854 research outputs found
Gamma-distribution and wealth inequality
We discuss the equivalence between kinetic wealth-exchange models, in which
agents exchange wealth during trades, and mechanical models of particles,
exchanging energy during collisions. The universality of the underlying
dynamics is shown both through a variational approach based on the minimization
of the Boltzmann entropy and a complementary microscopic analysis of the
collision dynamics of molecules in a gas. In various relevant cases the
equilibrium distribution is the same for all these models, namely a
gamma-distribution with suitably defined temperature and number of dimensions.
This in turn allows one to quantify the inequalities observed in the wealth
distributions and suggests that their origin should be traced back to very
general underlying mechanisms: for instance, it follows that the smaller the
fraction of the relevant quantity (e.g. wealth or energy) that agents can
exchange during an interaction, the closer the corresponding equilibrium
distribution is to a fair distribution.Comment: Presented to the International Workshop and Conference on:
Statistical Physics Approaches to Multi-disciplinary Problems, January 07-13,
2008, IIT Guwahati, Indi
Adaptive networks of trading agents
Multi-agent models have been used in many contexts to study generic
collective behavior. Similarly, complex networks have become very popular
because of the diversity of growth rules giving rise to scale-free behavior.
Here we study adaptive networks where the agents trade ``wealth'' when they are
linked together while links can appear and disappear according to the wealth of
the corresponding agents; thus the agents influence the network dynamics and
vice-versa. Our framework generalizes a multi-agent model of Bouchand and
Mezard, and leads to a steady state with fluctuating connectivities. The system
spontaneously self-organizes into a critical state where the wealth
distribution has a fat tail and the network is scale-free; in addition, network
heterogeneities lead to enhanced wealth condensation.Comment: 7 figure
Reshuffling spins with short range interactions: When sociophysics produces physical results
Galam reshuffling introduced in opinion dynamics models is investigated under
the nearest neighbor Ising model on a square lattice using Monte Carlo
simulations. While the corresponding Galam analytical critical temperature T_C
\approx 3.09 [J/k_B] is recovered almost exactly, it is proved to be different
from both values, not reshuffled (T_C=2/arcsinh(1) \approx 2.27 [J/k_B]) and
mean-field (T_C=4 [J/k_B]). On this basis, gradual reshuffling is studied as
function of 0 \leq p \leq 1 where p measures the probability of spin
reshuffling after each Monte Carlo step. The variation of T_C as function of p
is obtained and exhibits a non-linear behavior. The simplest Solomon network
realization is noted to reproduce Galam p=1 result. Similarly to the critical
temperature, critical exponents are found to differ from both, the classical
Ising case and the mean-field values.Comment: 11 pages, 5 figures in 6 eps files, to appear in IJMP
Blockbusters, Bombs and Sleepers: The income distribution of movies
The distribution of gross earnings of movies released each year show a
distribution having a power-law tail with Pareto exponent .
While this offers interesting parallels with income distributions of
individuals, it is also clear that it cannot be explained by simple asset
exchange models, as movies do not interact with each other directly. In fact,
movies (because of the large quantity of data available on their earnings)
provide the best entry-point for studying the dynamics of how ``a hit is born''
and the resulting distribution of popularity (of products or ideas). In this
paper, we show evidence of Pareto law for movie income, as well as, an analysis
of the time-evolution of income.Comment: 5 pages, 3 figures, to appear in Proceedings of International
Workshop on Econophysics of Wealth Distributions (Econophys-Kolkata I), March
15-19, 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
Power-Law Distributions in Circulating Money: Effect of Preferential Behavior
We introduce preferential behavior into the study on statistical mechanics of
money circulation. The computer simulation results show that the preferential
behavior can lead to power laws on distributions over both holding time and
amount of money held by agents. However, some constraints are needed in
generation mechanism to ensure the robustness of power-law distributions.Comment: 4 pages, 2 figure
Universal scaling in sports ranking
Ranking is a ubiquitous phenomenon in the human society. By clicking the web
pages of Forbes, you may find all kinds of rankings, such as world's most
powerful people, world's richest people, top-paid tennis stars, and so on and
so forth. Herewith, we study a specific kind, sports ranking systems in which
players' scores and prize money are calculated based on their performances in
attending various tournaments. A typical example is tennis. It is found that
the distributions of both scores and prize money follow universal power laws,
with exponents nearly identical for most sports fields. In order to understand
the origin of this universal scaling we focus on the tennis ranking systems. By
checking the data we find that, for any pair of players, the probability that
the higher-ranked player will top the lower-ranked opponent is proportional to
the rank difference between the pair. Such a dependence can be well fitted to a
sigmoidal function. By using this feature, we propose a simple toy model which
can simulate the competition of players in different tournaments. The
simulations yield results consistent with the empirical findings. Extensive
studies indicate the model is robust with respect to the modifications of the
minor parts.Comment: 8 pages, 7 figure
Bidding process in online auctions and winning strategy:rate equation approach
Online auctions have expanded rapidly over the last decade and have become a
fascinating new type of business or commercial transaction in this digital era.
Here we introduce a master equation for the bidding process that takes place in
online auctions. We find that the number of distinct bidders who bid times,
called the -frequent bidder, up to the -th bidding progresses as
. The successfully transmitted bidding rate by the
-frequent bidder is obtained as , independent of
for large . This theoretical prediction is in agreement with empirical data.
These results imply that bidding at the last moment is a rational and effective
strategy to win in an eBay auction.Comment: 4 pages, 6 figure
Power-law distributions from additive preferential redistributions
We introduce a non-growth model that generates the power-law distribution
with the Zipf exponent. There are N elements, each of which is characterized by
a quantity, and at each time step these quantities are redistributed through
binary random interactions with a simple additive preferential rule, while the
sum of quantities is conserved. The situation described by this model is
similar to those of closed -particle systems when conservative two-body
collisions are only allowed. We obtain stationary distributions of these
quantities both analytically and numerically while varying parameters of the
model, and find that the model exhibits the scaling behavior for some parameter
ranges. Unlike well-known growth models, this alternative mechanism generates
the power-law distribution when the growth is not expected and the dynamics of
the system is based on interactions between elements. This model can be applied
to some examples such as personal wealths, city sizes, and the generation of
scale-free networks when only rewiring is allowed.Comment: 12 pages, 4 figures; Changed some expressions and notations; Added
more explanations and changed the order of presentation in Sec.III while
results are the sam
Predicted and Verified Deviations from Zipf's law in Ecology of Competing Products
Zipf's power-law distribution is a generic empirical statistical regularity
found in many complex systems. However, rather than universality with a single
power-law exponent (equal to 1 for Zipf's law), there are many reported
deviations that remain unexplained. A recently developed theory finds that the
interplay between (i) one of the most universal ingredients, namely stochastic
proportional growth, and (ii) birth and death processes, leads to a generic
power-law distribution with an exponent that depends on the characteristics of
each ingredient. Here, we report the first complete empirical test of the
theory and its application, based on the empirical analysis of the dynamics of
market shares in the product market. We estimate directly the average growth
rate of market shares and its standard deviation, the birth rates and the
"death" (hazard) rate of products. We find that temporal variations and product
differences of the observed power-law exponents can be fully captured by the
theory with no adjustable parameters. Our results can be generalized to many
systems for which the statistical properties revealed by power law exponents
are directly linked to the underlying generating mechanism
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