Convergence to an exponential wealth distribution in a random market model

Abstract

We study the discrete-time model of López-Ruiz, López and Calbet, describing the evolution of a wealth distribution under random pairwise exchanges of wealth among agents. This requires the analysis of the behaviour of iterations of a non-linear operator defined on a space of probability distributions. We prove that, as conjectured by López-Ruiz, López and Calbet, starting from a general wealth distribution, the wealth distribution converges to the exponential equilibrium distribution. The proof employs a special metric defined on spaces of probability distributions through their Laplace transforms.

Keywords:

• Random market model
• wealth distribution
• econophysics
• convergence to equilibrium

AMS Subject Classifications:

• 91B80
• 91B55
• 47H09
• 47H20