A Probabilistic Approach to Extended Finite State Mean Field Games
A Probabilistic Approach to Extended Finite State Mean Field Games
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DOI：
10.1287/moor.2020.1071
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发表时间：
2021-05-01
影响因子：
1.7
通讯作者：
Wang, Peiqi
中科院分区：
文献类型：
--
作者：
Carmona, Rene;Wang, Peiqi
本文提出了一种求解连续时间有限状态平均场对策的概率方法。基于半鞅对连续时间马尔可夫链的另一种描述和随机最优控制的弱表述，我们的方法不仅可以同时处理状态的平均场和控制的平均场，而且可以将参与者的策略集从马尔可夫策略扩展到闭环策略。我们证明了平均场博弈的纳什均衡的存在唯一性，以及在不同的成本函数和状态间转移率的结构和规则假设下，平均场博弈的均衡如何由有限参与人博弈的近似纳什均衡组成。
We develop a probabilistic approach to continuous-time finite state mean field games. Based on an alternative description of continuous-time Markov chains by means of semimartingales and the weak formulation of stochastic optimal control, our approach not only allows us to tackle the mean field of states and the mean field of control at the same time, but also extends the strategy set of players from Markov strategies to closed-loop strategies. We show the existence and uniqueness of Nash equilibrium for the mean field game as well as how the equilibrium of a mean field game consists of an approximative Nash equilibrium for the game with a finite number of players under different assumptions of structure and regularity on the cost functions and transition rate between states.