Random Market Models with an H-Theorem

TL;DR

This paper analyzes random market models where agents trade pairwise, showing that they naturally evolve towards an exponential wealth distribution and satisfy an H-theorem, with stability sensitive to perturbations.

Contribution

It demonstrates the existence of an H-theorem in these models and explores the stability of the exponential equilibrium under perturbations.

Findings

Wealth distribution converges to exponential form asymptotically.

Entropy increases over time, confirming the H-theorem.

Small perturbations disrupt the exponential equilibrium.

Abstract

In this communication, some economic models given by functional mappings are addressed. These are models for random markets where agents trade by pairs and exchange their money in a random and conservative way. They display the exponential wealth distribution as asymptotic equilibrium, independently of the effectiveness of the transactions and of the limitation of the total wealth. The entropy increases with time in these models and the existence of an H-theorem is computationally checked. Also, it is shown that any small perturbation of the models equations make them to lose the exponential distribution as an equilibrium solution.