不确定需求下供应链合作广告与订货策略的博弈

200833:100026788(2008)0320056208,(,400044):,,,StackelbergNash,,.Nash.,.:;;;;:F224132:AGameanalysisofcooperativeadvertisingandorderingstrategiesinasupplychainunderdemanduncertaintyFUQiang,ZENGShun2qiu(CollegeofEconomicsandBusinessAdministration,ChongqingUniversity,Chongqing400044,China)Abstract:Basedonthetwo2echelonsupplychainstructureofnewsboy2type2product,thispaperrelaxestheassumptionthatthemarketdemandiscertain,andintroducesadecisionvariable-orderingquantity.Weinvestigatethemanufacturersandretailersoptimaladvertisingstrategies,retailersoptimalorderingstrategiesoftheStackelbergleader2followergameandNashco2opgamerespectively,andcomparethestrategiesselectionandsystemexpectedprofitsinthetwogameequilibrium.Meanwhile,wediscusstherestrainteffectofdemanduncertaintyonadvertisementexpendituresofthemanufacturerandtheretailer.ThentheNashbargainingmodelisutilizedtodeterminetheallocationoftheco2opprofit.Finally,anumericalexampleisgiventoconfirmtherelevantconclusion.Keywords:supplychain;co2opadvertising;ordering;game;bargaining:2006210223:(1963-),,,,,,:,,;(1982-),,,,:,,.1(),,.,,,,,(brandswitching).,.,198750(Rothschild,1988)[1],1990100(Rigg,1990)[2],1993200(Davis,1994)[3].,,.[4],(win2win).[5],Pareto.[6],,,,,.[7],(),.[8],(goodwillstock),.[9](discretechoicemodel),(quadratic).[10].,,.[11],Pareto.[12],Nash.,,.,,()(),.,,,,StackelbergNash,,,.2,.D(a,n)na,:D(a,n)=-a-n-.0,,,,.,D(a,n)an.,.,,.,C(n)=gn,C(a)=ea,ge,,ge0.,RD(a,n,)D(a,n)1,RD(a,n,)=D(a,n).f(x)F(x),g(x,a,n)=1D(a,n)fxD(a,n)(1)c,w,,p,r,s,q,t,0t1.,p,w,c,rs,,spwcr.,m=(w-c)q-gn-tgea(2)r=pmin{RD(a,n,),q}-wq+r[q-RD(a,n,)]+-s[RD(a,n,)-q]+-(1-t)gea(3)=m+r=pmin{RD(a,n,),q}-cq+r[q-RD(a,n,)]+-s[RD(a,n,)-q]+-ea-gn(4),[X]+=max[0,X].7533Stackelberg.,nt,,qa.E(r),maxa,qE(r)=pq0xg(x,a,n)dx++qqg(x,a,n)dx-wq+rq0(q-x)g(x,a,n)dx-s+q(x-q)g(x,a,n)dx-(1-t)gea(5)(1)(5),maxa,qE(r)=pqPD(a,n)0D(a,n)xf(x)dx++qPD(a,n)qf(x)dx-wq+rqPD(a,n)0(q-xD(a,n))f(x)dx-s+qPD(a,n)(xD(a,n)-q)f(x)dx-(1-t)gea(6),E(r)q.,a,E(r)q,5E(r)5q=(p-w+s)-(p-r+s)qPD(a,n)0f(x)dx=0(7)q=D(a,n)F-1(),=p-w+sp-r+s()(8)(8)(6),E(r)=(p-w+s)-(p-r+s)F-1()0f(x)dxD(a,n)F-1()+(p-r+s)D(a,n)F-1()0xf(x)dx-sD(a,n)-(1-t)gea(9)(7)D(a,n)=-a-n-,E(r)=(p-r+s)(-a-n-)F-1()0xf(x)dx-s(-a-n-)-(1-t)gea(10),(10)E(r)a,a,5E(r)5a=(p-r+s)a--1n-F-1()0xf(x)dx-sa--1n--e(1-t)=0(11),a=n-(-s)e(1-t)11+,=(p-r+s)F-1()0xf(x)dx().(12)(12)(8),q=-n-(-s)e(q-t)-1+n-F-1()(13)(12)(13)(2),maxt,nE(m)=(w-c)q-gn-tgea=(w-c)-n-(-s)e(1-t)-1+n-F-1()-gn-tgen-(-s)e(1-t)11+(14)5E(m)P5t=05E(m)P5n=0,,t3=(w-c)F-1()-(-s)-(-s)(w-c)F-1()-(-s)(15)8520083(w-c)F-1()(1+)(-s),t3=0.n3=eg1+((w-c)F-1()-(-s))11++(16)(15)(16)(12),a3=ge1+((w-c)F-1()-(-s))11++(17)(16)(17)(8),(15)(16)(13),q3=-eg((w-c)F-1()-(-s))--11++F-1()(18)1(8),,,;,;,,,.2(12),(t=0),()(5aP5t0),(Q5aP5n0).(indicator),,.3StackelbergNash(),,ePg.(15)(16)(17)(18)(6)(14),StackelbergE(3m)=(w-c)F-1()-(1++)eg((w-c)F-1()-(-s))11++(19)E(3r)=(-s)-(1+)(-s)eg((w-c)F-1()-(-s))--11++(20)E(3)=E(3m)+E(3r)(21)4Nash,,,,,.,()[13].,.411,,aq.maxa,n,qE()=pqPD(a,n)0D(a,n)xf(x)dx++qPD(a,n)qf(x)dx-cq+rqPD(a,n)0(q-xD(a,n))f(x)dx-s+qPD(a,n)(xD(a,n)-q)f(x)dx-ea-gn(22)E()q,,5E()P5q=0,5E()5q=(p-c+s)-(p-r+s)qPD(a,n)0f(x)dx=0(23)953q=D(a,n)F-1(…),…=p-c+sp-r+s(24)(24)(22),(23),E()=(p-r+s)(-a-n-)F-1(…)0xf(x)dx-s(-a-n-)-ea-gn(25)E()na,n=a-(…-s)g11+(26)a=n-(…-s)e11+(27)…=(p-r+s)F-1(…)0xf(x)dx,,…n3=eg1+(…-s)11++(28)…a3=ge1+(…-s)11++(29)(28)(29)(24),€q3=-eg(…-s)--11++F-1(…)(30)Nash(…a3,…n3,t,€q3)Y={(…a3,…n3,t,€q3):0t1}(31)(28)(29)(30)(22),NashE(…3)=(…-s)-(1++)eg(…-s)11++(32)4121,:U[,2-].f(x)=12(1-)x2-0(33)F(x)=0xx-2(1-)x2-1x2-(34),F-1()=+2(1-),F-1()0xf(x)dx=+(1-)2,=(p-w+s)(+(1-))…=(p-c+s)(+(1-)…).(16)(28)(17)(29),…-s(w-c)F-1()-(-s),…a3a3,…n3n3.,,(…-s)-[(w-c)F-1()-(-s)]=(1+)(-s)+…--(w-c)F-1()=(1+)(-s)+(1-)(w-c)2p-r+s0(35)…a3a3…n3n3,D(…a3,…n3)D(a3,n3).…,F-1(…)0620083F-1(),(8)(24),€q3q3.:4NashStackelberg.(…a3,…n3,€q3),E(…3)(a3,n3,q3)E(3).5NashStackelberg.6.,,D(a,n),,(p-c)D(a,n)-ea-gn.,,an,:^n3=eg1+(p-c)11++^a3=ge1+(p-c)11++(p-c)-(…-s)=(p-c+s)(1-)(1-…)0,^n3(28)…n3,^a3(29)…a3:^n3…n3^a3…a3..71,456().,,.,,.,,(…a3,…n3,t,€q3):E(m)=E(…3m(…a3,…n3,t,€q3))-E(3m)0,E(r)=E(…3r(…a3,…n3,t,€q3))-E(3r)0.(36),Pareto,.E(),,()..413Nash,E()=E(…3)-E(3)=E(m)+E(r),,.[14]Um(E(m))=1-exp(-mE(m))(37)Ur(E(r))=1-exp(-rE(r))(38)mr,.i(i=m,r),i=m,ri=1.Nash,()maxE(m),E(r)Us(E(m),E(r))=mUm(E(m))+rUr(E(r))=1-mexp(-mE(m))-rexp(-rE(r))(39)E(m)+E(r)=E()(39),5UsPE(m)=05UsPE(r)=0,E(m)=rm+rE()-1m+rlnrrmm(40)E(r)=mm+rE()+1m+rlnrrmm(41)163,rP(m+r),mP(m+r).(rrPmm)1,[1P(m+r)]ln(mmPrr).,.(40)(41),mr,mr.,.,mr,rPmmPr,m,r,.,,,.,,.…a3…n3€q3(14)(40),€t3=[(w-c)€q3-g…n3-3m-E(m)]P(e…a3).(:…a3€q3D(…a3,…n3)(6)(41)€t3).€t3.5().350P,650P,110P.100P,700P.,50.012015,10,5000500.011017,,.(015,115).=018,…=01992,F-1()=113,F-1(…)=11492,F-1()0xf(x)dx=0172F-1(…)0xf(x)dx=01988032.,=900,…=1235104,(15)t3=01265.(16)(17)(18)(28)(29)(30),,Stackelberg0139497,1157988,3514791,4611228.1974185789194.Nash0158803,213521,3910097,5812024.29401151176105.(14)(6)(32),Stackelberg8885153,6514198,1540015;Nash1675516