Higher-order sequential stabilities in the graph model for conflict resolution

Abstract

The Graph Model for Conflict Resolution (GMCR) is based on concepts of Game Theory and Conflict Analysis and is useful 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 (DM's) 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, it is not allowed to harm the opponent if it does not benefit from such movement. However, we show by means of an example that there are situations in which to perform such reaction the opponent must be leaving a SEQ state for him, making it non-credible. 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. Additionally, we introduce the concept of Higher-order Sequential Equilibria for coalitional analysis in the GMCR.