Existence and Uniqueness for Mean Field Games with State Constraints
By Piermarco Cannarsa, Rossana Capuani. 2017
61 citations recorded by the source corpus.
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.
Subfields: Economics and Econometrics, Finance, Modeling and Simulation
View Paper: https://www.semanticscholar.org/paper/26a624d6309f10c3a38bc3ad6062edf7d566b7fc
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In Economics and Econometrics
In Finance
In Modeling and Simulation
Citations in the corpus
- Finite Mean Field Games: Fictitious play and convergence to a first order continuous mean field game (2018, methodology): “ics. The denition of equilibrium that we adopted in this work corresponds to a relaxation of the PDE notion of equilibrium, and has been used, for instance, in [12], [5, Section 3] and, recently, in [7]. Throughout this section, we will suppose that the following assumption holds. (H3)(i) The functi”