In　this　paper,　we　introduce　the　selfish　bin　packing　problem　under　a　new　version　of　cost　sharing　mechanism　based　on　harmonic　mean.　The　items　(as　agents)　are　selfish　and　intelligent　to　minimize　the　cost　they　have　to　pay,　by　selecting　a　proper　bin　to　fit　in.　The　tricky　part　is　that　the　one　with　bigger　size　pays　less　and　vice　versa.　We　present　the　motivations　and　prove　the　existence　of　pure　Nash　Equilibrium　under　this　new　defined　cost　sharing　mechanism.　Then　we　study　the　Price　of　Anarchy,　which　is　the　ratio　between　the　objective　value　of　worst　Nash　Equilibrium　and　that　of　the　optimum　in　the　case　with　central　decision　maker.　We　prove　the　upper　bound　to　be　approximately　1.722　and　show　a　5/3　lower　bound　for　this　problem.　We　then　include　punishment　into　the　model　and　prove　that　in　this　new　model,　the　Price　of　Anarchy　could　be　decreased　to　3/2.