Convergence, fluctuations and large deviations for finite state mean field games via the Master Equation
Convergence, fluctuations and large deviations for finite state mean field games via the Master Equation
复制标题
通过主方程计算有限状态平均场博弈的收敛、波动和大偏差
DOI：
10.1016/j.spa.2018.12.002
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发表时间：
2017
影响因子：
1.4
通讯作者：
Guglielmo Pelino
中科院分区：
文献类型：
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作者：
Alekos Cecchin;Guglielmo Pelino
我们展示了有限状态对称N-玩家微分博弈的收敛性，其中玩家控制他们从状态到状态的转换率，到由两个耦合的向前向后常微分方程组成的有限状态平均场博弈系统给出的极限动态。我们利用所谓的主方程，这在这个有限维的框架是一个一阶偏微分方程的概率测度的单纯形，获得反馈纳什均衡的收敛性，价值函数和最佳轨迹。收敛性论证只需要主方程解的正则性。此外，我们利用收敛结果证明了一个中心极限定理和一个大偏差原理的发展的N-球员的经验措施。在单调性假设下，研究了主方程解的适定性和正则性。
We show the convergence of finite state symmetric N-player differential games, where players control their transition rates from state to state, to a limiting dynamics given by a finite state Mean Field Game system made of two coupled forward–backward ODEs. We exploit the so-called Master Equation, which in this finite-dimensional framework is a first order PDE in the simplex of probability measures, obtaining the convergence of the feedback Nash equilibria, the value functions and the optimal trajectories. The convergence argument requires only the regularity of a solution to the Master Equation. Moreover, we employ the convergence results to prove a Central Limit Theorem and a Large Deviation Principle for the evolution of the N-player empirical measures. The well-posedness and regularity of solution to the Master Equation are also studied, under monotonicity assumptions.
主要参与者和次要参与者的有限状态平均场博弈
DOI：
--
发表时间：
2018
期刊：
arXiv.org
影响因子：
--
作者：
Rene Carmona, Peiqi Wang
通讯作者：
Rene Carmona, Peiqi Wang