Obstacle mean-field game problem

Diogo A. Gomes, Stefania Patrizi

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

In this paper, we introduce and study a first-order mean-field game obstacle problem. We examine the case of local dependence on the measure under assumptions that include both the logarithmic case and power-like nonlinearities. Since the obstacle operator is not differentiable, the equations for first-order mean field game problems have to be discussed carefully. Hence, we begin by considering a penalized problem. We prove this problem admits a unique solution satisfying uniform bounds. These bounds serve to pass to the limit in the penalized problem and to characterize the limiting equations. Finally, we prove uniqueness of solutions. © European Mathematical Society 2015.
Original languageEnglish (US)
Pages (from-to)55-68
Number of pages14
JournalInterfaces and Free Boundaries
Volume17
Issue number1
DOIs
StatePublished - 2015

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