论文标题
MF-OMO：平均场游戏的优化配方
MF-OMO: An Optimization Formulation of Mean-Field Games
论文作者
论文摘要
本文提出了一个新的数学范式，以分析离散的平均场游戏。结果表明，为一般类别的平均频场游戏找到NASH平衡解决方案等同于解决有界变量和简单凸约限制（称为MF-OMO）的优化问题。这个等效框架使通过标准算法找到均值游戏的多个（甚至所有）NASH平衡解决方案。例如，预计的梯度下降被证明能够在有限的许多初始化时能够检索所有可能的NASH平衡解决方案。此外，通过线性奖励和平均场独立动力学分析平均场游戏将减少以求解有限数量的线性程序，因此可以在有限的时间内解决。该框架不依赖于纳什均衡的收缩和单调假设以及独特性。
This paper proposes a new mathematical paradigm to analyze discrete-time mean-field games. It is shown that finding Nash equilibrium solutions for a general class of discrete-time mean-field games is equivalent to solving an optimization problem with bounded variables and simple convex constraints, called MF-OMO. This equivalence framework enables finding multiple (and possibly all) Nash equilibrium solutions of mean-field games by standard algorithms. For instance, projected gradient descent is shown to be capable of retrieving all possible Nash equilibrium solutions when there are finitely many of them, with proper initializations. Moreover, analyzing mean-field games with linear rewards and mean-field independent dynamics is reduced to solving a finite number of linear programs, hence solvable in finite time. This framework does not rely on the contractive and the monotone assumptions and the uniqueness of the Nash equilibrium.
