用优势启发式计算双矩阵对策的均衡

R. Aras, A. Dutech, F. Charpillet
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引用次数: 3

摘要

我们提出了一个一般和双矩阵博弈作为二部有向图的公式,目的是建立图的相关结构集(特别是初等环)和博弈的纳什均衡集之间的对应关系。我们证明了求出图的初等环的集合允许求出平衡点的集合。对于图具有稀疏邻接矩阵的博弈,这是计算均衡集的良好启发式方法。启发式还允许丢弃不产生任何平衡的支持空间部分,从而作为通过支持枚举计算平衡的算法的有用预处理步骤
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Computing the Equilibria of Bimatrix Games Using Dominance Heuristics
We propose a formulation of a general-sum bimatrix game as a bipartite directed graph with the objective of establishing a correspondence between the set of the relevant structures of the graph (in particular elementary cycles) and the set of the Nash equilibria of the game. We show that finding the set of elementary cycles of the graph permits the computation of the set of equilibria. For games whose graphs have a sparse adjacency matrix, this serves as a good heuristic for computing the set of equilibria. The heuristic also allows the discarding of sections of the support space that do not yield any equilibrium, thus serving as a useful preprocessing step for algorithms that compute the equilibria through support enumeration
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