On a Boltzmann mean field model for knowledge growth
Burger M, Lorz A, Wolfram MT (2016)
Publication Type: Journal article
Publication year: 2016
Journal
Publisher: Society for Industrial and Applied Mathematics Publications
Book Volume: 76
Pages Range: 1799-1818
Issue: 5
DOI: 10.1137/15M1018599
Abstract
In this paper we analyze a Boltzmann-type mean field game model for knowledge growth, which was proposed by Lucas et al. [J. Political Econ., 122 (2014), pp. 1-51]. We discuss the underlying mathematical model, which consists of a coupled system of a Boltzmann-type equation for the agent density and a Hamilton-Jacobi-Bellman equation for the optimal strategy. We study the analytic features of each equation separately and show local in time existence and uniqueness for the fully coupled system. Furthermore we focus on the construction and existence of special solutions, which relate to exponential growth in time - so-called balanced growth path solutions. Finally, we illustrate the behavior of solutions for the full system and the balanced growth path equations with numerical simulations.
Authors with CRIS profile
Involved external institutions
Westfälische Wilhelms-Universität (WWU) Münster
Germany (DE)
University of Warwick
United Kingdom (GB)
University of Paris 6 - Pierre et Marie Curie / Université Paris VI Pierre et Marie Curie (UPMC)
France (FR)
Germany (DE)
University of Warwick
United Kingdom (GB)
University of Paris 6 - Pierre et Marie Curie / Université Paris VI Pierre et Marie Curie (UPMC)
France (FR)
How to cite
APA:
Burger, M., Lorz, A., & Wolfram, M.-T. (2016). On a Boltzmann mean field model for knowledge growth. SIAM Journal on Applied Mathematics, 76, 1799-1818. https://dx.doi.org/10.1137/15M1018599
MLA:
Burger, Martin, Alexander Lorz, and Marie-Therese Wolfram. "On a Boltzmann mean field model for knowledge growth." SIAM Journal on Applied Mathematics 76 (2016): 1799-1818.
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