Computational mean-field games on manifolds
Computational mean-field games on manifolds
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DOI：
10.1016/j.jcp.2023.112070
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发表时间：
2022-06
期刊：
影响因子：
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通讯作者：
Jiajia Yu;Rongjie Lai;Wuchen Li;S. Osher
中科院分区：
文献类型：
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作者：
Jiajia Yu;Rongjie Lai;Wuchen Li;S. Osher
传统的平均场博弈/控制研究大量在欧几里德空间中运动的理性主体的行为。在这项工作中，我们探讨了黎曼流形上的平均场对策。给出了流形上的平均场博弈纳什均衡。我们还建立了PDE系统与流形上相关变分形式的最优性条件的等价性。基于二维流形的三角网格表示，设计了一种变分平均场博弈的近端梯度方法。我们在各种流形上的综合数值实验证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 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.