Stationary mean-field games with logistic effects

Diogo Aguiar Gomes () and Ricardo de Lima Ribeiro ()
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Diogo Aguiar Gomes: King Abdullah University of Science and Technology (KAUST)
Ricardo de Lima Ribeiro: King Abdullah University of Science and Technology (KAUST)

Partial Differential Equations and Applications, 2021, vol. 2, issue 1, 1-34

Abstract: 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.

Keywords: 49N80 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s42985-020-00053-9

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