Existence of positive solutions for an approximation of stationary mean-field games


Here, we consider a regularized mean-field game model that features a low-order regularization. We prove the existence of solutions with positive density. To do so, we combine a priori estimates with the continuation method. In contrast with high-order regularizations, the low-order regularizations are easier to implement numerically. Moreover, our methods give a theoretical foundation for this approach.

Involve, a Journal of Mathematics
Chuliang Song
Chuliang Song

I am a theoretical ecologist driven by the curiosity of how biodiversity is generated and maintained.

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