2013/06/29 by Pierre Degond, Jian-Guo Liu, Jian‐Guo Liu +1
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Applied mathematics #Closure (psychology) #Complex Systems and Time Series Analysis #Distribution (mathematics) #Economic theories and models #Economics #Function (biology) #Inverse-gamma distribution #Mathematical analysis #Mathematical economics #Mathematical optimization #Mathematics #Nash equilibrium #Physics #Probability distribution #Quadratic equation #Scale (ratio) #Statistical physics #q-fin.GN
paper · pdf · doi:10.1007/s10955-013-0888-4
arxiv created 2013/06/29 · openalex publication_date 2013/11/19 · arxiv updated 2015/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.