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Evolution of the distribution of wealth in an economic environment driven by local Nash equilibria

Pierre Degond Institut de Mathématiques de Toulouse, Université de Toulouse Jian-Guo Liu Duke University Christian Ringhofer School of Mathematics and Statistical Sciences, Arizona State University

General Mathematics mathscidoc:1702.13002

Journal of Statistical Physics, 154, (3), 751–780, 2014.2
We present and analyze a model for the evolution of the wealth distribution within a heterogeneous economic environment. The model considers a system of rational agents interacting in a game theoretical framework, through fairly general assumptions on the cost function. This evolution drives the dynamic of the agents in both wealth and economic configuration variables. We consider a regime of scale separation where the large scale dynamics is given by a hydrodynamic closure with a Nash equilibrium serving as the local thermodynamic equilibrium. 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 as an equilibrium in the particular case of quadratic cost functions which has been previously considered in the literature.
Fokker-Planck equationGeometric Brownian motionNon-quadratic trading interactionGibbs measureInverse Gamma distributionPareto tailCollision invariant
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@inproceedings{pierre2014evolution,
  title={Evolution of the distribution of wealth in an economic environment driven by local Nash equilibria},
  author={Pierre Degond, Jian-Guo Liu, and Christian Ringhofer},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170208105356407969311},
  booktitle={Journal of Statistical Physics},
  volume={154},
  number={3},
  pages={751–780},
  year={2014},
}
Pierre Degond, Jian-Guo Liu, and Christian Ringhofer. Evolution of the distribution of wealth in an economic environment driven by local Nash equilibria. 2014. Vol. 154. In Journal of Statistical Physics. pp.751–780. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170208105356407969311.
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