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Anirban Chakraborti

Publications and source records attributed to Anirban Chakraborti.

89 records · Page 5Linked to original sources
arXiv2005

Influence of saving propensity on the power law tail of wealth distribution

Some general features of kinetic multi-agent models are reviewed, with particular attention to the relation between the agent saving propensities and the form of the equilibrium wealth distribution. The effect of a finite cutoff of the saving propensity distribution on the corresponding wealth distribution is studied. Various results about kinetic multi-agent models are collected and used to construct a realistic wealth distribution with zero limit for small values of wealth, an exponential form at intermediate and a power law tail at larger values of wealth.

physics.soc-ph↗
arXiv2005

Kinetic theory models for the distribution of wealth: power law from overlap of exponentials

Various multi-agent models of wealth distributions defined by microscopic laws regulating the trades, with or without a saving criterion, are reviewed. We discuss and clarify the equilibrium properties of the model with constant global saving propensity, resulting in Gamma distributions, and their equivalence to the Maxwell-Boltzmann kinetic energy distribution for a system of molecules in an effective number of dimensions $D_λ$, related to the saving propensity $λ$ [M. Patriarca, A. Chakraborti, and K. Kaski, Phys. Rev. E 70 (2004) 016104]. We use these results to analyze the model in which the individual saving propensities of the agents are quenched random variables, and the tail of the equilibrium wealth distribution exhibits a Pareto law $f(x) \propto x^{-α-1}$ with an exponent $α=1$ [A. Chatterjee, B. K. Chakrabarti, and S. S. Manna, Physica Scripta T106 (2003) 367]. Here, we show that the observed Pareto power law can be explained as arising from the overlap of the Maxwell-Boltzmann distributions associated to the various agents, which reach an equilibrium state characterized by their individual Gamma distributions. We also consider the influence of different types of saving propensity distributions on the equilibrium state.

physics.soc-ph↗
arXiv2004

A statistical model with a standard Gamma distribution

We study a statistical model consisting of $N$ basic units which interact with each other by exchanging a physical entity, according to a given microscopic random law, depending on a parameter $λ$. 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 $λ$. 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 $T(λ)$, where particles exchange energy in a space with an effective dimension $D(λ)$.

cond-mat.stat-mech↗
arXiv2003

Gibbs versus non-Gibbs distributions in money dynamics

We review a simple model of closed economy, where the economic agents make money transactions and a saving criterion is present. We observe the Gibbs distribution for zero saving propensity, and non-Gibbs distributions otherwise. While the exact solution in the case of zero saving propensity is already known to be given by the Gibbs distribution, here we provide the explicit analytical form of the equilibrium distribution for the general case of nonzero saving propensity. We verify it through comparison with numerical data and show that it can be cast in the form of a Poisson distribution.

cond-mat.stat-mech↗
arXiv2003

Searching good strategies in adaptive minority games

In this paper we introduce adaptation mechanism based on genetic algorithms in minority games. If agents find their performances too low, they modify their strategies in hope to improve their performances and become more successful. One aim of this study is to find out what happens at the system as well as at the individual agent level. We observe that adaptation remarkably tightens the competition among the agents, and tries to pull the collective system into a state where the aggregate utility is the largest. We first make a brief comparative study of the different adaptation mechanisms and then present in more detail parametric studies. These different adaptation mechanisms broaden the scope of the applications of minority games to the study of complex systems.

cond-mat.stat-mech↗
arXiv2003

Biology helps you to win a game

We present a game of interacting agents which mimics the complex dynamics found in many natural and social systems. These agents modify their strategies periodically, depending on their performances using genetic crossover mechanisms, inspired by biology. We study the performances of the agents under different conditions, and how they adapt themselves. In addition the dynamics of the game is investigated.

cond-mat.stat-mech↗
arXiv2002

Adaptation using hybridized genetic crossover strategies

We present a simple game which mimics the complex dynamics found in most natural and social systems. Intelligent players modify their strategies periodically, depending on their performances. We propose that the agents use hybridized one-point genetic crossover mechanism,inspired by genetic evolution in biology, to modify the strategies and replace the bad strategies. We study the performances of the agents under different conditions and investigate how they adapt themselves in order to survive or be the best, by finding new strategies using the highly effective mechanism we proposed.

cond-mat.stat-mech↗
arXiv2002

Intelligent Minority Game with genetic-crossover strategies

We develop a game theoretical model of $N$ heterogeneous interacting agents called the intelligent minority game. The ``intelligent'' agents play the basic minority game and depending on their performances, generate new strategies using the one-point genetic crossover mechanism. The performances change dramatically and the game moves rapidly to an efficient state (fluctuations in the number of agents performing a particular action, characterized by $σ^2$, reaches a low value). There is no ``phase transition'' when we vary $σ^2/N$ with $2^M/N$, where $M$ is the ``memory''of an agent.

cond-mat.stat-mech↗
arXiv2002

Distributions of money in model markets of economy

We study the distributions of money in a simple closed economic system for different types of monetary transactions. We know that for arbitrary and random sharing but locally conserving money transactions, the money distribution goes to the Gibb's distribution of statistical mechanics. We then consider the effects of savings, etc. and see how the distribution changes. We also propose a new model where the agents invest equal amounts of money in each transaction. We find that for short time-periods, the money distribution obeys a power-law with an exponent very close to unity, and has an exponential tail; after a very long time, this distribution collapses and the entire amount of money goes to a tiny fraction of the population.

cond-mat.stat-mech↗
arXiv2001

Market application of the percolation model: Relative price distribution

We study a variant of the Cont-Bouchaud model which utilizes the perco lation approach of multi-agent simulations of the stock market fluctuations. Here, instead of considering the relative price change as the difference of the total demand and total supply, we consider the relative price change to be proportiona l to the ``relative'' difference of demand and supply (the ratio of the difference in total demand and total supply to the sum of the total demand and total supply). We then study the probability distribution of the price changes.

cond-mat.stat-mech↗
arXiv2001

The average distance of the n-th neighbour in a uniform distribution of random points

We first review the derivation of the exact expression for the average distance $ $ of the n-th neighbour of a reference point among a set of N random points distributed uniformly in a unit volume of a D-dimensional geometric space. Next we propose a `mean-field\rq theory of $ $ and compare it with the exact result. The result of the `mean-field\rq theory is found to agree with the exact expression only in the limit $D \to \infty$ and $n \to \infty$. Thus the `mean-field\rq approximation is useless in this context.

cond-mat.stat-mech↗
arXiv2000

A Self-organising Model of Market with Single Commodity

We have studied here the self-organising features of the dynamics of a model market, where the agents `trade' for a single commodity with their money. The model market consists of fixed numbers of economic agents, money supply and commodity. We demonstrate that the model, apart from showing a self-organising behaviour, indicates a crucial role for the money supply in the market and also its self-organising behaviour is seen to be significantly affected when the money supply becomes less than the optimum. We also observed that this optimal money supply level of the market depends on the amount of `frustration' or scarcity in the commodity market.

cond-mat.stat-mech↗
arXiv2000

Statistical mechanics of money: How saving propensity affects its distribution

We consider a simple model of a closed economic system where the total money is conserved and the number of economic agents is fixed. In analogy to statistical systems in equilibrium, money and the average money per economic agent are equivalent to energy and temperature, respectively. We investigate the effect of the saving propensity of the agents on the stationary or equilibrium money distribution.The equilibrium probablity distribution of money becomes the usual Gibb's distribution, characteristic of non-interacting agents, when the agents do not save. However with saving, even for local or individual self-interest, the dynamics become cooperative and the resulting asymmetric Gaussian-like stationary distribution acquires global ordering properties. Intriguing singularities are observed in the stationary money distribution in the market, as function of the ``marginal saving propensity'' of the agents.

cond-mat.stat-mech↗
arXiv2000

The travelling salesman problem on randomly diluted lattices: results for small-size systems

If one places N cities randomly on a lattice of size L, we find that the normalized optimal travel distances per city in the Euclidean and Manhattan metrics vary monotonically with the city concentration p. We have studied such optimal tours for visiting all the cities using a branch and bound algorithm, giving exact optimized tours for small system sizes (N<100). Extrapolating the results for N tending to infinity, we find that the normalized optimal travel distances per city in the Euclidean and Manhattan metrics both equal unity for p=1, and they reduce to about 0.74 and 0.94, respectively, as p tends to zero. Although the problem is trivial for p=1, it certainly reduces to the standard TSP on continuum (NP-hard problem) for p tending to zero. We did not observe any irregular behaviour at any intermediate point. The crossover from the triviality to the NP-hard problem seems to occur at p=1.

cond-mat.stat-mech↗
arXiv2000

Anomalous Transmission in a Hierarchical Lattice

We present an analytical method of studying "extended" electronic eigenstates of a diamond hierarchical lattice, which may be taken as the simplest of the hierarchical models recently proposed for stretched polymers. We use intuitive arguments and a renormalization-group method to determine the distribution of amplitudes of the wave functions corresponding to some of these "extended" eigenstates. An exact analysis of the end-to-end transmission property of arbitrarily large finite lattices reveals an anomalous behavoiur. It is seen that while for a special value of the energy the lattice, however large, becomes completely transparent to an incoming electron, for the other energy eigenvalues the transmission decreases with system size. For one such energy eigenvalue we analytically obtain the precise scaling form of the transmission coefficient. The same method can easily be adopted for other energies.

cond-mat.stat-mech↗
arXiv2000

Statistical Physics of the Travelling Salesman Problem

If one places N cities on a continuum in an unit area, extensive numerical results and their analysis (scaling, etc.) suggest that the best normalized optimal travel distance becomes 0.72 for the Euclidean metric and 0.92 for the Manhattan metric. The analytic bounds, we discuss here, give 0.5 and 0.92 as the lower and upper bounds for the Euclidean metric, and 0.64 and 1.17 for the Manhattan metric. When the cities are randomly placed on a lattice with concentration p, we find that the normalized optimal travel distance vary monotonically with p. For p=1, the values in both Euclidean and Manhattan metric are 1, and as p tends to zero, the values are 0.72 and 0.92 in the Euclidean and Manhattan metrics respectively.The problem is trivial for p=1 but it reduces to the continuum TSP as p tends to zero. We do not get any irregular behaviour at any intermediate point, e.g., the percolation point. The crossover from the triviality to the NP- hard problem seems to occur at p<1.

cond-mat.stat-mech↗