Socio-economic utility and chemical potential

TL;DR

This paper introduces a concept of chemical potential into socio-economic models, linking it to utility equilibrium and enabling analysis of probabilistic decision-making, with validation through numerical simulations.

Contribution

It unifies the concepts of chemical potential and utility in socio-economic models, extending their applicability to probabilistic agent decisions.

Findings

Chemical potential can be related to utility in socio-economic systems.

The approach applies to a broad class of models beyond solvable cases.

Numerical simulations support the theoretical results.

Abstract

In statistical physics, the conservation of particle number results in the equalization of the chemical potential throughout a system at equilibrium. In contrast, the homogeneity of utility in socio-economic models is usually thought to rely on the competition between individuals, leading to Nash equilibrium. We show that both views can be reconciled by introducing a notion of chemical potential in a wide class of socio-economic models, and by relating it in a direct way to the equilibrium value of the utility. This approach also allows the dependence of utility across the system to be determined when agents take decisions in a probabilistic way. Numerical simulations of a urban economic model also suggest that our result is valid beyond the initially considered class of solvable models.