120, 253-277 (doi:10.1007/S10955-005-5456-0)). The trades, which include both saving propensity and the risks of the market, are here modified in the risk and saving parameters, which now are assumed to depend on the personal degree of knowledge. The numerical simulations show that the presence of knowledge has the potential to produce a class of wealthy agents and to account for a larger proportion of wealth inequality.
RESUMEN
The study of formations and dynamics of opinions leading to the so-called opinion consensus is one of the most important areas in mathematical modelling of social sciences. Following the Boltzmann-type control approach recently introduced by the first two authors, we consider a group of opinion leaders who modify their strategy accordingly to an objective functional with the aim of achieving opinion consensus. The main feature of the Boltzmann-type control is that, owing to an instantaneous binary control formulation, it permits the minimization of the cost functional to be embedded into the microscopic leaders' interactions of the corresponding Boltzmann equation. The related Fokker-Planck asymptotic limits are also derived, which allow one 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.