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.

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具有状态约束的平均场博弈：从PDE系统的温和解到点解

具有状态约束的平均场博弈是具有无限多个代理的微分博弈，每个代理都对其状态施加约束。本文的目的是提供与这些博弈相关的PDE系统的含义，即具有状态约束的所谓平均场博弈系统。为此，我们显示了带有状态约束的最优控制问题的值函数的全局半凹度属性。