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We present and analyze a model for the evolution of the wealth distributionwithin a heterogeneous economic environment. The model considers a system ofrational agents interacting in a game theoretical framework, through fairlygeneral assumptions on the cost function. This evolution drives the dynamic ofthe agents in both wealth and economic configuration variables. We consider aregime of scale separation where the large scale dynamics is given by ahydrodynamic closure with a Nash equilibrium serving as the local thermodynamicequilibrium. The result is a system of gas dynamics-type equations for thedensity and average wealth of the agents on large scales. We recover theinverse gamma distribution as an equilibrium in the particular case ofquadratic cost functions which has been previously considered in theliterature.

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