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

Pierre Degond , Imperial College London Jian-Guo Liu Duke University Christian Ringhofer s, Arizona State University

General Mathematics mathscidoc:1702.13001

Philosophical Transactions of the Royal Society A Mathematical Physical & Engineering Sciences, 372, 2014.10
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.
multi-agent market models, price strategies, mean field games, Pareto distribution, Fokker–Planck equation, general collision invariants
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@inproceedings{pierre2014evolution,
  title={Evolution of wealth in a nonconservative economy driven by local Nash equilibria},
  author={Pierre Degond, Jian-Guo Liu, and Christian Ringhofer},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170208001146853600292},
  booktitle={Philosophical Transactions of the Royal Society A Mathematical Physical & Engineering Sciences},
  volume={372},
  year={2014},
}
Pierre Degond, Jian-Guo Liu, and Christian Ringhofer. Evolution of wealth in a nonconservative economy driven by local Nash equilibria. 2014. Vol. 372. In Philosophical Transactions of the Royal Society A Mathematical Physical & Engineering Sciences. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170208001146853600292.
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