Eur. Phys. J. B 2, 267-276 (1998)
https://doi.org/10.1007/s100510050249

Wealth distributions in asset exchange models

Center for Polymer Studies and Department of Physics, Boston University, Boston, MA 02215, USA

Corresponding author: ^a redner@sid.bu.edu

Received: 13 August 1997
Revised: 31 December 1997
Accepted: 26 January 1998
Published online: 15 March 1998

Abstract

A model for the evolution of the wealth distribution in an economically interacting population is introduced, in which a specified amount of assets are exchanged between two individuals when they interact. The resulting wealth distributions are determined for a variety of exchange rules. For “random” exchange, either individual is equally likely to gain in a trade, while “greedy” exchange, the richer individual gains. When the amount of asset traded is fixed, random exchange leads to a Gaussian wealth distribution, while greedy exchange gives a Fermi-like scaled wealth distribution in the long-time limit. Multiplicative processes are also investigated, where the amount of asset exchanged is a finite fraction of the wealth of one of the traders. For random multiplicative exchange, a steady state occurs, while in greedy multiplicative exchange a continuously evolving power law wealth distribution arises.