In　this　paper,　we　quantify　the　efficiency　of　price-only　contracts　in　supply　chains　with　demand　distributions　by　imposing　prior　knowledge　only　on　the　support,　namely,　those　distributions　with　support　[a,b]　for　0　＜　a　＜=　b　＜　+　infinity　By　characterizing　the　price　of　anarchy　(PoA)　under　various　push　supply　chain　configurations,　we　enrich　the　application　scope　of　the　PoA　concept　in　supply　chain　contracts　along　with　complementary　managerial　insights.　One　of　our　major　findings　is　that　our　quantitative　analysis　can　identify　scenarios　where　the　price-only　contract　actually　maintains　its　efficiency,　namely,　when　the　demand　uncertainty,　measured　by　the　relative　range　b/a,　is　relatively　low,　entailing　the　price-only　contract　to　be　more　attractive　in　this　regard.　(C)　2013　Elsevier　Ltd.　All　rights　reserved.