Exponential wealth distribution in different discrete economic models

Abstract

Exponential distribution is ubiquitous in the framework of multi-agent systems. An alternative approach with an economic motivation to derive the exponential distribution in the framework of iterations in the space of distributions is disclosed. Comment: 1 page; Communication presented in ECIT 2010, Nant (France), Setember (2010)

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European Conference on Iteration Theory
September 12 - 17, 2010, Nant, France
EXPONENTIAL WEALTH DISTRIBUTION IN
DIFFERENT DISCRETE ECONOMIC MODELS
L´ opez-Ruiz RICARDO
Universidad de Zaragoza,
Zaragoza, Spain
e-mail: rilopez@unizar.es
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 [1]. 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 [2]. 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 [3, 4]. An alternative approach
to this problem in the framework of iterations in the space of distributions will be presented
[5]. Concretely, the new iteration given by
fn+1(x) =
∫ ∫
u+v>x
fn(u)fn(v)
u + v
dudv .(1)
It is found that the exponential distribution is a stable fixed point of this type of systems (1).
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.
References
[1] E. T. Jaynes, Information theory and statistical mechanics. Phys. Rev. E 106 (1957),
620-630.
[2] R. Lopez-Ruiz, J. Sa˜ nudo, X. Calbet, Geometrical derivation of the Boltzmann factor.
Am. J. Phys. 76 (2008), 780-781.
[3] J. R. Sanchez, J. Gonzalez-Estevez, R. Lopez-Ruiz, M. G. Cosenza, A Model of coupled
maps for economic dynamics. Eur. Phys. J. Special Topics 143 (2007), 241-243.
[4] C. Pellicer-Lostao, R. Lopez-Ruiz, A chaotic gas-like model for trading markets. J. Comp.
Sci. (JOCS) 1 (2010), 24-32.
[5] R. Lopez-Ruiz, J. L. Lopez, X. Calbet, Manuscript in preparation (2010).
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