Convergence to an exponential wealth distribution in a random market model |
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Authors: | Guy Katriel |
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Institution: | 1. Department of Mathematics, ORT Braude College, Karmiel, Israel.katriel@braude.ac.il |
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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. |
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Keywords: | Random market model wealth distribution econophysics convergence to equilibrium |
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