论文标题
歧管上的计算平均场游戏
Computational Mean-field Games on Manifolds
论文作者
论文摘要
常规的平均场游戏/控制研究在欧几里得空间中移动的大量理性代理的行为。在这项工作中，我们探索了Riemannian歧管上的平均场比赛。我们在歧管上制定了平均游戏NASH平衡。我们还建立了PDE系统与歧管上相关变异形式的最佳条件之间的等价性。基于二维流形的三角形网格表示，我们为各种平均场游戏设计了一种近端梯度方法。我们对各种流形的全面数值实验说明了所提出的模型和数值方法的有效性和灵活性。
Conventional Mean-field games/control study the behavior of a large number of rational agents moving in the Euclidean spaces. In this work, we explore the mean-field games on Riemannian manifolds. We formulate the mean-field game Nash Equilibrium on manifolds. We also establish the equivalence between the PDE system and the optimality conditions of the associated variational form on manifolds. Based on the triangular mesh representation of two-dimensional manifolds, we design a proximal gradient method for variational mean-field games. Our comprehensive numerical experiments on various manifolds illustrate the effectiveness and flexibility of the proposed model and numerical methods.
