论文标题
具有主要代理的LQG平均现场游戏：NASH确定性等效与概率方法
LQG Mean Field Games with a Major Agent: Nash Certainty Equivalence versus Probabilistic Approach
论文作者
论文摘要
在LQG设置中（Huang，2010）引入了由主要代理和大量未成年人组成的平均野外游戏（MFG）系统。当小型试剂的数量倾向于无穷大时，使用NASH的确定性等效性来获得限制系统的Markovian闭环NASH平衡。在过去的几年中，已经开发了几种主要的方法 - 平均野外游戏问题，主要是（i）NASH的确定性等效性和分析方法，（ii）主方程，（iii）渐变性可溶性，以及（iv）概率方法。对于LQG情况，最近的工作（Huang，2021）确定了通过（i）获得通过（i）获得的马尔可夫闭环NASH平衡的等效性。在这项工作中，我们证明了（i）的马尔可夫闭环nash平衡等效于LQG情况的（iv）。这两项研究回答了有关使用不同方法得出的主要少量LQG MFG系统解决方案一致性的长期问题。
Mean field game (MFG) systems consisting of a major agent and a large number of minor agents were introduced in (Huang, 2010) in an LQG setup. The Nash certainty equivalence was used to obtain a Markovian closed-loop Nash equilibrium for the limiting system when the number of minor agents tends to infinity. In the past years several approaches to major--minor mean field game problems have been developed, principally (i) the Nash certainty equivalence and analytic approach, (ii) master equations, (iii) asymptotic solvability, and (iv) the probabilistic approach. For the LQG case, the recent work (Huang, 2021) establishes the equivalency of the Markovian closed-loop Nash equilibrium obtained via (i) with those obtained via (ii) and (iii). In this work, we demonstrate that the Markovian closed-loop Nash equilibrium of (i) is equivalent to that of (iv) for the LQG case. These two studies answer the long-standing questions about the consistency of the solutions to major-minor LQG MFG systems derived using different approaches.
