An Extension of Higher-Order Sequential Stabilities for Multilateral Conflicts and for Coalitional Analysis in the Graph Model for Conflict Resolution

The Graph Model for Conflict Resolution (GMCR) is a model for analyzing and describing conflicts which is based on concepts of Conflict Resolution Analysis and Game Theory. The GMCR can be used to find possible conflict solutions through a stability analysis. In a conflict situation, decision makers (DMs) can behave differently. Thus, in the literature, there are several solution concepts to accommodate these different behaviors. Among the best-known solutions concepts are: Nash, General Metarationality (GMR) and Sequential Stability (SEQ). A state is considered Nash stable for a DM if it cannot in a single step move to a preferred state. In the case of SEQ and GMR stabilities, a DM anticipates if his/her opponents may react to his/her initial move leading the conflict to a state that is not preferable to the initial one. The difference between these two concepts is that, in SEQ, only reactions which are also beneficial to the opponents are taken into account. However, the definition of SEQ may require a sanction in which an opponent moves away from a state that is SEQ stable for the opponent, a move that seems implausible. Recently, in order to avoid these implausible reactions, Higher-Order Sequential Stabilities have been proposed for bilateral conflicts. In this paper, we extend these concepts for multilateral conflicts and also for coalitional stability analysis. We present results about these concepts and illustrate their importance in the analysis of a Private Brownfield Renovation conflict.