858 research outputs found
Bouchaud-M\'ezard model on a random network
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 function of wealth. The results shows that wealth-condensation,
indicated by the divergence of the variance of wealth, occurs at a larger
than that obtained by the mean-field theory, where represents the strength
of interaction between agents. We compared our results with numerical
simulation results and found that they were in good agreement.Comment: to be published in Physical Review
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
A statistical model with a standard Gamma distribution
We study a statistical model consisting of basic units which interact
with each other by exchanging a physical entity, according to a given
microscopic random law, depending on a parameter . We focus on the
equilibrium or stationary distribution of the entity exchanged and verify
through numerical fitting of the simulation data that the final form of the
equilibrium distribution is that of a standard Gamma distribution. The model
can be interpreted as a simple closed economy in which economic agents trade
money and a saving criterion is fixed by the saving propensity .
Alternatively, from the nature of the equilibrium distribution, we show that
the model can also be interpreted as a perfect gas at an effective temperature
, where particles exchange energy in a space with an effective
dimension .Comment: 5 pages, including 4 figures. Uses REVTeX styl
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
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
Scaling laws of strategic behaviour and size heterogeneity in agent dynamics
The dynamics of many socioeconomic systems is determined by the decision
making process of agents. The decision process depends on agent's
characteristics, such as preferences, risk aversion, behavioral biases, etc..
In addition, in some systems the size of agents can be highly heterogeneous
leading to very different impacts of agents on the system dynamics. The large
size of some agents poses challenging problems to agents who want to control
their impact, either by forcing the system in a given direction or by hiding
their intentionality. Here we consider the financial market as a model system,
and we study empirically how agents strategically adjust the properties of
large orders in order to meet their preference and minimize their impact. We
quantify this strategic behavior by detecting scaling relations of allometric
nature between the variables characterizing the trading activity of different
institutions. We observe power law distributions in the investment time
horizon, in the number of transactions needed to execute a large order and in
the traded value exchanged by large institutions and we show that heterogeneity
of agents is a key ingredient for the emergence of some aggregate properties
characterizing this complex system.Comment: 6 pages, 3 figure
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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