<p>Limited-move stability (LM) is an essential yet relatively under-utilized stability concept in the graph model for conflict resolution (GMCR). To extend the applicability of LM stability to practical conflict scenarios characterized by uncertainty, this paper proposes novel extensions of LM stability concepts under unknown preference structures based on decision makers’ (DMs’) tolerance for preference uncertainty. For comparative symmetry, two four-step stability concepts, double general metarationality (DGMR) and double sequential stability (DSEQ), are innovatively developed following the logic of commonly utilized GMCR stability definitions, and are further extended under unknown preference. The analysis highlights the critical importance of understanding DMs’ tolerance for preference uncertainty in achieving conflict equilibrium. These new extended stability forms offer a deeper understanding of strategic behavior and tolerance for uncertainty, providing fresh perspectives for addressing complex strategic decisions. The proposed theoretical advancements are applied to market price conflicts, thereby demonstrating the practical feasibility and applicability of this improved conflict analysis framework.</p>