Mean field games with state constraints: from mild to pointwise solutions of the PDE system

Mean Field Games with state constraints are differential games with infinitely many agents, each agent facing a constraint on his state. The aim of this paper is to provide a meaning of the PDE system associated with these games, the so-called Mean Field Game system with state constraints. For this, we show a global semiconvavity property of the value function associated with optimal control problems with state constraints.

Automated summary

This paper explores Mean Field Games with state constraints, providing a meaning to the associated PDE system and showing a global semiconvexity property of the value function in optimal control problems with state constraints.