Balanced growth path solutions of a Boltzmann mean field game model for knowledge growth

TL;DR

This paper analyzes a Boltzmann mean field game model for knowledge growth, proving the existence of balanced growth paths under certain initial conditions and exploring stochastic effects on knowledge evolution.

Contribution

It establishes the existence of balanced growth path solutions in a Boltzmann mean field game model for knowledge growth, including stochastic dynamics.

Findings

Existence of balanced growth paths under Pareto-tail initial distributions

Exponential growth of overall production along these paths

Insights into stochastic knowledge evolution via geometric Brownian motion

Abstract

In this paper we study balanced growth path solutions of a Boltzmann mean field game model proposed by Lucas et al [13] to model knowledge growth in an economy. Agents can either increase their knowledge level by exchanging ideas in learning events or by producing goods with the knowledge they already have. The existence of balanced growth path solutions implies exponential growth of the overall production in time. We proof existence of balanced growth path solutions if the initial distribution of individuals with respect to their knowledge level satisfies a Pareto-tail condition. Furthermore we give first insights into the existence of such solutions if in addition to production and knowledge exchange the knowledge level evolves by geometric Brownian motion.