J.R. Iglesias

Wealth redistribution in our small world

We present a simplified model for the exploitation of resources by interacting agents, in an economy with small-world properties. It is shown that Gaussian distributions of wealth, with some cutoff at a poverty line are present for all values of the parameters, while the frequency of maxima and minima strongly depends on the connectivity and the disorder of the lattice. Finally, we compare a system where the commercial links are frozen with an economy where agents can choose their commercial partners at each time step.

Correlation between risk aversion and wealth distribution

Different models of capital exchange among economic agents have been recently proposed trying to explain the emergence of Paretos wealth power-law distribution. One important factor to be considered is the existence of risk aversion. In this paper, we study a model where agents possess different levels of risk aversion, going from a uniform to a random distribution. In all cases the risk aversion level for a given agent is constant during the simulation. While for uniform and constant risk aversion the system self-organizes in a distribution that goes from an unfair “one takes all” distribution to a Gaussian one, a random risk aversion can produce distributions going from exponential to log-normal and power-law. Besides, interesting correlations between wealth and risk aversion are found.

Wealth redistribution with conservative exchanges

We present a simplified model for the exploitation of finite resources by interacting agents, where each agent receives a random fraction of the available resources. An extremal dynamics ensures that the poorest agent has a chance to change its economic welfare. After a long transient, the system self-organizes into a critical state that maximizes the average performance of each participant. Our model exhibits a new kind of wealth condensation, where very few extremely rich agents are stable in time and the rest stays in the middle class.We present a simplified model for the exploitation of resources by interacting agents, where each agent receives a random fraction of the available resources. An extremal dynamics ensures that the poorest agent has a chance to change its economic welfare. After a long transient; the system self-organizes into a critical state that maximizes the average performance of each participant. Our model exhibits a new kind of wealth condensation, where very few extremely rich agents are stable in time and the rest stays in the middle class.

Van Kampen's expansion approach in an opinion formation model

Abstract. We analyze a simple opinion formation model consisting of two parties, A and B, and a group I, of undecided agents. We assume that the supporters of parties A and B do not interact among them, but only interact through the group I, and that there is a nonzero probability of a spontaneous change of opinion (

Inequalities of wealth distribution in a conservative economy

A \leftrightarrows I

Effect of band filling in the Kondo lattice : a mean-field approach

,

The dynamics of opinion in hierarchical organizations

B \leftrightarrows I

Theory of the Kondo lattice : competition between Kondo effect and magnetic order

). From the master equation, and via van Kampens Ω-expansion approach, we have obtained the “macroscopic” evolution equation, as well as the Fokker-Planck equation governing the fluctuations around the deterministic behavior. Within the same approach, we have also obtained information about the typical relaxation behavior of small perturbations.

Entropy and equilibrium state of free market models

We analyze a conservative market model for the competition among economic agents in a society with conserved total wealth. A minimum dynamics ensures that the poorest agent has a chance to improve its economic welfare. After a transient, the system self-organizes into a critical state where the wealth distribution have a minimum threshold, with almost no agent below this poverty line. Also, very few extremely rich agents are stable in time. Above the poverty line the distribution follows an exponential behavior. The local solution exhibits a low Gini index, while the mean field solution of the model generates a wealth distribution similar to welfare states like Sweden.

Living in an irrational society: Wealth distribution with correlations between risk and expected profits

The usual Kondo lattice, including an antiferromagnetic exchange interaction between nearest-neighboring localized spins, is treated here in a mean-field scheme that introduces two mean-field parameters: one associated with the local Kondo effect, and the other related to the magnetic correlations between localized spins. Phases with short-range magnetic correlations or coexistence between those and the Kondo effect are obtained. By varying the number of electrons in the conduction band, we notice that the Kondo effect tends to be suppressed away from half filling, while magnetic correlations can survive if the Heisenberg coupling is strong enough. An enhanced linear coefficient of the specific heat is obtained at low temperatures in the metallic state.