Introduction to First order Mean Field Games with State Constraints
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Speakers: Rossana Capuani, Department of Mathematics, University of Arizona
Title: Introduction to First order Mean Field Games with State Constraints
Abstract: This talk will address deterministic mean field games for which agents are restricted in a closed domain with smooth boundary. 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 solutions to the minimization problem which is solved by each agent is no longer guaranteed. Therefore we attack the problem by considering a relaxed version of it, for which the existence of equilibria can be proved by set-valued fixed point arguments. Finally, by analyzing the regularity and sensitivity with respect to space variables of the relaxed solution, we will show that it satisfies the Mean Field Games system in a suitable point-wise sense.