论文标题
具有控制疗法动力学的确定性平均现场游戏的近似
Approximation of deterministic mean field games with control-affine dynamics
论文作者
论文摘要
我们考虑确定性平均场游戏，其中典型代理的动力学相对于状态变量不线和相对于控制变量的仿射。这里考虑的问题的特定实例是平均野外游戏，并控制加速度。我们通过离散时间和有限状态空间中的类似问题将注意力集中在这种平均现场游戏的近似上。对于这些近似值，我们显示了存在的存在，并在额外的单调性假设下是解决方案的唯一性。在我们的主要结果中，我们确定了离散平均野外游戏问题与连续均衡的平衡问题的均衡。最后，我们为两个MFG问题提供了一些数值结果。在第一个中，相对于状态，典型玩家的动力学是非线性的，在第二个状态下，典型的玩家控制了其加速度。
We consider deterministic mean field games where the dynamics of a typical agent is non-linear with respect to the state variable and affine with respect to the control variable. Particular instances of the problem considered here are mean field games with control on the acceleration. We focus our attention on the approximation of such mean field games by analogous problems in discrete time and finite state space. For these approximations, we show the existence and, under an additional monotonicity assumption, uniqueness of solutions. In our main result, we establish the convergence of equilibria of the discrete mean field games problems towards equilibria of the continuous one. Finally, we provide some numerical results for two MFG problems. In the first one, the dynamics of a typical player is nonlinear with respect to the state and, in the second one, a typical player controls its acceleration.
