Convergence to equilibrium for a class of exchange economies

TL;DR

This paper proves that for a specific class of stochastic exchange economy models, the probability distribution converges exponentially to a unique equilibrium determined by initial conditions and agent parameters.

Contribution

It establishes exponential convergence to equilibrium for fully connected Cobb-Douglas exchange economies, a novel result for this class of stochastic models.

Findings

Probability distribution converges exponentially to equilibrium.

Convergence is in total variation metric.

Equilibrium is uniquely determined by model parameters.

Abstract

For a class of stochastic dynamical models of exchange economies that we call ``fully connected Cobb-Douglas'', the paper proves convergence of the probability distribution to an equilibrium, in total variation metric as time goes to infinity. The convergence is exponential and the equilibrium is determined uniquely by the number of agents, their ``exponents'', and the initial amounts of money and goods in the economy.