论文标题
用于计算多游戏矩阵游戏NASH平衡的多线性公式
Multilinear formulations for computing Nash equilibrium of multi-player matrix games
论文作者
论文摘要
我们提出了多线性和混合企业多线性程序，以在多玩家非合作游戏中找到NASH均衡。我们将配方与Gambit中的常见算法进行了比较，并得出结论，多线性可行性程序比我们将其比较的任何方法都更快地找到了NASH平衡，包括大型游戏建议的定量响应平衡方法。因此，多线性可行性程序是在多玩家游戏中找到NASH平衡的另一种方法，并且表现优于许多常见算法。混合企业的配方是对两人游戏的已知混合企业计划的概括，但是与两人游戏不同，这些混合智能程序的性能并没有比现有算法更好。
We present multilinear and mixed-integer multilinear programs to find a Nash equilibrium in multi-player noncooperative games. We compare the formulations to common algorithms in Gambit, and conclude that a multilinear feasibility program finds a Nash equilibrium faster than any of the methods we compare it to, including the quantal response equilibrium method, which is recommended for large games. Hence, the multilinear feasibility program is an alternative method to find a Nash equilibrium in multi-player games, and outperforms many common algorithms. The mixed-integer formulations are generalisations of known mixed-integer programs for two-player games, however unlike two-player games, these mixed-integer programs do not give better performance than existing algorithms.
