152 research outputs found
Pareto and Boltzmann-Gibbs behaviors in a deterministic multi-agent system
A deterministic system of interacting agents is considered as a model for
economic dynamics. The dynamics of the system is described by a coupled map
lattice with near neighbor interactions. The evolution of each agent results
from the competition between two factors: the agent's own tendency to grow and
the environmental influence that moderates this growth. Depending on the values
of the parameters that control these factors, the system can display Pareto or
Boltzmann-Gibbs statistical behaviors in its asymptotic dynamical regime. The
regions where these behaviors appear are calculated on the space of parameters
of the system. Other statistical properties, such as the mean wealth, the
standard deviation, and the Gini coefficient characterizing the degree of
equity in the wealth distribution are also calculated on the space of
parameters of the system.Comment: 9 pages, 9 color .eps figures, submitted to Physica
Exponential wealth distribution: a new approach from functional iteration theory
Exponential distribution is ubiquitous in the framework of multi-agent
systems. Usually, it appears as an equilibrium state in the asymptotic time
evolution of statistical systems. It has been explained from very different
perspectives. In statistical physics, it is obtained from the principle of
maximum entropy. In the same context, it can also be derived without any
consideration about information theory, only from geometrical arguments under
the hypothesis of equiprobability in phase space. Also, several multi-agent
economic models based on mappings, with random, deterministic or chaotic
interactions, can give rise to the asymptotic appearance of the exponential
wealth distribution. An alternative approach to this problem in the framework
of iterations in the space of distributions has been recently presented.
Concretely, the new iteration given by . It is found that the
exponential distribution is a stable fixed point of the former functional
iteration equation. From this point of view, it is easily understood why the
exponential wealth distribution (or by extension, other kind of distributions)
is asymptotically obtained in different multi-agent economic models.Comment: 6 pages, 5 figure
Geometrical Derivation of Equilibrium Distributions in some Stochastic Systems
In this chapter, we present a straightforward geometrical argument that in a
certain way recalls us the equivalence between the canonical and the
microcanonical ensembles in the thermodynamic limit for the particular context
of physical sciences. In the more general context of homogeneous multi-agent
systems, we conclude by highlighting the statistical equivalence of the
volume-based and surface-based calculations in this type of systems.Comment: 18 pages, 3 figures. arXiv admin note: substantial text overlap with
arXiv:0708.3761, arXiv:1001.3327, arXiv:0708.1866; Chapter to appear in
InTech Books (2012
Optimal Income Crossover for Two-Class Model Using Particle Swarm Optimization
Personal income distribution may exhibit a two-class structure, such that the
lower income class of the population (85-98%) is described by exponential
Boltzmann-Gibbs distribution, whereas the upper income class (15-2%) has a
Pareto power-law distribution. We propose a method, based on a theoretical and
numerical optimization scheme, which allows us to determine the crossover
income between the distributions, the temperature of the Boltzmann-Gibbs
distribution and the Pareto index. Using this method, the Brazilian income
distribution data provided by the National Household Sample Survey was studied.
The data was stratified into two dichotomies (sex/gender and color/race), so
the model was tested using different subsets along with accessing the economic
differences between these groups. Lastly, we analyse the temporal evolution of
the parameters of our model and the Gini coefficient discussing the implication
on the Brazilian income inequality. To our knowledge, for the first time an
optimization method is proposed in order to find a continuous two-class income
distribution, which is able to delimit the boundaries of the two distributions.
It also gives a measure of inequality which is a function that depends only on
the Pareto index and the percentage of people in the high income region. It was
found a temporal dynamics relation, that may be general, between the Pareto and
the percentage of people described by the Pareto tail.Comment: 16 pages, 14 figures, submitted to Physical Review
Discrete Choices under Social Influence: Generic Properties
We consider a model of socially interacting individuals that make a binary
choice in a context of positive additive endogenous externalities. It
encompasses as particular cases several models from the sociology and economics
literature. We extend previous results to the case of a general distribution of
idiosyncratic preferences, called here Idiosyncratic Willingnesses to Pay
(IWP). Positive additive externalities yield a family of inverse demand curves
that include the classical downward sloping ones but also new ones with non
constant convexity. When j, the ratio of the social influence strength to the
standard deviation of the IWP distribution, is small enough, the inverse demand
is a classical monotonic (decreasing) function of the adoption rate. Even if
the IWP distribution is mono-modal, there is a critical value of j above which
the inverse demand is non monotonic, decreasing for small and high adoption
rates, but increasing within some intermediate range. Depending on the price
there are thus either one or two equilibria. Beyond this first result, we
exhibit the generic properties of the boundaries limiting the regions where the
system presents different types of equilibria (unique or multiple). These
properties are shown to depend only on qualitative features of the IWP
distribution: modality (number of maxima), smoothness and type of support
(compact or infinite). The main results are summarized as phase diagrams in the
space of the model parameters, on which the regions of multiple equilibria are
precisely delimited.Comment: 42 pages, 15 figure
Econophysics: agent-based models
This article is the second part of a review of recent empirical and theoretical developments usually grouped under the heading Econophysics. In the first part, we reviewed the statistical properties of financial time series, the statistics exhibited in order books and discussed some studies of correlations of asset prices and returns. This second part deals with models in Econophysics from the point of view of agent-based modeling. Of the large number of multiagent- based models, we have identified three representative areas. First, using previous work originally presented in the fields of behavioral finance and market microstructure theory, econophysicists have developed agent-based models of order-driven markets that we discuss extensively here. Second, kinetic theory models designed to explain certain empirical facts concerning wealth distribution are reviewed. Third, we briefly summarize game theory models by reviewing the now classic minority game and related problems.
Discrete Choices under Social Influence: Generic Properties
We consider a model of socially interacting individuals that make a binary choice in a context of positive additive endogenous externalities. It encompasses as particular cases several models from the sociology and economics literature. We extend previous results to the case of a general distribution of idiosyncratic preferences, called here Idiosyncratic Willingnesses to Pay (IWP).Positive additive externalities yield a family of inverse demand curves that include the classical downward sloping ones but also new ones with non constant convexity. When , the ratio of the social influene strength to the standard deviation of the IWP distribution, is small enough, the inverse demand is a classical monotonic (decreasing) function of the adoption rate. Even if the IWP distribution is mono-modal, there is a critical value of above which the inverse demand is non monotonic, decreasing for small and high adoption rates, but increasing within some intermediate range. Depending on the price there are thus either one or two equilibria.Beyond this first result, we exhibit the {\em generic} properties of the boundaries limiting the regions where the system presents different types of equilibria (unique or multiple). These properties are shown to depend {\em only} on qualitative features of the IWP distribution: modality (number of maxima), smoothness and type of support (compact or infinite).The main results are summarized as {\em phase diagrams} in the space of the model parameters, on which the regions of multiple equilibria are precisely delimited.discrete choice; social influence; externalities; heterogeneous agents; socioeconomic behavior
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