JI Kai [a],* INTRODUCTION

Transcription

1 Management Science and Engineeing Vol. 10, No. 4, 016, pp DOI: /9183 ISSN [Pint] ISSN X [Online] Reseach on Coopeative Advetising Decisions in Dual-Channel Supply Chain Unde Asymmetic Demand Infomation When Online Channel Implements Discount Pomotion JI Kai [a],* [a] College of Business Administation, South China Univesity of Technology, Guangzhou, China. *Coesponding autho. Received 5 Septembe 016; accepted 11 Novembe 016 Published online 6 Decembe 016 Abstact This pape analyzes the both online-channel pice discount and advetising decisions in a dual-channel supply chain involved one manufactue and one etaile. A Stackelbeg game dominated by the manufactue is established. The influence of asymmetic demand infomation is analyzed. The study shows that etaile has a motivation to lie about the offline demand infomation and it always announces a highe advetising impact facto. To induce the etaile to eveal to tue demand infomation, a fanchise-fee contact is designed. Key wods: Coopeative advetising; Pice discount; Dual channel; Demand infomation asymmety Ji, K. (016. Reseach on Coopeative Advetising Decisions in Dual-Channel Supply Chain Unde Asymmetic Demand Infomation When Online Channel Implements Discount Pomotion. Management Science and Engineeing, 10(4, Available fom: URL: DOI: INTRODUCTION With the development of E-commece, geat changes have happened in maketing methods and manufactues distibution channels. Nowadays, lage numbes of manufactues have opened thei own websites to sell poducts online, while though the offline etailing channel. Many manufactues have opeated thei maket though this kind of online and offline dual channel, such as Samsung, IBM, Lenovo and Apple. Usually, online websites can only povide bief poducts infomation fo consumes, but offline etailing channels can help consumes acquie full infomation about poducts. In ode to impove online maket shae and obtain moe evenue, manufactues often povide pice discount on thei own websites. This kind of discount pomotion stategy helps the manufactues incease online consumes, but also huts the offline consume amount. As a esult, etailes will get dissatisfied with this stategy. In this condition, manufactues can use coopeative advetising method, which is widely used in pactical opeation, to elieve the channel conflict. So, it is necessay fo manufactues to keep a balance between the use of online discount stategy and coopeative advetising method. Futhemoe, etailes actually have a bette knowledge about demand infomation than manufactues, because etailes always have diect contact with consumes. Asymmetic demand infomation may exist between manufactues and etailes. Theefoe, it is highly possible fo etailes to lie about the demand infomation, and it is impotant to help manufactues pohibit etailes lying behavio. As a coodination method between manufactue and etailes, coopeative advetising has attacted lots of attention fom wold-wide eseaches. Ou pape focuses on the coopeative advetising poblem in dual channel. Zhang et al. (014 examine the effects of supply chains membes coopeative advetising and costs shaing behavio on dual channel coodination on condition that manufactue opens online and etail channel at the same time. Results show that no matte what effect etaile s pomotion has on band image, when manufactue pays pat of etaile s advetising cost, the outcome of two membes would be bette than that in the decentalized channel, but wose than that in the centalized situation. Opening a new online channel besides the offline channel, Bege et al. (006 examine integation decisions fom a coopeative advetising pespective to detemine the pofitability of vaious integation stategies. Yan et al. (006 obtain equilibium picing and co-op advetising 13 Copyight Canadian Reseach & Development Cente of Sciences and Cultues

2 Reseach on Coopeative Advetising Decisions in Dual-Channel Supply Chain Unde Asymmetic Demand Infomation When Online Channel Implements Discount Pomotion policies unde two diffeent competitive scenaios: Betand and Stackelbeg equilibium. They also compae the pofit gains unde these two maketing games. Wang and Zhou (009 analyze the picing and advetising decision unde diffeent picing schemes. The impact of coopeative advetising on the optimal decisions is investigated. Huang et al. (011 study the influence of coopeative advetising stategy on channel supply chain picing decision, the two-echelon supply chain system composed of one manufactue and one etaile was consideed. Li et al. (015 conside a dyadic supply chain consisting of a manufactue and a taditional etaile. In addition, the effect of a fainess concen of the manufactue is investigated. Chen et al. (016 focus on the coopeative advetising in a dual-channel supply chain whee pice competition and advetising competition exist simultaneously between manufactue s online channel and etaile s taditional channel. Besides consideing both pice discount and coopeating in a dual channel, ou pape also investigates the demand infomation asymmety between manufactue and etaile. Özalp et al. (006 study how to assue cedible foecast infomation shaing between a supplie and a manufactue. When the buye has bette knowledge about demand than supplie, Bunetas et al. (007 investigates how a supplie can use a quantity discount schedule to influence the stocking decisions of a downsteam buye that faces a single peiod of stochastic demand. Gan et al. (010 study a dop-shipping supply chain in which the etaile eceives a custome s ode and the supplie fills it. In such a chain, the supplie keeps inventoy and beas inventoy isks; the etaile focuses on maketing and custome acquisition, and fowads the odes to the supplie. Babich et al. (01 solve a buyback contact design poblem fo a supplie who is woking with a etaile who possesses pivate infomation about the demand distibution. When demand is uncetain and unobsevable to the supplie, Heese et al. (014 conside a supply chain with a supplie that sells to a etaile unde a evenue-shaing aangement. Yang et al. (015 analyze the advetising decisions in a dual-channel supply chain involved one manufactue and one etaile. The influence of asymmetic demand infomation and dual-channel on the coopeative advetising decisions is also analyzed. Reviewing the above liteatue, we find that the most elevant pape to ou pape is Yang et al. (015. Howeve, the do not conside the impact of online pice discount on both etaile and manufactue s decisions. Meanwhile, they do not conduct futhe analysis on the effect of demand infomation. 1. BASIC MODEL 1.1 Model Desciption and Assumption A supply chain compised of a manufactue and a etaile is investigated in the basic Stackelbeg game model. In this basic model, manufactue is the leade and etaile is the followe. The manufactue opens its online channel while sells poducts though an offline etaile. Assuming the etaile s sales epesented by p, manufactue sets the wholesale pice as w. Though poviding a pice discount on the online channel, manufactue s online pice is p e, w <p e p. In this way, the pice discount povided online is σ=1 p e / p. Then, we see that the pice discount σ must be confined to a closed inteval, say 0 σ<1 w/p. Given p fixed, we can infe that highe pice discount σ can lead to a lowe online pice. Meanwhile, define the value of paamete b(b 0 as the etaile s advetising effot on poducts. Like many fome eseaches, the total advetising cost will be epesented in a quadatic fom C(b=b /. Manufactue shaes a pat of the total advetising cost with etaile, and the pat atio is 1 t. So, the manufactue will affod the expense (1 tb / and the etaile s shaed cost will be tb /. Chen et al. (016 set the demand model in the fom of pice discount effect multiplied the advetising effect. Howeve, thei model may be uneasonable when advetising effot is zeo. Unlike Cheng et al. s (016 eseach and simplify the poblem, ou pape assumes the demand function in the fom of linea model. We can get demand functions of the both online and offline channels: D e =s a+θ e σ+ e b, (1 D =(1 s a θ σ+ b. ( Fom Fomulas (1 and (, total maket size is a. When manufactue does not povide pice discount and etaile does not invest in advetisement, online initial maket shae is s a and the offline maket shae is (1 s a. Poviding the pice discount, moe consumes may be attacted by the poducts. So, the total maket size will incease. Because some of the offline consumes ae picesensitive, pat of the consumes will tansfe fom offline to online. When σ inceases, it is easonable to believe that online demand D e inceases and offline demand D deceases. θ e and θ ae σ s impact facto on online and offline demand, θ e >θ >0. Diffeent fom σ, advetising effot b has a positive impact on both offline and online demand, e >0 and >0. As this pape focuses on the influence of pice discount and coopeative advetising, the model is simplified in thee aspects. The fist is that we do not conside pice s effect on demand. The sales pice p and wholesale pice w ae given exogenously. The second is that we only conside the etaile s advetising behavio, but do not conside manufactue s own advetising effot. It is easonable not to conside manufactue s advetising effot. Because the pice discount pomotion stategy has the same effect like advetisement to some extent. It is not necessay fo manufactue to opeate pice discount and advetising simultaneously. Without loss of geneality, the thid assumption is that manufactuing cost of the poduct is zeo. Revenue functions of the both manufactue and etaile ae: Copyight Canadian Reseach & Development Cente of Sciences and Cultues 14

3 JI Kai (016. Management Science and Engineeing, 10(4, π m = p (1 σ (s a+θ e σ+ e b +w [(1 s a θ σ+ b] (1 t b /, (3 π =( p w [(1 s a θ σ+ b] tb /. (4 Accoding to the peceding aticle, the manufactue acts as the leade, who fist announces its pice discount σ and advetisement shaing atio 1 t to maximize its evenue. In esponse to σ and 1 t, the taditional etaile (the followe updates its advetising effot b to maximize its evenue. Though the standad backwad induction, we can easily deive the optimal decision of both etaile and manufactue in. unde asymmetic infomation. 1. Decision Analysis Given manufactue s decision of σ and 1 t, the etaile s advetising effot eaction is: b=(p w /t (5 and the etaile s optimal evenue as a function of σ and b is: π =(p w [(1 s a θ σ+ b] b ( p w /. (6 Fom Fomula (5, we can infe that b has a linea coelation with t. To solve the decision of t, we can instead solve the decision of b. Substituting Fomula (5 into Fomula (4 and simplifying, we get π m = p (1 σ (s a+θ e σ+ e b w [(1 s a θ σ+ b] b / b ( p w /. (7 It is easily to know that π m is espectively concave in σ and b. We use the two-stage optimization method to maximize the manufactue s evenue π m, i.e., we fist deive the optimal pice discount σ fo any given advetising effot b, then we detemine the optimal advetising effot b to maximize π m. The optimal pice discount and advetising effot ae: σ * =[ w θ (p +w e p /+ p e p (θ e s a] /( p e p θ e, (8 b * =[ (p +w θ e p p e w θ p e (θ e +s a] /( p e p θ e. (9 To examine Fomula (9, b * is detemined not to be negative. So, we can have b * =[ (p +w θ e p p e w θ p e (θ e +s a] /( p e p θ e 0. (10 Accoding Fomula (10, we can know that p e p θ e <0. (11 While analyzing fomula (7, the hessian matix of π m (σ,b is p θe p θe H = p θe 1. Combine Fomula (11, we can deive that H = p θ e p e >0. That is to say, π m (σ,b is jointly concave in σ and b. Then we can get the theoem 1 Theoem 1 Unde the symmetic demand infomation scenaio, the optimal equilibium advetising effot, pice discount and cost shaing atio fo the etaile and manufactue ae given by b * =[ (p +w θ e p p e w θ p e (θ e +s a] /( p e p θ e, σ * =[w θ (p +w e p /+ p e p (θ e s a] /( p e p θ e, t * =(p -w / b *. To examine the impact of s, e and on the online etaile s optimal advetising decision, we take the fistode deivatives of b * with espect to s, e and. Then it is also inteesting to examine the impact of s, θ e and θ on the online manufactue s optimal decisions, we also take the fist-ode deivatives of σ * and t * with espect to s, θ e and θ. We can obtain poposition 1. Poposition 1 (i b * / s>0; b * / e >0; b * / >0 (ii σ * / s<0; σ * / θ e <0; σ * / θ <0 (iii t * / s<0; t * / e <0; t * / θ <0 Fom poposition 1(i, we can get that: etaile should always incease the advetisement expense when the etaile s initial maket shae (1 s is getting smalle. Meanwhile, once the advetising is easie to convet to demand in any distibution channel, it is moe pofitable fo etaile to invest in moe advetisement fee. Fom (ii and (iii, we can popose that: manufactue should decease thei pice discount σ * and incease cost shaing atio 1 t * when the online initial maket shae is getting lage. In contast, it should decease σ * when it becomes easie to attact online consumes though poviding pice discount. 1 t * should be inceased when it becomes easie to attact online consumes though advetising. In the end, if it is easie to attact consumes fom offline to online by poviding pice discount, manufactue should decease σ * and incease 1 t *. Fo the manufactue, all changes of 1 t * ae contay to the changes of σ *, because pice discount is a competitive tool to get consume fom etaile, while the cost shaing atio is an effective tool to coodinate conflict caused by competition.. DECISION ANALYSIS AND CONTRACT DESIGN UNDER ASYMMETRIC DEMAND INFORMATION Because etaile always has diect contact with offline consumes while manufactue does not. Thee is a high pobability fo etaile not to announce the demand infomation fo its own evenue. This section, a dualchannel Stackelbeg model will be consideed. In this model, we assume the demand infomation is etaile s pivate infomation which is unknown to manufactue. Accoding to (Lei et al., 015, etaile has aleady known its demand infomation θ and befoe making decisions. 15 Copyight Canadian Reseach & Development Cente of Sciences and Cultues

4 Reseach on Coopeative Advetising Decisions in Dual-Channel Supply Chain Unde Asymmetic Demand Infomation When Online Channel Implements Discount Pomotion But manufactue does not know effects on offline demand caused by pice discount and advetising effot. Apat fom this, we assume that s, a, θ, e ae common knowledge between manufactue and etaile..1 Retaile s Lying Behavio Due to the asymmetic demand infomation, etaile is possible to lie about the impact factos θ and. In 3.1, we will investigate whethe the etaile has the motivation to lie about the demand infomation. Assume the impact factos etaile announces to etaile is θ and, accoding to Fomulas (6, (8, and (9, the etaile s evenue, pice discount and advetising effot will be: π (θ, =( p w [(1 s a θ σ(θ, + b(θ, ] b(θ, ( p w /, σ(θ, =[ w θ +(p +w e p /+ p e p (θ e s a] /( p e p θ e, b(θ, =[ (p +w θ e p p e w θ p e (θ e +s a] /( p e p θ e. Given θ, taking the second-deivative of π (θ, with espect to, we get: π (θ, / =(p w (p +w p θ e /( p e p θ e <0. So, given θ, the optimal decision of is: = + e [ p (θ e θ +s a+ w (θ θ ] /[ (p +w θ e ], (1 given the, take a fist-deivative of π (θ, with espect to θ. We can get: π (θ, / θ =w ( e p / e p θ /( p e p θ e. (13 Combine Fomulas (1 and (13, we deive theoem : Theoem (i if (θ =0 e p / e p θ <0 θ =0, = + e [ p (θ e θ +s a w θ ] /[ (p +w θ e ]. (ii if (θ =θ e e p / e p θ >0 θ =θ e, = + e [ p (θ e θ +s a+ w (θ e θ ] /[ (p +w θ e ]. (iii if (θ =0 e p / e p θ <0< (θ =θ e e p / e p θ θ =[ (p +w θ e ( e p + θ e p (θ e θ +s a+ w θ ]/( e w, = ( e p +θ /( p e. Fom theoem, we can know that the etaile may announce diffeent impact factos of pice discount and advetising effot based on diffeent conditions. So, we can obtain poposition. Poposition Retaile has a motivation to lie about the impact factos of pice discount and advetising effot. (i When etaile lies a low θ (θ =0, if the coesponding (θ =0 is high enough, the optimal decision of θ should acquie a vey low value (θ =0. The optimal decision of has following chaactes: / s>0; / a>0; / e >0; / w<0; / θ <0. (ii When etaile lies a high θ (θ =θ e, if the coesponding (θ =θ e is low enough, the optimal decision of θ should acquie a vey high value (θ =θ e. The optimal decision of has the same chaactes in (i. (iii Except the above condition, etaile may lie a modeate θ (0<θ <θ e. The optimal decision of has following chaactes: / θ >0, / p >0, / e <0. Also, we should point out that etaile will always lie a highe impact facto of advetising effot than the eal one ( >. Futhemoe, it is easy to pove that etaile s lying behavio may cause evenue loss of manufactue (π m (θ, * >π m (θ,. Accoding to poposition (i, the etaile s lying behavio contains thee diffeent conditions. When etaile s optimal announcement of pice discount impact facto θ is athe low θ =0 o high θ =θ e, the optimal announcement of advetising effot impact facto has the same chaactes. When the total maket size a, manufactue s initial online maket shae s and offline advetising effot e incease, etaile may lie highe. Howeve, when wholesale pice w and offline pice discount impact facto θ incease, the etaile may lie lowe. On othe conditions, etaile may lie a modeate θ. The advetising effot impact facto decision will have an opposite chaacte fom (i, (ii.. Contact Desciption In poposition, we have poposed that etaile will lie about the demand infomation to obtain highe evenue. This lying behavio will hut manufactue s evenue. So, it is necessay fo manufactue to take some action to deal with this condition. Fom the pespective of manufactue, effective stategies like contact designing should be conducted to pohibit etaile fom lying. In this pat, an optimal contact menu is obtained to induce etaile to eal demand infomation. The contact menu should conside both individual ational (IR constaint and incentive compatibility (IC constaint. The individual ational constaint means that etaile may acquie a highe evenue if it accepts the evenue-shaing than not. The incentive compatibility constaint means that etaile will be induced to shae the tue demand infomation. Though the manufactue does not know etaile s demand infomation θ and, it esots to a pio belief and consides them continuous andom vaiables with values in [ θ, θ ] and [, ] with c.d.f. F θ (, F ( and p.d.f. f θ (, f (. θ and ae independent fom each othe. The timing of ou model is as follows: (i The etaile knows the demand infomation while manufactue knows the demand distibution; (ii The Copyight Canadian Reseach & Development Cente of Sciences and Cultues 16

5 JI Kai (016. Management Science and Engineeing, 10(4, manufactue designs the solutions set as {σ(θ,, t(θ,, L(θ, }, σ(θ, is pice discount, t(θ, is advetisement shaing atio, L(θ, is the fanchise fee fom the etaile to the manufactue; (iii The etaile is induce to tell tue demand infomation and to make advetising effot b. The θ and etaile announces ae θ and. The manufactue s evenue function: π m (σ(θ,,t(θ,,l(θ, =p (1 σ(θ, ( s a+θ e σ(θ, + e b(θ, +w [(1 s a θ σ(θ, + b(θ, ] (1 t(θ, b(θ, /+ L(θ,. (14 The etaile s evenue function: π (σ(θ,,t(θ,,l(θ,,θ, =(p w [(1 s a θ σ(θ, + b(θ, ] t(θ, b(θ, /+ L(θ, (15 Accoding to incentive compatibility (IC constaint, etaile will be induced to shae the tue demand infomation: π (σ(θ,,t(θ,,l(θ,, θ, π (σ(θ,,t(θ,,l(θ,, θ,. (16 Accoding to individual ational (IR constaint, etaile may acquie a highe evenue if it accepts the fanchise-fee contact than not: π (σ(θ,,t(θ,,l(θ,, θ, π min. (17 Take etaile s optimal decision of b into etaile s evenue function, we can get: π (σ(θ,,t(θ,,l(θ,, θ, = (p w [(1 s a θ σ(θ, + (p w /( t(θ, ] L(θ, given, thee should be given θ, thee should be π (θ, / θ = π (σ(θ,,t(θ,,l(θ,, θ, / θ θ =θ, = = (p w σ(θ, ; π (θ, / = π (σ(θ,,t(θ,,l(θ,, θ, / θ =θ, = =(p w /t(θ,. The etaile s poblem can be conveted into: θ ' ' ' ' ' ' max π m ( σ ( θ,, t( θ,, L( θ, fθ ( θ (,, f dθ d σ t L θ, (18 s.t. (p w [(1 s a θ σ(θ, +(p w /( t(θ, ] L(θ, (p w [(1 s a θ σ(θ, + (p w /( t(θ, ] L(θ,, (19 Lemma 1 Accoding to the two IC and IR constaints, it can be easily deived that: σ(θ, is only deceasing in θ ; t(θ, is only deceasing in. Fom Lemma1, we can know that when both the infomation of θ and ae asymmetic. It is had to deive the optimal contact to maximize manufactue s evenue, while inducing etaile to tell the tue infomation. (i (p w [(1 s a θ σ(θ, +(p w /( t(θ, ] L(θ, π min. (0.3 Contact Design In this pat, we conside a special case of the initial poblem. We assume that impact of pice discount is known to both manufactue and etaile. That is to say, only the is pivate infomation of etaile s infomation. Futhemoe, we design the optimal fanchise-fee contact menu {σ(θ,,t(θ,,l(θ, }to solve the poblem in (18-(0. We can get: ( p y ( = dy + mi (1 t( θ, ( p ( p y = θ σ + π min t(. t( π π L( ( p w [(1 s a ( ] dy (ii ( Manufactue s expected evenue will be: ( p p (1 σ ( ( s a + θe σ ( + e t( ( p + w [(1 s a θ σ ( + ] t( E( π m = f ( d π min. 1 ( p (1 ( [ w ] t + ( p w [(1 s a θ σ ( t( ( p ( p y + ] dy t( t( 17 Copyight Canadian Reseach & Development Cente of Sciences and Cultues

6 Reseach on Coopeative Advetising Decisions in Dual-Channel Supply Chain Unde Asymmetic Demand Infomation When Online Channel Implements Discount Pomotion Theoem σ f ( =1 [a s +θ e +θ +(p +p +w w e /] /[ ( θ e p e ], (3 t f ( = (p w ( θ e p e /[p (θ e +θ e +θ e e +θ e +a s e +w θ e ( ], (4 L f ( = (p w [(1 s a θ σ f ( +(p w /( t f ( ] π min. (5 See (4, we can find t f ( is deceasing in, which fulfils the equiements of IC and IR constaints. Futhemoe, we can obtain poposition 3. Poposition 3 (i σ f / s<0; σ f / θ e >0; σ f / θ <0 (ii t f / s <0; t f / θ e <0; t f / θ <0 Poposition 3(i(ii is nealy the same as poposition, we will not explain it in details. In addition, fom poposition 3(iii, we can deive that when the manufactue s initial online maket gows up, manufactue should acquie a lage fanchise fee fom etaile. When it becomes easie to attact offline consumes to online, manufactue may also acquie a lage fanchise fee. CONCLUSION In this pape, we have investigated a eseach on online pice discount in an online and offline dual channel. Unde the symmetic demand infomation scenaio, once the advetising is easie to convet to demand in any distibution channel, it is moe pofitable fo etaile to invest in moe advetisement fee. We also find pice discount is a competitive tool to get consume fom etaile, while the cost shaing atio is an effective tool to coodinate conflict caused by competition. Unde the asymmetic demand infomation scenaio, we have deived that etaile has a motivation to lie about the impact factos of pice discount and advetising effot. In diffeent situations, etaile will adjust thei lying about demand infomation in thee diffeent ways. Futhemoe, etaile will always lie a highe impact facto of advetising effot than the eal one. And the etaile s lying behavio may cause evenue loss of manufactue. To help manufactue deal with the poblem, we design a fanchise-fee contact. Howeve, when both the infomation of pice discount impact and advetising effot impact ae asymmetic. In contact menu, optimal pice discount is only deceasing in offline picediscount impact factos; etaile s advetisement shaing atio is only deceasing in offline advetising effot impact factos. It is had to deive the optimal contact to maximize manufactue s evenue, while inducing etaile to tell the tue infomation. Finally, we conside a special case of the initial poblem. We assume that only the impact of pice discount is known to both manufactue and etaile. Optimal fanchise-fee contact can be obtained. REFERENCES Babich, V., Li, H., Ritchken, P., & Wang, Y. (01. Contacting with asymmetic demand infomation in supply chains. Euopean Jounal of Opeational Reseach, 17(, Bege, P. D., Lee, J., & Weinbeg, B. D. (006. Optimal coopeative advetising integation stategy fo oganizations adding a diect online channel. Jounal of the Opeational Reseach Society, 57(8, Bunetas, A., Gilbet, S. M., & Smith, C. E. (007. Quantity discounts in single-peiod supply contacts with asymmetic demand infomation. IIE Tansactions, 39(5, Chen, G. P., C., Zhang, X. M., & Xiao, J. (016. Coodination model fo coopeative advetising in dual-channel supply chain when online channel implements discount pomotion. Jounal of Industial Engineeing and Engineeing Management, 30(4. Gan, X., Sethi, S. P., & Zhou, J. (010. Commitment-penalty contacts in dop-shipping supply chains with asymmetic demand infomation. Euopean Jounal of Opeational Reseach, 04(3, Heese, H. S., & Kemahlioglu-Ziya, E. (014. Enabling oppotunism: Revenue shaing when sales evenues ae unobsevable. Poduction and Opeations Management, 3(9, Huang, S., Yang, C., & Zhang, X. (011. Picing and coopeative advetising decision models in dual-channel supply chain. Compute Integated Manufactuing Systems, 17(1. Li, B., Hou, P. W., & Li, Q. H. (015. Coopeative advetising in a dual-channel supply chain with a fainess concen of the manufactue. IMA Jounal of Management Mathematics. doi: /imaman/dpv05 Özalp, Ö., & Wei, W. (006. Stategic commitments fo an optimal capacity decision unde asymmetic foecast infomation. Management Science, 5(8, Wang, H., & Zhou, J. (009. Study on decisions of dual channel supply chain with diffeent picing schemes. Chinese Jounal of Management Science, 17(6, Yan, R. (006. Coopeative advetising in a dual channel supply chain. Intenational Jounal of Electonic Maketing & Retailing, 1(, Yang, L., Ji, J. N., & & Zhang, Z. Y. (015. Reseach on coopeative advetising decisions in a dual-channel supply chain unde asymmetic demand infomation. Contol and Decision, 30(1, Zhang, Z. Y., Hua-Juan, L. I., Lei, Y., & Shi, Y. Q. (014. Dualchannel coodination stategies on advetising coopeation based on diffeential game. Kongzhi Yu Juece/contol & Decision, 9(5, Copyight Canadian Reseach & Development Cente of Sciences and Cultues 18

7 JI Kai (016. Management Science and Engineeing, 10(4, APPENDIX The poof of Lemma 1: Consideing π (θ, s fist-ode deivatives of θ and, we can get:. Fom this equation, Lemma 1 can be obtained. 19 Copyight Canadian Reseach & Development Cente of Sciences and Cultues