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On absence of steady state in the Bouchaud-M\'ezard network model

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  • Zhiyuan Liu
  • R. A. Serota

Abstract

In the limit of infinite number of nodes (agents), the It\^o-reduced Bouchaud-M\'ezard network model of economic exchange has a time-independent mean and a steady-state inverse gamma distribution. We show that for a finite number of nodes the mean is actually distributed as a time-dependent lognormal and inverse gamma is quasi-stationary, with the time-dependent scale parameter.

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  • Zhiyuan Liu & R. A. Serota, 2017. "On absence of steady state in the Bouchaud-M\'ezard network model," Papers 1704.02377, arXiv.org.
    • Handle: RePEc:arx:papers:1704.02377
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    5. Jean-Philippe Bouchaud, 2015. "On growth-optimal tax rates and the issue of wealth inequalities," Papers 1508.00275, arXiv.org, revised Aug 2015.
    6. Bouchaud, Jean-Philippe & Mézard, Marc, 2000. "Wealth condensation in a simple model of economy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 282(3), pages 536-545.
    7. Ma, Tao & Holden, John G. & Serota, R.A., 2013. "Distribution of wealth in a network model of the economy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(10), pages 2434-2441.
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