Socio-economic utility and chemical potential

¹ LET Transport Economics Laboratory, Université Lyon-2 and CNRS - 14 Avenue Berthelot, F-69007 Lyon, France, EU
² IXXI Complex Systems Institute - 5 rue du Vercors F-69007 Lyon, France, EU
³ Université de Lyon, Laboratoire de Physique, ENS Lyon, CNRS - 46 Allée d'Italie, F-69007 Lyon, France, EU

Received: 15 October 2010
Accepted: 20 January 2011

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.