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Papanicolaou, George; Ryzhik, Lenya; Velcheva, Katerina

Traveling waves in a mean field learning model. (English) Zbl 1469.91033

Nonlinearity 34, No. 10, 6799-6842 (2021).
Summary: R. E. Lucas jun. and B. Moll have proposed in [“Knowledge growth and the allocation of time”, J. Polit. Econ. 122, No. 1, 1–51 (2014)] 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.

Cited in 3 Documents

MSC:

91B62 Economic growth models
91A16 Mean field games (aspects of game theory)
35C07 Traveling wave solutions
35Q91 PDEs in connection with game theory, economics, social and behavioral sciences

Keywords:

diffusion of knowledge; mean field games; traveling waves
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Full Text: DOI arXiv

References:

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