论文标题
有限州平均野外游戏，带有赖特·费舍尔普通噪声作为$ n $玩家加权游戏的限制
Finite state mean field games with Wright Fisher common noise as limits of $N$-player weighted games
论文作者
论文摘要
通过相关形式的共同噪声强迫有限状态的平均野外游戏是一个微妙的问题，直到最近才解决。除其他外，一种可能的方法是通过所谓的赖特 - 法派噪声对平衡的简单动态进行衡量，这在种群遗传学中非常非常本着随机模型的精神。一个关键功能是，这样的随机强迫保留了单纯形的结构，这无非是在这种情况下，是游戏状态空间上的概率空间。因此，本文的目的是阐明有限的玩家版本，因此证明$ n $ - 玩家的均衡确实会融合到解决这种赖特 - 菲什尔平均野外游戏的解决方案方面。尽管在公共噪声的存在下已经证明相应的主方程已被证明是唯一可解决的，但分析的一部分变得更容易，但是在标准环境中，它变得比标准环境更加微妙，因为现在玩家之间的平均场地相互作用现在通过加权的经验度量发生。换句话说，每个玩家都有自己的体重，因此可能与$ 1/n $不同，最重要的是随着共同的噪音而演变。
Forcing finite state mean field games by a relevant form of common noise is a subtle issue, which has been addressed only recently. Among others, one possible way is to subject the simplex valued dynamics of an equilibrium by a so-called Wright-Fisher noise, very much in the spirit of stochastic models in population genetics. A key feature is that such a random forcing preserves the structure of the simplex, which is nothing but, in this setting, the probability space over the state space of the game. The purpose of this article is hence to elucidate the finite player version and, accordingly, to prove that $N$-player equilibria indeed converge towards the solution of such a kind of Wright-Fisher mean field game. Whilst part of the analysis is made easier by the fact that the corresponding master equation has already been proved to be uniquely solvable under the presence of the common noise, it becomes however more subtle than in the standard setting because the mean field interaction between the players now occurs through a weighted empirical measure. In other words, each player carries its own weight, which hence may differ from $1/N$ and which, most of all, evolves with the common noise.
