Computational Mean-Field Games on Manifolds
The paper titled 'Computational Mean-field Games on Manifolds' explores the dynamics of rational agents in Riemannian manifolds. It formulates the Nash Equilibrium for mean-field games on these manifolds and establishes a connection between the PDE system and optimality conditions. The authors also present a proximal gradient method for variational mean-field games, supported by numerical experiments demonstrating the model's effectiveness.
- ▪The study focuses on mean-field games in Riemannian manifolds rather than traditional Euclidean spaces.
- ▪A Nash Equilibrium formulation for mean-field games on manifolds is presented.
- ▪The authors establish an equivalence between the PDE system and the optimality conditions of the associated variational form.
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Mathematics > Optimization and Control arXiv:2206.01622 (math) [Submitted on 3 Jun 2022] Title:Computational Mean-field Games on Manifolds Authors:Jiajia Yu, Rongjie Lai, Wuchen Li, Stanley Osher View a PDF of the paper titled Computational Mean-field Games on Manifolds, by Jiajia Yu and 3 other authors View PDF Abstract: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.
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