Existence of positive solutions for an approximation of stationary mean-field games
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- November 2015
- DOI:
- 10.48550/arXiv.1511.06999
- arXiv:
- arXiv:1511.06999
- Bibcode:
- 2015arXiv151106999A
- Keywords:
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- Mathematics - Analysis of PDEs
- E-Print:
- 15 pages