Abstract: The family doctor contract service system represents a multi-actor governance arrangement involving the joint participation of the government, hospitals, family doctors, and patients. this paper develops an integrated analytical framework combining the grey ordinal priority approach (OPA-G) and the graph model for conflict resolution (GMCR) to analyze their strategic conflicts and identify stable equilibrium outcomes. The OPA-G method is first employed to determine the strategic preferences of each stakeholder under uncertain and incomplete information. These preference vectors are then incorporated into the GMCR framework to construct state transitions and assess equilibrium stability under Nash, GMR, SMR, and SEQ criteria. Using the GMCR Plus v0.4 software, the analysis identifies state S1 (YNYYNNYNYNN) as the only strongly stable equilibrium across all four stability definitions. In this state, the government implements strong incentives with strict performance assessments, hospitals enforce internal regulation and evaluation, family doctors actively fulfill contracts and deliver high-quality services, and patients cooperate with service delivery. The proposed Grey OPA–GMCR approach offers methodological guidance for enhancing coordination and optimizing the implementation of family doctor contract services, and more broadly provides a systematic mixed-method framework for modeling multi-actor conflicts in primary healthcare governance.