Existence and uniqueness for Mean Field Games with state constraints
Optimization and Control
2017-11-07 v2
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.
Cite
@article{arxiv.1711.01063,
title = {Existence and uniqueness for Mean Field Games with state constraints},
author = {Piermarco Cannarsa and Rossana Capuani},
journal= {arXiv preprint arXiv:1711.01063},
year = {2017}
}