论文标题
在一阶平均野外游戏系统上，具有共同的噪音
On first order mean field game systems with a common noise
论文作者
论文摘要
我们认为没有特质但带有布朗类型的常见噪音的平均野外游戏。我们引入了随机部分微分方程的相关向后前向系统的解决方案的概念。我们表明该解决方案存在，并且对于单调耦合函数是独一无二的。这是平均野外游戏系统解决方案的第一个总体结果，该系统具有常见和没有特殊噪声的通用噪声。我们还使用该解决方案来找到具有常见但没有特殊噪声的N玩家差异游戏的近似最佳策略（NASH Equilibria）。分析的一个重要步骤是研究随机后退汉密尔顿 - 雅各比方程的良好性。
We consider Mean Field Games without idiosyncratic but with Brownian type common noise. We introduce a notion of solutions of the associated backward-forward system of stochastic partial differential equations. We show that the solution exists and is unique for monotone coupling functions. This the first general result for solutions of the Mean Field Games system with common and no idiosynctratic noise. We also use the solution to find approximate optimal strategies (Nash equilibria) for N-player differential games with common but no idiosyncratic noise. An important step in the analysis is the study of the well-posedness of a stochastic backward Hamilton-Jacobi equation.
