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

Burger M, Lorz A, Wolfram MT (2017)


Publication Type: Journal article

Publication year: 2017

Journal

Publisher: American Institute of Mathematical Sciences

Book Volume: 10

Pages Range: 117-140

Issue: 1

DOI: 10.3934/krm.2017005

Abstract

In this paper we study balanced growth path solutions of a Boltzmann mean field game model proposed by Lucas and Moll [15] 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 prove 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.

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APA:

Burger, M., Lorz, A., & Wolfram, M.-T. (2017). Balanced growth path solutions of a Boltzmann mean field game model for knowledge growth. Kinetic and Related Models, 10, 117-140. https://dx.doi.org/10.3934/krm.2017005

MLA:

Burger, Martin, Alexander Lorz, and Marie-Therese Wolfram. "Balanced growth path solutions of a Boltzmann mean field game model for knowledge growth." Kinetic and Related Models 10 (2017): 117-140.

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