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Exponential distribution is ubiquitous in the framework of multi-agent systems. An alternative approach with an economic motivation to derive the exponential distribution in the framework of iterations in the space of distributions is…
As a significant factor in urban planning, traffic forecasting and prediction of epidemics, modeling patterns of human mobility draws intensive attention from researchers for decades. Power-law distribution and its variations are observed…
We study a stochastic $N$-particle system representing economic agents in a population randomly exchanging their money, which is associated to a class of one-dimensional kinetic equations modelling the evolution of the distribution of…
Most decision theories, including expected utility theory, rank dependent utility theory and cumulative prospect theory, assume that investors are only interested in the distribution of returns and not in the states of the economy in which…
We follow the time sequence of binary elastic collisions in a small collection of hard-core particles. Intervals between the collisions are characterized by the numbers of collisions of different pairs in a given time. It was shown…
To know the statistical distribution of a variable is an important problem in management of resources. Distributions of the power law type are observed in many real systems. However power law distributions have an infinite variance and thus…
We introduce a simple model of economy, where the time evolution is described by an equation capturing both exchange between individuals and random speculative trading, in such a way that the fundamental symmetry of the economy under an…
We address the issue of the distribution of firm size. To this end we propose a model of firms in a closed, conserved economy populated with zero-intelligence agents who continuously move from one firm to another. We then analyze the size…
Understanding the properties of response time distributions is a long-standing problem in cognitive science. We provide a tutorial overview of several contemporary models that assume power law scaling is a plausible description of the…
Economic systems are similar with physic systems for their large number of individuals and the exist of equilibrium. In this paper, we present a model applying the equilibrium statistical model in economic systems. Consistent with…
Polynomial distribution can be applied to dynamical systems in certain situations. Macroeconomic systems characterized by economic variables such as income and wealth can be modelled similarly using polynomials. We extend our previous work…
We analyze waiting times for price changes in a foreign currency exchange rate. Recent empirical studies of high frequency financial data support that trades in financial markets do not follow a Poisson process and the waiting times between…
This paper presents a novel study on gas-like models for economic systems. The interacting agents and the amount of exchanged money at each trade are selected with different levels of randomness, from a purely random way to a more chaotic…
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…
We consider the problem of estimating the joint distribution of a continuous-time perpetuity and the underlying factors which govern the cash flow rate, in an ergodic Markov model. Two approaches are used to obtain the distribution. The…
The sustainability of cooperation is crucial for understanding the progress of societies. We study a repeated game in which individuals decide the share of their income to transfer to other group members. A central feature of our model is…
We have numerically simulated the ideal-gas models of trading markets, where each agent is identified with a gas molecule and each trading as an elastic or money-conserving two-body collision. Unlike in the ideal gas, we introduce…
An analytical study of the return time distribution of extreme events for stochastic processes with power-law correlation has been carried on. The calculation is based on an epsilon-expansion in the correlation exponent:…
In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a…
Adaptive populations such as those in financial markets and distributed control can be modeled by the Minority Game. We consider how their dynamics depends on the agents' initial preferences of strategies, when the agents use linear or…