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.
Cannarsa, P., Capuani, R. (2018). Existence and Uniqueness for Mean Field Games with State Constraints. In PDE models for multi-agent phenomena (pp. 49-71). Springer, Cham [10.1007/978-3-030-01947-1_3].
Existence and Uniqueness for Mean Field Games with State Constraints
Cannarsa P.
;Capuani R.
2018-01-01
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.File | Dimensione | Formato | |
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