Inequalities of wealth distribution in a conservative economy

We analyze a conservative market model for the competition among economic agents in a close society. 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.Comment: 7 pages, 4 figures, submitted to Physica A, Proceedings of the VIII LAWNP, Salvador, Brazil, 200

Living in an Irrational Society: Wealth Distribution with Correlations between Risk and Expected Profits

Different models to study the wealth distribution in an artificial society have considered a transactional dynamics as the driving force. Those models include a risk aversion factor, but also a finite probability of favoring the poorer agent in a transaction. Here we study the case where the partners in the transaction have a previous knowledge of the winning probability and adjust their risk aversion taking this information into consideration. The results indicate that a relatively equalitarian society is obtained when the agents risk in direct proportion to their winning probabilities. However, it is the opposite case that delivers wealth distribution curves and Gini indices closer to empirical data. This indicates that, at least for this very simple model, either agents have no knowledge of their winning probabilities, either they exhibit an ``irrational'' behavior risking more than reasonable.Comment: 7 pages, 8 figure

Economic exchanges in a stratified society: End of the middle class?

We study the effect of the social stratification on the wealth distribution on a system of interacting economic agents that are constrained to interact only within their own economic class. The economical mobility of the agents is related to its success in exchange transactions. Different wealth distributions are obtained as a function of the width of the economic class. We find a range of widths in which the society is divided in two classes separated by a deep gap that prevents further exchange between poor and rich agents. As a consequence, the middle wealth class is eliminated. The high values of the Gini indices obtained in these cases indicate a highly unequal society. On the other hand, lower and higher widths induce lower Gini indices and a fairer wealth distribution.Comment: 7 pages, 2 figures, 1 table, to appear in Physica

Correlation between Risk Aversion and Wealth distribution

Different models of capital exchange among economic agents have been proposed recently trying to explain the emergence of Pareto's 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 posses different levels of risk aversion, going from uniform to a random distribution. In all cases the risk aversion level for a given agent is constant during the simulation. While for a 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.Comment: 8 pages, 7 figures, submitted to Physica A, Proceedings of the VIII LAWNP, Salvador, Brazil, 200

Entropy and equilibrium state of free market models

Many recent models of trade dynamics use the simple idea of wealth exchanges among economic agents in order to obtain a stable or equilibrium distribution of wealth among the agents. In particular, a plain analogy compares the wealth in a society with the energy in a physical system, and the trade between agents to the energy exchange between molecules during collisions. In physical systems, the energy exchange among molecules leads to a state of equipartition of the energy and to an equilibrium situation where the entropy is a maximum. On the other hand, in the majority of exchange models, the system converges to a very unequal condensed state, where one or a few agents concentrate all the wealth of the society while the wide majority of agents shares zero or almost zero fraction of the wealth. So, in those economic systems a minimum entropy state is attained. We propose here an analytical model where we investigate the effects of a particular class of economic exchanges that minimize the entropy. By solving the model we discuss the conditions that can drive the system to a state of minimum entropy, as well as the mechanisms to recover a kind of equipartition of wealth

Emergence of communities on a coevolutive model of wealth interchange

We present a model in which we investigate the structure and evolution of a random network that connects agents capable of exchanging wealth. Economic interactions between neighbors can occur only if the difference between their wealth is less than a threshold value that defines the width of the economic classes. If the interchange of wealth cannot be done, agents are reconnected with another randomly selected agent, allowing the network to evolve in time. On each interaction there is a probability of favoring the poorer agent, simulating the action of the government. We measure the Gini index, having real world values attached to reality. Besides the network structure showed a very close connection with the economic dynamic of the system.Comment: 5 pages, 7 figure

Wealth redistribution with finite resources

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.Comment: 4 pages, 3 figures, RevTeX 4 styl

Doniach diagram for ordered, disordered and underscreened Kondo lattices

The Doniach's diagram has been originally proposed to describe the competition between the local Kondo effect and the intersite RKKY interactions in cerium compounds. Here we discuss the extension of this diagram to different variations of Kondo lattice model. We consider a) ordered cerium compounds where the competition between magnetic order and Kondo effect plays an important role, as $CeRh_2Si_2$, b) disordered cerium systems with competing spin glass phase, magnetic ordered phases and a Kondo phase, as the heavy fermion cerium alloy $CeCu_xNi_{1-x}$ and, c) uranium compounds where a coexistence between Kondo effect and ferromagnetic order has been observed, as UTe. We show that all these cases can be described by a generalized Doniach phase diagram.Comment: Presented in the Latin American Workshop on Magnetism and Magnetic Materials (LAW3M) Rio de Janeiro, Brazil, August 12-16, 2007. Proceedings to be published in JMM

The dynamics of opinion in hierarchical organizations

We study the mutual influence of authority and persuasion in the flow of opinion. Many social organizations are characterized by a hierarchical structure where the propagation of opinion is asymmetric. In the normal flow of opinion formation a high-rank agent uses its authority (or its persuasion when necessary) to impose its opinion on others. However, agents with no authority may only use the force of its persuasion to propagate their opinions. In this contribution we describe a simple model with no social mobility, where each agent belongs to a class in the hierarchy and has also a persuasion capability. The model is studied numerically for a three levels case, and analytically within a mean field approximation, with a very good agreement between the two approaches. The stratum where the dominant opinion arises from is strongly dependent on the percentage of agents in each hierarchy level, and we obtain a phase diagram identifying the relative frequency of prevailing opinions. We also find that the time evolution of the conflicting opinions polarizes after a short transient.Comment: 6 pages, 5 figures, submitted to Phys. Rev.

Irregular graph pyramids and representative cocycles of cohomology generators

Structural pattern recognition describes and classifies data based on the relationships of features and parts. Topological invariants, like the Euler number, characterize the structure of objects of any dimension. Cohomology can provide more refined algebraic invariants to a topological space than does homology. It assigns ‘quantities’ to the chains used in homology to characterize holes of any dimension. Graph pyramids can be used to describe subdivisions of the same object at multiple levels of detail. This paper presents cohomology in the context of structural pattern recognition and introduces an algorithm to efficiently compute representative cocycles (the basic elements of cohomology) in 2D using a graph pyramid. Extension to nD and application in the context of pattern recognition are discussed