论文标题
潜在的控件平均现场游戏的解决方案较弱
Weak Solutions for Potential Mean Field Games of Controls
论文作者
论文摘要
我们分析了一个偏微分方程的系统，该系统对控制的潜在平均场游戏进行了模拟，即简要介绍MFGC。这样的游戏描述了许多无限忽略的玩家竞争以优化个人价值功能的相互作用，该功能取决于国家，最著名的是控制所有其他玩家的选择。系统的解决方案对应于NASH平衡，这是一个组的最佳策略，没有一个玩家可以通过更改自己的动作来改进该策略。我们研究了二阶，可能是归类的情况，它具有非刻板椭圆扩散算子和局部耦合函数的情况。主要结果利用了采用各种技术为系统提供独特弱解决方案的潜力，并在其他假设下具有额外的空间和时间规律性结果。通过引入额外的耦合，这取决于状态分布和反馈。
We analyze a system of partial differential equations that model a potential mean field game of controls, briefly MFGC. Such a game describes the interaction of infinitely many negligible players competing to optimize a personal value function that depends in aggregate on the state and, most notably, control choice of all other players. A solution of the system corresponds to a Nash Equilibrium, a group optimal strategy for which no one player can improve by altering only their own action. We investigate the second order, possibly degenerate, case with non-strictly elliptic diffusion operator and local coupling function. The main result exploits potentiality to employ variational techniques to provide a unique weak solution to the system, with additional space and time regularity results under additional assumptions. New analytical subtleties occur in obtaining a priori estimates with the introduction of an additional coupling that depends on the state distribution as well as feedback.
