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# Exponential wealth distribution: a new approach from functional iteration theory

## Author

Listed:
• Ricardo Lopez-Ruiz
• Jose-Luis Lopez
• Xavier Calbet

## Abstract

Exponential distribution is ubiquitous in the framework of multi-agent systems. Usually, it appears as an equilibrium state in the asymptotic time evolution of statistical systems. It has been explained from very different perspectives. In statistical physics, it is obtained from the principle of maximum entropy. In the same context, it can also be derived without any consideration about information theory, only from geometrical arguments under the hypothesis of equiprobability in phase space. Also, several multi-agent economic models based on mappings, with random, deterministic or chaotic interactions, can give rise to the asymptotic appearance of the exponential wealth distribution. An alternative approach to this problem in the framework of iterations in the space of distributions has been recently presented. Concretely, the new iteration given by $f_{n+1}(x) = \int\int_{u+v>x}{f_n(u)f_n(v)\over u+v} dudv.$. It is found that the exponential distribution is a stable fixed point of the former functional iteration equation. From this point of view, it is easily understood why the exponential wealth distribution (or by extension, other kind of distributions) is asymptotically obtained in different multi-agent economic models.

## Suggested Citation

• Ricardo Lopez-Ruiz & Jose-Luis Lopez & Xavier Calbet, 2011. "Exponential wealth distribution: a new approach from functional iteration theory," Papers 1103.1501, arXiv.org.
• Handle: RePEc:arx:papers:1103.1501
as

File URL: http://arxiv.org/pdf/1103.1501

## References listed on IDEAS

as
1. Victor M. Yakovenko & J. Barkley Rosser, 2009. "Colloquium: Statistical mechanics of money, wealth, and income," Papers 0905.1518, arXiv.org, revised Dec 2009.
Full references (including those not matched with items on IDEAS)

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