Limited Move Stability with Probabilistic Preferences for Bilateral Conflicts

Abstract The Graph Model for Conflict Resolution (GMCR) is a flexible and user-friendly tool for representing and analyzing conflict situations. Several stability notions have been proposed in order to capture different behaviors that decision makers (DMs) may exhibit in a conflict. These stability concepts can be classified as either fixed-horizon or variable-horizon, depending on whether the analysis allows flexibility in choosing more than one horizon. On the other hand, modeling the preferences of DMs is a major challenge, and to encompass a wider range of situations, various preference structures have already been proposed in GMCR. However, to date, no study has addressed the combination of probabilistic preferences with a variable analysis horizon. This paper fills this gap by proposing the notion of $$(\alpha ,\beta ){\text {-}}L_h$$ stability for bilateral conflicts, which considers that at each move, the DMs seek to maximize the probability of preferring the final state of the conflict over the initial state, provided that this probability exceeds thresholds determined by the parameters $$\alpha $$ and $$\beta $$ . To better understand the proposed concept, its relationship with other stability notions for probabilistic preferences is examined, and an application to a hypothetical conflict is presented.