On a Boltzmann mean field model for knowledge growth

Journal article

Publication Details

Author(s): Burger M, Lorz A, Wolfram MT
Journal: SIAM Journal on Applied Mathematics
Publisher: Society for Industrial and Applied Mathematics Publications
Publication year: 2016
Volume: 76
Pages range: 1799-1818
ISSN: 0036-1399


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.

External institutions with authors

University of Paris 6 - Pierre et Marie Curie / Université Paris VI Pierre et Marie Curie (UPMC)
University of Warwick
Westfälische Wilhelms-Universität (WWU) Münster

How to cite

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

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.


Last updated on 2018-03-12 at 12:38