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.　©　Springer　Nature　Switzerland　AG　2020.