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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 Operation
2、al 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 Journal of Operational
3、 Research 135,527-544.,Keyword:Decision analysis;Game theory;Co-op advertising;Equilibrium;Coordination;Bargaining problems;Utilities.,5,1.Introduction,Vertical co-op advertising is an interactive relationship between a manufacturer and a retailer in which the retailer initiates and implements a loc
4、al advertising and the manufacturer pays part of the cost.The main reason for a manufacturer to use co-op advertising is to strengthen the image of the brand and to motivate immediate sales at retailer level.,6,1.Introduction,Most studies to date on vertical co-op advertising have focused on a relat
5、ionship where the manufacturer is a leader and the 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:manufact
6、urer is a leader;2.a noncooperative simultaneous 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 investmentt fraction of total local advertising expenditures which manufacturer
7、 shares,9,2.Assumptions,One-period sales 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 t
8、he retailer as a sequential noncooperative 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 z
9、ero:Then we have Eq(5):,13,3.Stackelberg 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,Ne
10、xt the optimal value of and are determined 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
11、,Solving Eq(9),and substituting the 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,T
12、hree implications:(1)if retailers 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(th
13、e lower)the retailers(manufacturers)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.Stackel
14、berg equilibrium,In this 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 in
15、creased their power relative 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 sym
16、metric relationship 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
17、optimal problem is:,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 o
18、btain 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 volume function,independent actions taken by both members simultaneously make no impact of the sharing policie
19、s on the determination of the retailers local advertising level;,27,4.Nash equilibrium,(2),(3),28,4.Nash equilibrium,Comparisons among results between two different noncooperative game:Proposition 2:(a)The manufacturer always prefers the leader-follower structure rather than the simultaneous move st
20、ructure;,29,4.Nash equilibrium,(b)If the retailer prefers the simultaneous move game structure,otherwise he prefers the leader-follower game structure.,30,4.Nash equilibrium,Proposition 3:(a)The manufacturers brand name investment is higher at Nash than at Stackelberg;(c)The manufacturers advertisin
21、g allowance for retailer is zero.,31,4.Nash equilibrium,(b)If the retailers local advertising expenditure is higher at Nash than at Stackelberg,otherwise it is lower at Nash than at Stackelberg.,32,5.An efficiency co-op advertising model,In this section we will retain the assumption of the symmetric
22、 relationship between the manufacturer and the retailer.We will discuss the efficiency of manufacturer and retailer transactions in vertical co-op advertising agreements.,33,5.An efficiency co-op advertising model,We consider Pareto efficient advertising schemes in our co-op advertising arrangements
23、.,A scheme is called Pareto efficient if one cannot find any other scheme(a,t,q)such that neither the manufacturers nor the retailers profit is less at(a,t,q)but at least one of the manufacturers and retailers profits is higher at(a,t,q)than at.,34,5.An efficiency co-op advertising model,Since and a
24、re quasi-concave,the set of Pareto efficient schemes consists of those points where the manufacturers and the retailers iso-profit surfaces are tangent to each other,i.e.,for some=0,35,5.An efficiency co-op advertising model,This leads to the following proposition,36,5.An efficiency co-op advertisin
25、g model,This theorem tells us that all Pareto efficient schemes are associated with a single local advertising expenditure and a single manufacturers brand name investment and with the fraction t of the manufacturers share of the local advertising expenditures between 0 and 1.The locus of tangency l
26、ies on a vertical line segment at in(a,t,q)space.,37,5.An efficiency co-op advertising model,Proposition 5:An advertising scheme is Pareto efficient if and only if it is an optimal solution of the joint system profit maximization problem.,This theorem tells us that,among all possible advertising sch
27、emes,the system profit(i.e.,the sum of the manufacturers and the retailers profits)is maximized for Every Pareto efficient scheme,but not for any other schemes.,38,5.An efficiency co-op advertising model,Proposition 6:(a)The system profit is higher at any Pareto efficient scheme than at both noncoop
28、erative equilibriums;(c)The local advertising expenditure is higher at any Pareto efficient scheme than at both noncooperative equilibriums;,39,5.An efficiency co-op advertising model,(b)If then the manufacturers brand name investment is higher at any Pareto efficient scheme than at both noncooperat
29、ive equilibriums,otherwise the manufacturers brand name investment at any Pareto efficient scheme is higher than at Stackelberg equilibrium and is lower than at Nash equilibrium.,40,5.An efficiency co-op advertising model,Proposition 6 leads to the possibility that both the manufacturer and the reta
30、iler can gain more profits compared with Stackelberg equilibriums.,But it should be noted that not all Pareto efficient schemes are feasible to both the manufacturer and the retailer.Neither the manufacturer nor the retailer would be willing to accept less profits at full cooperation than with nonco
31、operation.,41,5.An efficiency co-op advertising model,An advertising scheme is called feasible Pareto efficient if,42,5.An efficiency co-op advertising model,the feasible Pareto efficient set of advertising schemes.,Since only schemes satisfying(24)and(25)are acceptable for both the manufacturer and
32、 the retailer when they do coordinate,we then call,43,5.An efficiency co-op advertising model,Referring to Proposition 2,we know that:(1)(2)If then otherwise,44,5.An efficiency co-op advertising model,Therefore,For the purpose of simplicity,we assume that,45,5.An efficiency co-op advertising model,H
33、ence relationships in Eq(24)and(25)can be rewritten as,46,5.An efficiency co-op advertising model,Let Here we assume,47,5.An efficiency co-op advertising model,Then and Z can be simplified as,48,5.An efficiency co-op advertising model,It can be shown thatTherefore,for any given t which satisfies we
34、have,This simply implies that there exist Pareto efficient advertising schemes such that both the manufacturer and the retailer are better off at full coordination than at noncooperative equilibrium.,49,5.An efficiency co-op advertising model,We are interested in finding an advertising scheme in Z w
35、hich will be agreeable to both the manufacturer and the retailer.According to Proposition 6,for any Pareto scheme where is a positive constant.,50,5.An efficiency co-op advertising model,This property implies that the more the manufacturers share of the system profit gain,the less the retailers shar
36、e of the system profit gain,and vice versa.So the manufacturer and the retailer will agree to change the local advertising expenditures to and the brand name investments to.However,they will negotiate over the manufacturers share of the local advertising expenditures.,51,6.Bargaining results,Assume
37、that the manufacturer and the retailer agree to change local advertising expenditures to and brand name investments to from and,respectively,and engage in bargaining for the determination of reimbursement percentage to divide the system profit gain.,52,6.Bargaining results,A fraction closer to is pr
38、eferred by the retailer,and a fraction closer to is preferred by the manufacturer.,To determine the division of the system profit gain,we must give some further assumptions.,53,6.Bargaining results,Since there is an environment uncertainty in sales volume,both members are assumed to be uncertain abo
39、ut the system profit gain,.For each Pareto efficient advertising schemes,the uncertainty is represented in terms of a probability distribution for.We assume that both members agree on the probability distributions of interest.,54,6.Bargaining results,Suppose both the manufacturer and the retailer ha
40、ve preferences for the amount of shares of the system profit gain,which preferences are represented by each system members von NeumannMorgenstern cardinal utility function for.,The manufacturers and the retailers utility functions are denoted by and,respectively.,55,6.Bargaining results,We assume th
41、e utility functions are additive,that is to say it can be written in the form where is the conditional utility function of member i(i=m,r)for(j=m,r).,56,6.Bargaining results,It has been also shown that,for additive individual utility functions,the system utility function,is also additive under the l
42、inear aggregation rule.The form of us is as follows:where is the vector of aggregation weights and.,57,6.Bargaining results,In order to incorporate the manufacturers and the retailers risk attitude into our analysis,we define the PrattArrow risk aversion function as follows:is the risk aversion func
43、tion of member i(i=m,r)to the share of the jth member(j=m,r).,58,6.Bargaining results,Here we present the Nash(1950)bargaining model determining the bargaining reimbursement fraction over the line segment of Pareto efficient solutions described byThe bargaining outcome is obtained by maximizing the
44、product individual marginal utilities over Pareto efficient locus.,59,6.Bargaining results,To demonstrate this approach,we consider two degenerated exponential utility functions for the manufacturer and the retailer as follows:where and are positive constant.,60,6.Bargaining results,Eqs.(37)and(38)i
45、mply that both the manufacturer and the retailer have constant risk aversion functions with and,61,6.Bargaining results,Since the product of and can be rewritten as the form in terms of:,62,6.Bargaining results,Taking the first derivative of with respect to and setting it to be zero:,63,6.Bargaining
46、 results,Now we consider several special cases.First,assume that both the manufacturer and the retailer have the same degree of risk aversion measures,i.e.Then solving(40),we have,64,6.Bargaining results,Therefore,the best Pareto advertising reimbursement is So if the manufacturer and the retailer h
47、ave the same degree of risk aversion measures,the model suggests that the members should equally share the system profit gain.,65,6.Bargaining results,Second,assume that the manufacturer has a higher degree of risk aversion measures than the retailer and Then solving(40),we have,66,6.Bargaining resu
48、lts,67,6.Bargaining results,Therefore,the best Pareto advertising reimbursement is,68,6.Bargaining results,So when the manufacturers degree of risk aversion is higher than the retailers,he receives a lower share of the system profit gain,which is consistent with the result in the case of negotiation
49、 with bargaining power.A similar analysis can be accomplished for the case where the retailers degree of risk aversion is higher than the manufacturers.,69,7.Concluding remarks,This paper attempts to investigate the efficiency of transaction for the system of manufacturerretailer co-op advertising i
50、n the context of game theory.,70,7.Concluding remarks,There are three possible avenues for future research:First,the single manufactureretailer system assumption can be relaxed to a duopoly situation of manufacturers who sell their products through a common monopolistic retailer who sells multiple c
