Wealth distributions in asset exchange models

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.

[1]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[2]  N. Wax,et al.  Selected Papers on Noise and Stochastic Processes , 1955 .

[3]  B. Hayes.  The American Scientist , 1962, Nature.

[4]  M. Gell-Mann,et al.  Physics Today. , 1966, Applied optics.

[5]  P. A. P. Moran,et al.  An introduction to probability theory , 1968 .

[6]  Diffusion Processes and their Sample Paths. , 1968 .

[7]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[8]  S. Orszag,et al.  Advanced Mathematical Methods For Scientists And Engineers , 1979 .

[9]  Elliott W. Montroll,et al.  Nonequilibrium phenomena. II - From stochastics to hydrodynamics , 1984 .

[10]  Harvey Gould,et al.  Kinetics of Aggregation and Gelation , 1985 .

[11]  W. Arthur,et al.  The Economy as an Evolving Complex System II , 1988 .

[12]  The Theory of Income and Wealth Distribution , 1988 .

[13]  Stuart A. Kauffman,et al.  The origins of order , 1993 .

[14]  Arantxa Etxeverria.  The Origins of Order , 1993 .

[15]  H. McKean,et al.  Diffusion processes and their sample paths , 1996 .

[16]  E. Bonabeau.  How nature works: The science of self-organized criticality (copernicus) , 1997 .

[17]  David M. Raup,et al.  How Nature Works: The Science of Self-Organized Criticality , 1997 .

[18]  D. Sornette.  Linear stochastic dynamics with nonlinear fractal properties , 1998 .

[19]  T. Liggett,et al.  Stochastic Interacting Systems: Contact, Voter and Exclusion Processes , 1999 .

[20]  J. Bouchaud,et al.  Theory Of Financial Risk And Derivative Pricing , 2000 .