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Evolution of wealth in a nonconservative economy driven by local Nash equilibria

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  • Pierre Degond

    ()
    (Department of Mathematics - Imperial College London - Imperial College London)

  • Jian-Guo Liu

    ()
    (Duke Physics - Duke University)

  • Christian Ringhofer

    ()
    (Department of Mathematics - Arizona State University)

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    Abstract

    We develop a model for the evolution of wealth in a non-conservative economic environment, extending a theory developed earlier by the authors. The model considers a system of rational agents interacting in a game theoretical framework. This evolution drives the dynamic of the agents in both wealth and economic configuration variables. The cost function is chosen to represent a risk averse strategy of each agent. That is, the agent is more likely to interact with the market, the more predictable the market, and therefore the smaller its individual risk. This yields a kinetic equation for an effective single particle agent density with a Nash equilibrium serving as the local thermodynamic equilibrium. We consider a regime of scale separation where the large scale dynamics is given by a hydrodynamic closure with this local equilibrium. A class of generalized collision invariants (GCIs) is developed to overcome the difficulty of the non-conservative property in the hydrodynamic closure derivation of the large scale dynamics for the evolution of wealth distribution. The result is a system of gas dynamics-type equations for the density and average wealth of the agents on large scales. We recover the inverse Gamma distribution, which has been previously considered in the literature, as a local equilibrium for particular choices of the cost function.

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    Paper provided by HAL in its series Working Papers with number hal-00967662.

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    Date of creation: 30 Mar 2014
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    Handle: RePEc:hal:wpaper:hal-00967662

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    1. David Mckenzie & Hillel Rapoport, 2004. "Network Effects and the Dynamics of Migration and Inequality: Theory and Evidence from Mexico," Working Papers 2004-3, Department of Economics, Bar-Ilan University.
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    3. Corneo, Giacomo & Jeanne, Olivier, 2001. " Status, the Distribution of Wealth, and Growth," Scandinavian Journal of Economics, Wiley Blackwell, vol. 103(2), pages 283-93, June.
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    9. Victor M. Yakovenko & J. Barkley Rosser, 2009. "Colloquium: Statistical mechanics of money, wealth, and income," Papers 0905.1518, arXiv.org, revised Dec 2009.
    10. Oded Galor & Joseph Zeira, 2013. "Income Distribution and Macroeconomics," Working Papers 2013-12, Brown University, Department of Economics.
    11. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
    12. Robson, Arthur J, 1992. "Status, the Distribution of Wealth, Private and Social Attitudes to Risk," Econometrica, Econometric Society, vol. 60(4), pages 837-57, July.
    13. Jean-Philippe Bouchaud & Marc Mezard, 2000. "Wealth condensation in a simple model of economy," Science & Finance (CFM) working paper archive 500026, Science & Finance, Capital Fund Management.
    14. Silver, Jonathan & Slud, Eric & Takamoto, Keiji, 2002. "Statistical Equilibrium Wealth Distributions in an Exchange Economy with Stochastic Preferences," Journal of Economic Theory, Elsevier, vol. 106(2), pages 417-435, October.
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