论文标题
控制和最佳停止平均现场游戏：线性编程方法
Control and optimal stopping Mean Field Games: a linear programming approach
论文作者
论文摘要
我们将线性编程方法开发为在一般环境中的含义场上游戏。这种轻松的控制方法可以证明在弱假设下的存在结果，并很好地实现了数值实施。我们考虑代表代理人选择最佳控制和退出游戏的最佳时间，即瞬时奖励函数以及状态过程的系数可能取决于其他代理的分布，我们考虑了平均场景问题。此外，我们建立了通过线性编程方法获得的均值游戏平衡与通过受控/停止的Martingale方法获得的平均值之间的等效性，这是在仅具有控制的情况下以前几篇论文中使用的另一种放松方法。
We develop the linear programming approach to mean-field games in a general setting. This relaxed control approach allows to prove existence results under weak assumptions, and lends itself well to numerical implementation. We consider mean-field game problems where the representative agent chooses both the optimal control and the optimal time to exit the game, where the instantaneous reward function and the coefficients of the state process may depend on the distribution of the other agents. Furthermore, we establish the equivalence between mean-field games equilibria obtained by the linear programming approach and the ones obtained via the controlled/stopped martingale approach, another relaxation method used in a few previous papers in the case when there is only control.
