论文标题
平均野外游戏的虚拟游戏：连续的时间分析和应用
Fictitious Play for Mean Field Games: Continuous Time Analysis and Applications
论文作者
论文摘要
在本文中，我们将连续时间虚拟播放学习算法的分析加深了考虑各种有限状态平均现场游戏设置（有限的地平线，$γ$ discousted）的考虑，尤其允许引入其他常见的噪音。 我们首先对连续时间虚拟播放过程进行理论收敛分析，并证明诱导的可利用性以$ o（\ frac {1} {t}）$降低。这种分析强调使用可利用性作为相关的指标，以评估平均野外游戏中纳什均衡的收敛性。这些理论贡献由基于模型或无模型设置提供的数值实验支持。我们在此首次为平均野外游戏融合学习动态的情况下，在存在共同噪音的情况下。
In this paper, we deepen the analysis of continuous time Fictitious Play learning algorithm to the consideration of various finite state Mean Field Game settings (finite horizon, $γ$-discounted), allowing in particular for the introduction of an additional common noise. We first present a theoretical convergence analysis of the continuous time Fictitious Play process and prove that the induced exploitability decreases at a rate $O(\frac{1}{t})$. Such analysis emphasizes the use of exploitability as a relevant metric for evaluating the convergence towards a Nash equilibrium in the context of Mean Field Games. These theoretical contributions are supported by numerical experiments provided in either model-based or model-free settings. We provide hereby for the first time converging learning dynamics for Mean Field Games in the presence of common noise.
