Coopetitionhasbecomethecurrentstrategictrendoftheeconomicdevelopment.Inthispaper,coopetitiongameandtheequi'ibriumhavebeendevelopedthroughcomparingthecharacteristicsofcooperationgamewiththoseofcompetitiongame.Furthmore,analgorithmusingonekindofminimaxtheoremproposedbyDingzhu-Duin1990isputforwardtosolvecoopetitiorgame.Thealgorithmhasgreatadvantagesoverothermethods,whichcansolveirregularandnon-differentialconcaveorconvexfunctionofthegames.Acoopetitiongameofcournotmodelwithasymmetricoligarchsisadvancedandthecoopetitionequilibriumshavebeenobtainedbysimulation.ThesimulationresultsarecomparedwiththatofNashequilibrium.Conclusionscanbemadethatmoremembersinacoalitioncouldgethighersatisfactiondegreesatcoopetitionequilibriums,whichisdependentoncostandpotentialmarketdemands.