Stationary mean-field games with logistic effects

Embargo End Date
2022-01-12

Type
Article

Authors
Gomes, Diogo A.
Ribeiro, Ricardo de Lima

KAUST Department
Applied Mathematics and Computational Science Program
Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

KAUST Grant Number
OSR-CRG2017-3452

Online Publication Date
2021-01-12

Print Publication Date
2021-02

Date
2021-01-12

Abstract
In its standard form, a mean-field game is a system of a Hamilton-Jacobi equation coupled with a Fokker-Planck equation. In the context of population dynamics, it is natural to add to the Fokker-Planck equation features such as seeding, birth, and non-linear death rates. Here, we consider a logistic model for the birth and death of the agents. Our model applies to situations in which crowding increases the death rate. The new terms in this model require novel ideas to obtain the existence of a solution. Here, the main difficulty is the absence of monotonicity. Therefore, we construct a regularized model, establish a priori estimates for the solution, and then use a limiting argument to obtain the result.

Citation
Gomes, D. A., & Ribeiro, R. de L. (2021). Stationary mean-field games with logistic effects. SN Partial Differential Equations and Applications, 2(1). doi:10.1007/s42985-020-00053-9

Acknowledgements
D. Gomes was partially supported by KAUST baseline funds and KAUST OSR-CRG2017-3452.

Publisher
Springer Nature

Journal
SN Partial Differential Equations and Applications

DOI
10.1007/s42985-020-00053-9

Additional Links
http://link.springer.com/10.1007/s42985-020-00053-9

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