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20041111:100026788(2004)11201002061,2,1,1(11,610031;21,400044):(newsboy),,LL:;;;;:O227:AGameAnalysisofOptimalAdvertisingInvestmentandOrderPolicyforPerishableGoodsBUXiang2zhi1,ZHAOQuan2wu2,HUANGQing1,WUZhen2ye1(11SchoolofEconomicsandManagement,SouthwestJiaotongUniversity,Chendu610031,China;21SchoolofEconomicsandBusinessAdministration,ChongqingUniversity,Chongqing400044,China)Abstract:Throughincorporatingtheeffectofadvertisinginvestmentondemandintothenewsboyproblem,thegamemodellinkingadvertisinginvestmentandorderpolicyisestablishedamongfinitenumbersofenterprisesunderuncertaintyenvironment,theexistenceanduniquenessoftheequilibriumofwhichisproved.theeffectofparametersofthemodelontheequilibriumisanalyzedbyanappliedexample.Keywords:perishablegoods;advertising;newsboymodel;game;nashequilibrium:2003212216:(70272022):(1976-),,,,:1(PerishableGoods),Newsboy,,L,L,50,(Newsboy)L1988,50[1]L,PetruzziDada[2];EmmosGilbertLKhouja[3];LauLau[5]L,LippmanMcCardleMahajanRyzin[6,7],,LChen,[8]L,,L[1][9],,L,,L,©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.,,,,,L2n,,,,,,Z,,,Z,,Z,Z,Z,RDi(u)Di(u)1Ei,u=(u1,u2,,un)(u,uii,),Ei(iid),f()F()Z,RDi(u,Ei)=Di(u)Ei,,,Di(u):1,,,iSi=[0,uMi],,S=S1S2Sn;25Di(u)5ui0(i=1,2,,n);35Di(u)5uj0(i,j=1,2,,n;ji);452Di(u)5u2i0(i=1,2,,n)2i,3i,4,i,Di(u)Zp,c,s,,pcsZqii,u-i=(u1,u2,,ui-1,ui+1,,un)iZu-i,iPi(ui,u-i,qi),Pi(ui,u-i,qi)=EEi{põmin[qi,RDi(u,Ei)]+s[qi-RDi(u,Ei)]+-cqi-ui},[x]+=max[0,x]Ziu3iq3i,Pi(u3i,u-i,q3i)=maxui,qiPi(ui,u-i,qi)(1)u-i,inewsboy,Pi(ui,u-i,qi)=EEi{(p-c)qi-(p-s)[qi-RDi(u,Ei)]+-ui}=(p-c)qi-(p-s)Di(u)qiDi(u)0Fi(t)dt-ui(2)(1)(2),,iq3i:q3i=Di(u)õF-1i(Q)(3)Q=p-cp-s,F-1i(Q)Eix=QZDi(u)=D0,q3i=D0F-1i(Q)newsboyZ(3)(2),,Pi(ui,u-i)=(p-s)õDi(u)õF-1i(Q)0tõfi(t)dt-ui(4)10111©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.(4)iZ3,:11iPi(u,u-i)ui,u-i,(4)u3iZ:(4),5Pi(ui,u-i)5ui=(p-s)5Di(u)5uiF-1i(Q)0tfi(t)dt-1,(5)52Pi(ui,u-i)5u2i=(p-s)52Di(u)5u2iF-1i(Q)0tfi(t)dt.(6)5Di(u)5uiui=00,5Di(u)5uiui=uMi=0,ps,,5Pi(ui,u-i)5uiui=00,5Pi(ui,u-i)5uiui=uMi0,,(0,uMi),5Pi(ui,u-i)5ui=0Z,52Di(u)5u2i0,52Pi(ui,u-i)5u2i0,Pi(ui,u-i)ui,5Pi(ui,u-i)5ui,5Pi(ui,u-i)5ui=0ui(4)u3iZ311u3S,Pi(u3i,u3-i)Pi(ui,u3-i)uiSi(i=1,2,,n)Z1,Z(FudenbergTirole1991)[10]:n,Si,,Piui,ZSi=[0,uMi],ZDi(u),1,Piui,,,,Z1,[1],,,Z312Pa=ni=1Pi(ui,ui-i),uz=argmaxPa,u3Z,5Pa(u3)5ui=5Pi(u3i,u3-i)5ui+ji5Pj(u3j,u3-j)5ui5Pi(u3i,u3-i)5ui=0,5Pj(u3j,u3-j)5ui=(p-s)õ5Dj(u3)5uiõF-1ji(Q)0tfj(t)-10,,5Pa(u3)5ui0(7),5Pa(uz)5ui=5Pi(uzi,uz-i)5ui+ji5Pj(uzj,uz-j)5ui=0,,5Pi(uzi,uz-i)5ui=-ji5Pj(uzj,uz-j)5ui0(8)201200411©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.,:2,,,,Z(7),,,,,,Z(8),,,,,Z4,,:Di(u)=ai-biexp(-Kiui)+jiCijexp(-Kjuj),,Di(u)1ZEi1,f(x)=e-xx00Zp=50,c=40,s=20,Ki=0101,ai=5000,bi=1000,Cij=100(ij),(i=1,2,,n)Z1n248u3öuz(%)101.88106.25118.68q3öqu(%)100.0599.9399.55P3öPz(%)99.9999.7499.03,Z1,,,Z,,K,KZ1,K212,2Z2K212K20.0010.0050.010.050.1u1293.9293.9293.9293.9293.9q12027.52010.32008.22006.52006.3P19156.19076.19066.19058.19057.1u2636.6449.2293.991.052.4q21815.11986.72008.22025.42027.5P27823.48810.89066.193499397.621,K21,K22,,Z2,2K2,1K2Z33,2b2,b2,b2,Z4,b22,b21Z30111©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.3b212b2100500100015003000u1293.92293.92293.92293.92293.92q12027.52010.32008.22007.52006.8P19156.19076.19066.19062.89059.4u263.658224.6293.92334.46403.78q22008.22008.22008.22008.22008.2P29296.39135.49066.19025.58956.212K22K232b24b25,,,Z,Z,,,,Z401200411©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.:[1]KhoujiaM.andS.SRobbins.Linkingadvertisingandquantitydecisionsinthesingle2periodinventorymodel[J].InternationalJournalofProductionEconomics,2003,86:93-105.[2]PetruzziNC,MDada.Pricingandthenewsvendorproblem:Areviewwithextensions[J].OperationsResearch,1999,47(2):183-194.[3]EmmosH,S.M.Gilbert.Theroleofreturnspoliciesinpricingandinventorydecisionsforcataloguegoods[J].ManagementScience,1998,44:276-283.[4]KhoujiaM.TheNewsboyproblemunderprogressivemultiplediscounts[J].EuropeanJournalofOperationsResearch,1995,84:154-157.[5]LauH.S,A.H.Lau.Reorderingstrategiesforanewsboy2typeproduct[J].EuropeanJournalofOperationsResearch,1997,103:557-572.[6]LippmanS.A.andK.F.McCardle.Thecompetitivenewsboy[J].OperationsResearch,1997,45(1):54-65.[7]MahajanS.,GvanRyzin.Inventorycompetitionunderdynamicconsumerchoice[J].OperationsResearch,2001,49(5):646-657.[8]ChenY,YanH,LYao.Newsvendorpricinggame[R].WorkingPaper,ChineseUnivofHongKong,2002.[9],.Newsboy[J].,2002,22(11):59-63.ZHOUYong2wu,YANGShan2lin.Jointdeterminationofoptimaladvertisementcostandorderpolicyfornewsboy2type2merchandise[J].SystemsEngineering-Theory&Practice,2002,22(11):59-63.[10]FudenbergD,TiroleJ.GameTheory[M].MassachusettsInsituteofTechnology,1991.419-434.[11]CachonGP,NetessineS.Gametheoryinsupplychainanalysis[Z].AninvitedchapterforthebookSupplychainanalysisinthee2businessera,tothepublishedbyKluer,2003.(87)[12]XuB.Ondelay2independentstabilityoflarge2scalesystemswithtimedelay[J].IEEETransonAutomatContr,1995,40:930-933.[13],,.[J].,2002,22(4):15-18.GuanX,LiuY,DuanG.Ro