Equilibrium distributions and relaxation times in gaslike economic models: an analytical derivation

Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Mar;83(3 Pt 2):036108. doi: 10.1103/PhysRevE.83.036108. Epub 2011 Mar 16.


A step-by-step procedure to derive analytically the exact dynamical evolution equations of the probability density functions (PDFs) of well-known kinetic wealth exchange economic models is shown. This technique gives a dynamical insight into the evolution of the PDF, for example, allowing the calculation of its relaxation times. Their equilibrium PDFs can also be calculated by finding its stationary solutions. This gives as a result an integro-differential equation, which can be solved analytically in some cases and numerically in others. This should provide some guidance into the type of PDFs that can be derived from particular economic agent exchange rules or, for that matter, any other kinetic model of gases with particular collision physics.