Nash Stability in a Multi-objective Graph Model with Interval Preference Weights: Application to a US-China Trade Dispute

In many real-world conflict situations, decision-makers (DMs) integrate multiple objectives rather than considering just one objective or dimension. A multi-objective graph model (MOGM) is proposed to balance each DM's objectives in both two-DM and multi-DM conflicts. To identify Nash stability in MOGMs, a comprehensive preference matrix with weight parameters on objectives is developed for each DM, along with a unilateral move matrix including preference weights (UMP). Then, considering the subjective uncertainty of DMs, interval numbers are used to represent the degree of uncertainty of preference. Subsequently, Nash equilibria and interval Nash equilibria are developed for MOGMs, and the dependence of these equilibria on weights is shown. To illustrate how MOGM can be applied in practice and provide valuable strategic insights, it is used to investigate a US-China trade dispute model. The stability results suggest potential strategic resolutions of bilateral trade disputes, and how DMs can attain them. The case analysis process suggests that a peaceful settlement of the dispute may be achievable.