Traveling waves in a mean field learning model
Abstract
Lucas and Moll have proposed in [22] a system of forward-backward partial differential equations that model knowledge diffusion and economic growth. It arises from a microscopic model of learning for a mean-field type interacting system of individual agents. In this paper, we prove existence of traveling wave solutions to this system. They correspond to what is known in economics as balanced growth path solutions. We also study the dependence of the solutions and their propagation speed on various economic parameters of the system.
- Publication:
-
Nonlinearity
- Pub Date:
- October 2021
- DOI:
- 10.1088/1361-6544/abcc4d
- arXiv:
- arXiv:2002.06287
- Bibcode:
- 2021Nonli..34.6799P
- Keywords:
-
- diffusion of knowledge;
- mean field games;
- traveling waves;
- 91A16;
- Mathematics - Analysis of PDEs
- E-Print:
- doi:10.1088/1361-6544/abcc4d