论文标题
线性解决平均现场游戏的虚拟游戏有限差分方法
A fictitious-play finite-difference method for linearly solvable mean field games
论文作者
论文摘要
提出了平均野外游戏（MFG）的迭代有限差方案。目标MFG来自具有对流术语的多维系统的控制问题。对于此类MFG，引入了使用COLE-HOPF转换和使用虚拟游戏的迭代计算的线性化。这导致了一种迭代地解决明确方案的实现算法。通过迭代跟踪变量的误差，可以在数学上证明所提出的方案的收敛属性。数值计算表明，该提出的方法对于一维控制问题均可稳定。
An iterative finite difference scheme for mean field games (MFGs) is proposed. The target MFGs are derived from control problems for multidimensional systems with advection terms. For such MFGs, linearization using the Cole-Hopf transformation and iterative computation using fictitious play are introduced. This leads to an implementation-friendly algorithm that iteratively solves explicit schemes. The convergence properties of the proposed scheme are mathematically proved by tracking the error of the variable through iterations. Numerical calculations show that the proposed method works stably for both one- and two-dimensional control problems.
