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Non-Bayesian social learning theory provides a framework that models distributed inference for a group of agents interacting over a social network. In this framework, each agent iteratively forms and communicates beliefs about an unknown…
In this work we consider the classical non-linear Boltzmann equation, where the unknown is the distribution function $f$, which depends on the time $t$, the vector $\mathbf{x}$ (the position of a molecule) and its velocity $\mathbf{\xi}$.…
Bridging the gap between individual agent behavior and macroscopic societal patterns is a central challenge in the social sciences. In this work, we propose a solution to this problem via a kinetic theory formulation. We demonstrate that…
We studied the Bouchaud-M\'ezard(BM) model, which was introduced to explain Pareto's law in a real economy, on a random network. Using "adiabatic and independent" assumptions, we analytically obtained the stationary probability distribution…
We consider a constrained hierarchical opinion dynamics in the case of leaders' competition and with complete information among leaders. Each leaders' group tries to drive the followers' opinion towards a desired state accordingly to a…
We introduce and discuss a kinetic framework describing the time evolution of the statistical distributions of a population divided into the compartments of susceptible, infectious, recovered, and resistant in the presence of a microbial…
We study the impact of contact heterogeneity on epidemic dynamics. A system characterized by multiple susceptible populations is considered. The description of the spread of an infectious disease is obtained through the study of a system of…
Several problems arising in Economics and Finance are analyzed using concepts and quantitative methods from Physics. Here is the abridged abstact: Chapter 1: By analogy with energy, the equilibrium probability distribution of money must…
In this paper, we study the inequality indices for some models of wealth exchange. We calculated Gini index and newly introduced k-index and compare the results with reported empirical data available for different countries. We have found…
In this work the system of agents is applied to establish a model of the nonlinear distributed signal processing. The evolution of the system of the agents - by the prediction time scale diversified trend followers, has been studied for the…
We develop a formalism to study linearized perturbations around the equilibria of a pure exchange economy. With the use of mean field theory techniques, we derive equations for the flow of products in an economy driven by heterogeneous…
Kinetic exchange models have been successful in explaining the shape of the income/wealth distribution in the economies. However, such models usually make some ad-hoc assumptions when it comes to determining the savings factor. Here, we…
We discuss several multi-agent models that have their origin in the kinetic exchange theory of statistical mechanics and have been recently applied to a variety of problems in the social sciences. This class of models can be easily adapted…
A network of agents interacting both with competitive and/or cooperative mechanisms is modeled by using fermionic ladder operators. The time evolution of the network is assumed to be governed by a Hermitian time-independent Hamiltonian…
We consider a $N$-particle model describing an alignment mechanism due to a topological interaction among the agents. We show that the kinetic equation, expected to hold in the mean-field limit $N \to \infty$, as following from the previous…
We focus on the problem of how wealth is distributed among the units of a networked economic system. We first review the empirical results documenting that in many economies the wealth distribution is described by a combination of…
We investigate the effect of tax evasion on the income distribution and the inequality index of a society through a kinetic model described by a set of nonlinear ordinary differential equations. The model allows to compute the global…
This paper attempts to find a relationship between agents' risk aversion and inequality of incomes. Specifically, a model is proposed for the evolution in time of surplus/deficit distribution, and the long-time distributions are…
Increasingly, a huge amount of statistics have been gathered which clearly indicates that income and wealth distributions in various countries or societies follow a robust pattern, close to the Gibbs distribution of energy in an ideal gas…
We show, analytically and numerically, that wealth distribution in the Bouchaud-M\'ezard network model of the economy is described by a three-parameter generalized inverse gamma distribution. In the mean-field limit of a network with any…