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

TL;DR

This paper develops a model for wealth distribution evolution in a heterogeneous economy using game theory, deriving hydrodynamic equations and recovering known equilibrium distributions.

Contribution

It introduces a novel framework combining game theory and hydrodynamic limits to analyze wealth dynamics and equilibrium states.

Findings

Derives a system of gas dynamics-type equations for wealth and density.

Recovers the inverse gamma distribution as an equilibrium in specific cases.

Provides a new perspective on wealth distribution evolution in economic environments.

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.