论文标题
通过平均野战游戏的单数控制的N玩家随机游戏的近似
Approximation of N-player stochastic games with singular controls by mean field games
论文作者
论文摘要
本文确定，一类$ n $ - 玩家随机游戏具有单数控制，无论是有限速度还是有限变化，都可以通过平均野战游戏（MFG）近似具有有界速度的单数控制。更具体地说，它显示了（i）具有界速度$θ$的单一控制的MFG的最佳控制表明，显示为$ε_n$ -ne对$ n $ -n $ - 玩家游戏，具有有界速度的单数控制，并具有$ε_n= o（\ε_n= o（\ frac {\ frac {1}） MFG是$（ε_n +ε_θ）$ - NE至$ n $ - 玩家游戏，具有有限变化的单数控件，其中$ε_θ$是一个错误术语，取决于$θ$。这项工作通过允许不连续的控件来概括MFGS上近似$ n $玩家游戏的经典结果。
This paper establishes that a class of $N$-player stochastic games with singular controls, either of bounded velocity or of finite variation, can both be approximated by mean field games (MFGs) with singular controls of bounded velocity. More specifically, it shows (i) the optimal control to an MFG with singular controls of a bounded velocity $θ$ is shown to be an $ε_N$-NE to an $N$-player game with singular controls of the bounded velocity, with $ε_N = O(\frac{1}{\sqrt{N}})$, and (ii) the optimal control to this MFG is an $(ε_N + ε_θ)$-NE to an $N$-player game with singular controls of finite variation, where $ε_θ$ is an error term that depends on $θ$. This work generalizes the classical result on approximation $N$-player games by MFGs, by allowing for discontinuous controls.
