In this paper, matrix methods are developed to determine stable states in the graph model for conflict resolution (GMCR) with probabilistic preferences with n decision makers. The matrix methods are used to determine more easily the stable states according to five stability definitions proposed for this model, namely: \(\alpha \)-Nash stability, (\(\alpha \), \(\beta \))-metarationality, (\(\alpha \), \(\beta \))-symmetric metarationality, (\(\alpha \), \(\beta \), \(\gamma \))-sequential stability and (\(\alpha \), \(\beta \), \(\gamma \))-symmetric sequential stability. With the help of such methods, we are able to analyze for which values of parameters \(\alpha \), \(\beta \) and \(\gamma \) the states satisfy each one of these stability notions. These parameters regions can be used to compare the equilibrium robustness of the states. As a byproduct of our method, we point out an existing problem in the literature regarding matrix representation of solution concepts in the GMCR.

在本文中，开发了矩阵方法来确定具有n个决策者的概率偏好的冲突解决方案（GMCR）的图形模型中的稳定状态。根据针对该模型提出的五个稳定性定义，可以使用矩阵方法更轻松地确定稳定状态，即：\（\ alpha \）-纳什稳定性，（\（\ alpha \），\（\ beta \））-对称性，（\（\ alpha \），\（\ beta \））-对称性metarationality，（\（\ alpha \），\（\ beta \），\（\ gamma \））-顺序稳定性和（\（（ \ alpha \），\（\ beta \），\（\ gamma \））对称的顺序稳定性。借助于这样的方法，我们能够分析出状态满足参数\（\ alpha \），\（\ beta \）和\（\ gamma \）的哪个值满足这些稳定性概念中的每一个。这些参数区域可用于比较状态的平衡鲁棒性。作为我们方法的副产品，我们指出了文献中有关GMCR中解决方案概念的矩阵表示的问题。