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Obstacle mean field game problem

Bibliography:

D. Gomes and S. Patrizi, Obstacle mean field game problemTo appear in Interfaces and Free Boundaries.​

Authors:

D. Gomes and S. Patrizi

Keywords:

Mean-field games, obstacle problem, variational inequalities

Year:

2014

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.​

ISSN:

2014