Higher-order Sequential Stabilities in the Graph Model for Conflict Resolution for Bilateral Conflicts

The Graph Model for Conflict Resolution (GMCR) is a flexible model and has been widely used for describing and analyzing conflicts. Stability analysis is used in the GMCR to determine possible solutions for the conflict. Several solution concepts have been proposed which accommodate different decision makers’ (DMs) behavior. Some of them are: Nash, General Metarationality (GMR) and Sequential Stability (SEQ). For a state to be Nash stable for a DM, such DM cannot move to a more preferred state in a single step. For GMR and SEQ, while considering moving to a more preferred state, the DM foresees whether the opponent can react leading the conflict to a state not preferred to the current one. What differs GMR and SEQ is that, in SEQ the opponent’s move simultaneously sanctions the focal DM and benefits the opponent. We show, by means of an example, that there are situations in which the opponent’s reaction is implausible in the sense that it involves the opponent leaving an SEQ stable state for him. In order to avoid that problem, we propose new solution concepts for the GMCR, called Higher-order Sequential Stabilities, and explore their relation with other solution concepts commonly used in the GMCR.