In this paper, our objective is to propose matrix results in order to determine Maximin \(_h\) (and some of its variants) stable states in the graph model for conflict resolution (GMCR). In the original Maximin \(_h\) stability concept, no prior information about other decision makers’ (DMs) preferences is necessary. Moreover, it is easily suited for modeling conflicts in which DMs have cautious profiles. Classical stability concepts, such as symmetric metarationality, general metarationality and Nash stability have already been shown to be particular cases of the \(\hbox {Maximin}_h\) stability. With the methods proposed in this paper, stability analysis in strategic conflicts involving several movements of action and counter-reaction or a high number of states or DMs can be done efficiently. Additionally, our approach extends the \(\hbox {Maximin}_h\) concept to a broader class of conflicts, including those in which indifference arises between states. To illustrate the practical relevance of the matrix results developed in this study, we examine two application cases: the Sun Belt Vs. British Columbia Government conflict, and the 1990 conflict along the Euphrates River. These cases allow for an in-depth analysis of the strategic dynamics, taking into account multiple moves made by the DMs over the course of the conflicts.
