Existence and Uniqueness for Mean Field Games with State Constraints
Author(s)
Cannarsa, Piermarco
Date Issued
2018
Type
bookPart
Volume
28
Start Page
49
End Page
71
Abstract
In this paper, we study deterministic mean field games for agents who operate in a bounded domain. In this case, the existence and uniqueness of Nash equilibria cannot be deduced as for unrestricted state space because, for a large set of initial conditions, the uniqueness of the solution to the associated minimization problem is no longer guaranteed. We attack the problem by interpreting equilibria as measures in a space of arcs. In such a relaxed environment the existence of solutions follows by set-valued fixed point arguments. Then, we give a uniqueness result for such equilibria under a classical monotonicity assumption.