Wealth distribution of simple exchange models coupled with extremal dynamics

Abstract

Punctuated Equilibrium (PE) states that after long periods of evolutionary quiescence, species evolution can take place in short time intervals, where sudden differentiation makes new species emerge and some species extinct. In this paper, we introduce and study the effect of punctuated equilibrium on two different asset exchange models: The yard sale model (YS, winner gets a random fraction of a poorer player's wealth) and the theft and fraud model (TF, winner gets a random fraction of the loser's wealth). The resulting wealth distribution is characterized using the Gini index. In order to do this, we consider PE as a perturbation with probability $\rho$ of being applied. We compare the resulting values of the Gini index at different increasing values of $\rho$ in both models. We found that in the case of the TF model, the Gini index reduces as the perturbation $\rho$ increases, not showing dependence with the agents number. While for YS we observe a phase transition which happens around ${\rho }_c=0.79$. For perturbations $\rho <{\rho }_c$ the Gini index reaches the value of one as time increases (an extreme wealth condensation state), whereas for perturbations bigger or equal than ${\rho }_c$ the Gini index becomes different to one, avoiding the system reaches this extreme state. We show that both simple exchange models coupled with PE dynamics give more realistic results. In particular for YS, we observe a power low decay of wealth distribution.

arXiv comment15 pages, 5 figures. An Econophysics paper

References in corpus (17)

• Exponential and power-law probability distributions of wealth and income in the United Kingdom and the United States
• Statistical mechanics of money
• Statistical mechanics of money: How saving propensity affects its distribution
• Optimization with Extremal Dynamics
• Wealth Distributions in Models of Capital Exchange
• Pareto Law in a Kinetic Model of Market with Random Saving Propensity
• Nature's Way of Optimizing
• Distributions of money in model markets of economy
• The Social Architecture of Capitalism
• Stochastic Maps, Wealth Distribution in Random Asset Exchange Models and the Marginal Utility of Relative Wealth
• On the High-dimensional Bak-Sneppen model
• Evolution of economic entities under heterogeneous political/environmental conditions within a Bak-Sneppen-like dynamics
• Pareto and Boltzmann-Gibbs behaviors in a deterministic multi-agent system
• The distribution of wealth in the presence of altruism for simple economic models
• Regulation effects on market with Bak-Sneppen model in high dimensions
• Bacterial Evolution and Bak-Sneppen Model
• A Monte Carlo Renormalization Group Approach to the Bak-Sneppen model

Cited by in corpus (1)

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