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1、1,文献综述：博弈论在供应链管理中的应用,数9 艾松,2,博弈论在供应链管理中的应用,现在还处于探索的阶段,所用的博弈论理论还比较浅； 更多的是用博弈论中的概念、已有的结论等，最常用的就是Nash均衡，Game的模型，Stackelberg模型等； 部分模型用显示原理、 Nash均衡的存在性定理来求解均衡结果。,3,文献综述,Huang,Z.M., S.X.Li. 2001. Co-op advertising models in manufacturer-retailer supply chains:A game theory approach. European Journal of Op
2、erational Research 135,527-544. Li,S.X., Z.M.Huang, J.Zhu, P.Y.K.Chau. 2002. Cooperative advertising,game theory and manufacturer-retailer supply chains. Omega 30,347357.,4,Huang,Z.M., S.X.Li. 2001. Co-op advertising models in manufacturer-retailer supply chains:A game theory approach. European Jour
3、nal of Operational Research 135,527-544.,Keyword: Decision analysis; Game theory; Co-op advertising; Equilibrium; Coordination; Bargaining problems; Utilities.,6,1.Introduction,Most studies to date on vertical co-op advertising have focused on a relationship where the manufacturer is a leader and th
4、e retailer is a follower. This paper is intended to discuss the relationship between co-op advertising and efficiency of manufacturer- retailer transactions.,7,1.Introduction,Three co-op advertising model: 1.a leader-follower noncooperative game:manufacturer is a leader; 2.a noncooperative simultane
5、ous move game; 3.a cooperative game.,8,2.Assumptions,Sretailers sales response volume function of product; a retailers local advertising level; qmanufacturers national brand name investment t fraction of total local advertising expenditures which manufacturer shares,9,2.Assumptions,One-period sales
6、response volume function: Expected sales response volume:,10,2.Assumptions,The manufacturers,retailers,systems expected profit functions are as follows:,Note: “cq” should be “q”,11,3.Stackelberg equilibrium,We model the relationship between the manufacturer and the retailer as a sequential noncooper
7、ative game with the manufacturer as the leader and the retailer as the follower.,12,3.Stackelberg equilibrium,We first solve for the reaction function in the second stage of the game: is a concave function of Setting the first derivative of with respect to to be zero: Then we have Eq(5):,13,3.Stacke
8、lberg equilibrium,We can observe that: So the manufacturer can use his co-op advertising policy and his national brand name investment to induce the retailer to increase or decrease local advertising expenditure at a level he expects.,14,3.Stackelberg equilibrium,Next the optimal value of and are de
9、termined by maximizing the manufacturers profit subject to the constraint imposed by Eq(5).Hence,the manufacturers problem can be formulated as,15,3.Stackelberg equilibrium,Substituting into the objective yields the following problem (9):,16,3.Stackelberg equilibrium,Solving Eq(9),and substituting t
10、he outcome into Eq(5),we have the unique equilibrium point of the two-stage game:,17,3.Stackelberg equilibrium,Proposition 1:If (1)the manufacturer offers positive advertising allowance to the retailer ,otherwise he will offer nothing; (2),18,3.Stackelberg equilibrium,Three implications: (1) if reta
11、ilers marginal profit is high,retailer has strong incentive to spend money in local advertising to stimulate the sales, even though the manufacturer only shares a small fraction of local advertising expenditures or doesnt help;,19,3.Stackelberg equilibrium,(2)the higher (the lower) the retailers (ma
12、nufacturers) marginal profit,the lower the manufacturers advertising allowance for the retailer; (3)the increase of such that will cause an increase in the sales and then will give the retailer incentive to do local advertising without manufacturers financial help.,20,3.Stackelberg equilibrium,In th
13、is game,the manufacturer holds extreme power and has almost complete control over the behavior of the retailer.,The relationship is that of an employer and an employee!,21,4.Nash equilibrium,Recent studies in marketing have demonstrated that in many industries retailers have increased their power re
14、lative to manufacturers over the past two decades. Especially,for durable goods such as appliances and automobiles, the retailer has more influence on the consumers purchase decision.,22,4.Nash equilibrium,In this section,we relax the leader-follower relationship and assume a symmetric relationship
15、between the manufacturer and the retailer. The manufacturer and the retailer simultaneously and noncooperatively maximize their profits with respect to any possible strategies set by the other member .,23,4.Nash equilibrium,Hence,the manufacturers optimal problem is:,The retailers optimal problem is
16、:,24,4.Nash equilibrium,It is obvious that the manufacturers optimal fraction level, ,is zero,because of its negative coefficient in the objective. A Nash equilibrium advertising scheme can be obtained by simultaneously solving the following conditions:,25,4.Nash equilibrium,We then obtain the unique Nash equilibrium advertising scheme as follows:,26,4.Nash equilibrium,Three implications: (1)since the manufacturers allowance policies does not influence the sales response
