InsightfultheoremsareestablishedoninterrelationshipsamongcoalitionandnoncooperativestabilityconceptsdefinedwithintheparadigmoftheGraphModelforConflictResolution.Morespecifically,thenewlydefinedcoalitionstabilitydefinitionsthatareconsideredarecoalitionNashstability(CNash),coalitiongeneralmetarationality(CGMR),coalitionsymmetricmetarationality(CSMR)andcoalitionsequentialstability(CSEQ),alongwiththeirearlier-definednoncooperativeversions.Arangeofinterestingnewtheoremsarederivedtoestablishconnectionsamongthesecoalitionstabilityconceptsaswellasbetweennoncooperativeandcoalitionstabilitydefinitions.ApplicationswithrespecttothegamesofPrisoner′sDilemmaandChicken,aswellasagroundwatercontaminationdispute,demonstratehowthevariousstabilitydefinitionscanbeappliedinpracticeandconfirmthevalidityofsomeofthetheoremsaswellaspointout,byexample,certaintypesofrelationshipswhichcannothold.
