### Abstract

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.

Original language | English (US) |
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Pages (from-to) | 751-780 |

Number of pages | 30 |

Journal | Journal of Statistical Physics |

Volume | 154 |

Issue number | 3 |

DOIs | |

Publication status | Published - Feb 2014 |

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### Keywords

- Collision invariant
- Fokker-Planck equation
- Geometric Brownian motion
- Gibbs measure
- Inverse Gamma distribution
- Non-quadratic trading interaction
- Pareto tail

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Statistical Physics*,

*154*(3), 751-780. https://doi.org/10.1007/s10955-013-0888-4