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Stationary mean-field games with logistic effects

Author

Listed:
  • Diogo Aguiar Gomes

    (King Abdullah University of Science and Technology (KAUST))

  • Ricardo de Lima Ribeiro

    (King Abdullah University of Science and Technology (KAUST)
    Universidade Tecnológica Federal do Paraná (UTFPR))

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.

Suggested Citation

  • Diogo Aguiar Gomes & Ricardo de Lima Ribeiro, 2021. "Stationary mean-field games with logistic effects," Partial Differential Equations and Applications, Springer, vol. 2(1), pages 1-34, February.
    • Handle: RePEc:spr:pardea:v:2:y:2021:i:1:d:10.1007_s42985-020-00053-9
    DOI: 10.1007/s42985-020-00053-9
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    References listed on IDEAS

    as
    1. Noha Almulla & Rita Ferreira & Diogo Gomes, 2017. "Two Numerical Approaches to Stationary Mean-Field Games," Dynamic Games and Applications, Springer, vol. 7(4), pages 657-682, December.
    2. Diogo A. Gomes & Levon Nurbekyan & Mariana Prazeres, 2018. "One-Dimensional Stationary Mean-Field Games with Local Coupling," Dynamic Games and Applications, Springer, vol. 8(2), pages 315-351, June.
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