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Wealth distribution on complex networks.

Takashi Ichinomiya¹

¹Department of Biomedical Informatics, Gifu University Graduate School of Medicine, Yanagido 1-1, Gifu 501-1194, Japan.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|February 2, 2013

Summary

We developed a theory explaining wealth distribution in the Bouchaud-Mézard model on complex networks. Our findings match simulations, except for specific Watts-Strogatz networks where assumptions break down.

Area of Science:

Statistical physics
Network science
Agent-based modeling

Background:

The Bouchaud-Mézard model describes wealth distribution.
Previous studies relied on numerical simulations to understand this distribution.
The influence of network topology on wealth distribution was observed but not theoretically explained.

Purpose of the Study:

To derive a theoretical explanation for wealth distribution in the Bouchaud-Mézard model on complex networks.
To establish equations for the probability distribution function based on network topology.
To validate the theoretical model against simulation results.

Main Methods:

Application of "adiabatic" and "independent" assumptions.
Utilizing the central-limit theorem.

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Derivation of analytical equations for the probability distribution function.

Main Results:

A theoretical framework was established to determine wealth distribution.
The derived equations show good agreement with simulation results across various network types.
Discrepancies were noted for Watts-Strogatz networks with low rewiring rates, indicating a breakdown of the "independent" assumption.

Conclusions:

The developed theory successfully explains wealth distribution in the Bouchaud-Mézard model for many complex networks.
The "independent" assumption is crucial and its limitations highlight specific network structures where the model may not apply.
This work provides a theoretical foundation for understanding economic phenomena on networks.