Abstract: Conflicts are inherent to many human interactions and substantial costs are associated with unresolved conflicts. In this talk, I will give an introduction about the Graph Model for Conflict Resolution (GMCR), which has been successfully applied to model and analyze many real world strategic conflicts. After recalling the main stability concepts used within GMCR, I will focus on the Maximin stability, which has been shown to generalize to higher horizons of analysis some classic stability notions. I will present the Maximin both in the traditional forward approach that determines which conflict scenarios are stable given the actions than can be taken by decision makers and their preferences, and also in the preference adjustment approach, where a linear integer optimization model to determine minimal preference adjustment to make a desired scenario a Maximin equilibrium is proposed.