Vertical Information Sharing in a Volatile Market

Transcription

1 Vetical Infoation Shaing in a Volatile Maket Chuan He 1 Johan Maklund Thoas Vossen 419 UCB Leeds School of Business Univesity of Coloado at Boulde Boulde, CO Eail: chuan.he@coloado.edu Phone: (303) Fax: (303) Depatent of Industial Manageent and Logistics Lund Univesity P.O. Box 118 SE-100 Lund Sweden May Authos ae listed in alphabetical ode, each autho contibuted equally. We would like to thank Sven Axsäte, Yongin Chen, Yuxin Chen, Diti Kuksov, Rakesh Niaj, Elie Ofek, Aba Rao, the aea edito and two anonyous eviewes at Maketing Science fo thei helpful coents. The topic of this pape was inspied by a convesation with Pofesso Chakavathi Naasihan duing the fist SICS confeence in 003.

2 Vetical Infoation Shaing in a Volatile Maket Abstact When deand is uncetain, anufactues and etailes often have pivate infoation on futue deand, and such infoation asyety ipacts stategic inteaction in distibution channels. In this pape, we investigate a channel consisting of a anufactue and a downstea etaile facing a poduct aket chaacteized by shot poduct life, uncetain deand, and pice igidity. Assuing the fis have asyetic infoation about the deand volatility, we exaine the potential benefits of shaing infoation and contacts that facilitate such coopeation. We conclude that unde a wholesale pice egie, infoation shaing ay not ipove channel pofits when the etaile undeestiates the deand volatility but the anufactue does not. Although infoation shaing is always beneficial unde a two-pat taiff egie, it is in geneal not sufficient to achieve infoation shaing and additional contactual aangeents ae necessay. The contact types we conside to facilitate shaing ae pofit shaing and buy back contacts. Keywods: Channels of Distibution, Decisions unde Uncetainty, Gae Theoy, Supply Chains

3 If he had 003 to do ove again, M. Maineau (CEO of Levi Stauss) said, he wouldn t have launched the copany s hyped Type 1 jeans, which adoned the cove of the copany s 00 annual epot. Levi aketing ateials poised the boldest, ost povocative Levi s jeans in decades. But the line was too cutting-edge fo ainstea consues and the copany was slow to coect fashion istakes when deand failed to ateialize, Levi executives said, afte posting its lagest annual loss. The Wall Steet Jounal, Mach 3, Intoduction Deand uncetainty is ubiquitous in essentially any aketplace. Undestanding it is one of the constant challenges fis face on the oad towads success. As the exaple illustates, failue to do so often has devastating effects on the botto line. Levi Stauss, like any othe anufactues of appael, intoduces new fashions evey yea. Given its yeas of expeience, Levi Stauss has a elatively clea pictue on what the deand will be on aveage. The actual deand ealization, howeve, is uncetain. Soe of the nueous factos that influence the deand ealization ae weathe, opinion leades attitudes, populaity of copeting poducts, etc. Put diffeently, thee is a ange of possibilities suounding the aveage deand so that the actual deand ealization can be eithe highe o lowe than the aveage deand. Although the anufactue has a good sense of the aveage deand, the ange of the actual deand ealization is ipacted by so any diffeent factos beyond the anufactue s contol that the only appopiate notion is that it is deteined by natue. We can epeat the above scenaio by eplacing the te anufactue with etaile; we ay also eplace fashion appael with any othe highly peishable goods such as fesh poduce, ovies. In distibution channels, infoation asyety acoss channel ebes with espect to deand uncetainty futhe coplicates attes. In industies anging fo gocey to aeospace, 1

4 anufactues and etailes often ake independent deand estiates with diffeent degees of accuacy. Many factos, such as the poxiity to consues, the availability and quality of custoe databases, sophistication of decision suppot tools, and expeience, contibute to the accuacy of the deand estiate. Consistent with the opening exaple, we otivate the coe issue of this pape in the context of a distibution channel of fashion appael. Befoe the season begins, the etaile needs to place an ode fo the anufactue. The etaile knows that if she odes too late (say, afte the season begins), she will fogo sales. At this point, the only infoation available is the deand estiates (pivate infoation) of the anufactue and the etaile and each paty s pofile (public infoation). Howeve, neithe the anufactue no the etaile knows the othe paty s estiate unless it is puposely evealed. Is thee any value in shaing the two paties deand estiates? If the answe is positive, what echanis(s) can help accoplish infoation shaing? Thee is aple evidence that ebes of a distibution channel can benefit geatly by shaing deand infoation. Accoding to an A.T. Keaney epot (Field, 005), the aveage anufactue has enjoyed benefits equivalent to $1 illion in savings fo evey $1 billion of sales by synchonizing thei deand databases with thei etailes. Howeve, it is not clea that infoation shaing is always feasible in decentalized channels as it is aed by incentive and cedibility pobles. In the PC industy, anufactues often suspect thei distibutos of subitting phanto odes, i.e., foecasts of high futue deand that do not ateialize (Zaley and Daoe, 1996). Theefoe, the value of infoation shaing and the echaniss fo facilitating infoation shaing ae topics of geat anageial ipotance and have eceived consideable attention in the liteatue (e.g., Cachon and Fishe, 000; Cachon and Laiviee, 001; Chen, 003; Gal-O, 1986; Gu and Chen, 005; Kulp, Lee and Ofek, 004; Lee, Padanabhan and Whang, 1997; Lee, So and Tang, 000; Li, 00; Niaj and Naasihan, 00; Villas-Boas, 1994; Vives, 1984). In this pape, we focus on a poduct aket chaacteized by shot poduct life, uncetain deand, and pice igidity (lack of pice pootion). A catalogue akete of fashion goods is a pototypical

5 exaple of such a aket. Due to the inheent uncetainty about consue tastes, fashion goods ae synonyous with apid change and subject to significant deand vaiability. We investigate a distibution channel with one anufactue and one etaile, each with pivate infoation about the distibution of futue deand. Ou objective is to exaine the benefits of shaing infoation about futue deand volatility and contacts that facilitate such coopeation. Moe pecisely, we conside ultiplicative deand uncetainty, unifoly distibuted between an uppe and a lowe bound about which the ebes of the channel have asyetic infoation. To captue the ipact of uncetainty, we odel the etaile as a newsvendo poble with endogenous picing. This allows us to balance the expected cost of odeing too uch with the expected oppotunity cost of odeing too little, when axiizing the etaile pofits. The anufactue is assued to opeate unde a constant aginal cost, without any capacity constaints. Seveal notable featues eege fo ou odel setup. Fist, the envionent unde consideation is a one-shot, highly volatile setting; fis engage in shot-te elationships and cannot efine thei deand estiates by using histoical data. Second, fis deand estiates ay eithe oveshoot o undeshoot the tue deand volatility because the deand is intinsically stochastic, and the coelation between the fis deand estiates is unknown. Thus, thee is no obvious way to cobine o pool the into a oe accuate estiate. We find that shaing infoation about aket deand volatility does not always ipove channel pofits. In paticula, unde a wholesale pice only egie, when the etaile undeestiates the deand vaiability but the anufactue does not, shaing can lead to lowe channel pofits. In addition, we show that the feasibility of infoation shaing not only depends on the asyetic estiates of the deand volatility but also on the channel ebes knowledge of the quality of each ebe s foecast. Specifically, we deonstate that a pofit shaing contact is a viable echanis when each channel ebe is awae of the quality of the othe ebe s deand foecast elative to its own, 3

6 wheeas buy back contacts can ipove channel coodination when only one ebe knows whose deand foecast is oe accuate. We also find that unde a two-pat taiff egie, shaing infoation about aket deand volatility always ipoves channel pofits, but additional contactual aangeents ae needed fo shaing to occu. In contast to the syetic case, unde asyetic infoation about deand volatility, a two-pat taiff does not always coodinate the channel. Thee steas of liteatue ae elevant to ou study: the liteatue on channel coodination, the liteatue on newsvendo odels with endogenous picing decisions, and the eeging liteatue on infoation shaing. The extant channel liteatue geneally assues deteinistic deand (e.g., Jeuland and Shugan, 1983; McGuie and Staelin, 1983). The liited channel liteatue that incopoates deand uncetainty usually assues that uncetainty is a white noise and has no consequence as fis axiize expected pofits (e.g., Lal, 1990), o odels uncetainty as consisting of a high state and a low state (e.g., Biyalogosky and Koenigsbeg, 004; Desai, 000; Padanabhan and Png, 1997; Gu and Chen, 005). These papes piaily conside the ipact of uncetainty in the deand tend (i.e., the ean), but do not focus on the ipact of asyetic infoation about deand volatility. Such teatent allows eseaches to obtain a high level of pasiony, which facilitates the analysis of coplex issues such as channel stuctue, upstea/downstea copetition, ulti-peiod inteaction, etc. Howeve, this pasiony is obtained at the cost of geneality. In paticula, the actual deand ealization ay be eithe above o below the deand tend and fis incu costs in eithe case. By focusing on deand tend but ignoing volatility, one assues that the costs associated with undeshooting and oveshooting ae identical (we shall evisit this point in details in Section 3.3). This assuption becoes vey toublesoe when deand volatility is lage, as in the case of highly peishable goods. We copleent this liteatue by looking at deand uncetainty fo a diffeent pespective, focusing on the ipact of asyetic estiates of the deand volatility in a newsvendo setting with unifoly distibuted deand uncetainty. 4

7 The classical newsvendo appoach offes an intuitive way to incopoate the effect of deand volatility into the analysis of channel behavio. In a one-peiod setting, the etaile (newsvendo) tades off the aginal cost of undestocking with that of ovestocking when deteining how uch to ode. In its taditional foulation, the newsvendo odel deteines the quantity to ode unde the assuption that pice is an exogenously set paaete which does not affect deand (See Poteus (1990) fo a copehensive eview of geneal newsvendo pobles). The ipact of adding picing decisions to the newsvendo poble was fist consideed by Whitin (1955). Mills (1959) consides this poble unde the assuption of additive deand uncetainty, while Kalin and Ca (196) assue ultiplicative deand uncetainty. Fo a copehensive eview of the newsvendo poble with endogenous picing we efe to Petuzzi and Dada (1999), who popose a unified view of the above entioned appoaches. Deand uncetainty and the use of local deand infoation often lead to sevee distotion and loss of channel pofits. A elated issue is the inheent aplification of deand vaiability as local deand infoation is tansitted along a distibution channel. The phenoenon, which is due to successive distotion of the deand infoation, is often efeed to as the bullwhip effect. It was fist illustated in Foeste (1958) and oe ecently analyzed by Lee, Padanabhan and Whang (1997), the latte spawning a lage nube of publications on this issue, fo which one eedy is infoation shaing. Lee, So and Tang (000) study infoation shaing in supply chains with long-te elationships and find that the value of infoation shaing is high when the deand coelation ove tie is high and when the deand vaiance within each tie peiod is high. Howeve, infoation shaing is coplicated by incentive and cedibility pobles that aise fo infoation asyety. Cachon and Laiviee (001) exploe capacity decisions in a supply chain with one anufactue and one supplie (etaile). They show that the use of focing contacts (involuntay copliance) vs. self-enfocing contacts (voluntay copliance) significantly ipacts the outcoe of deand foecast shaing. Li 5

8 (00) exaines the incentives fo fis to shae infoation vetically in a supply chain with one anufactue and any etailes. He shows that voluntay infoation shaing is often infeasible when the etailes ae engaged in a Counot copetition and ae endowed with soe pivate infoation. Fo excellent eviews of infoation shaing and contacts in supply chain coodination, eades ae efeed to Cachon (003) and Chen (003). Ou pape diffes fo the above entioned liteatue in two aspects. Fist, we study the value of infoation shaing in a distibution channel in which the ebes have asyetic infoation about deand volatility. Second, we exaine the echaniss fo facilitating infoation shaing in the context of shot-te elationships, whee coopeative behavio is ae and focing contacts of any kind ae difficult to ipleent. The eainde of the pape is oganized as follows. Section lays out the key eleents of the odel. Section 3 analyzes the basic odel, in which a anufactue and a etaile with asyetic infoation about deand volatility opeate unde a wholesale pice only egie without infoation shaing. Section 4 exploes the value of shaing this type of infoation, and how to facilitate shaing using diffeent contactual ageeents. Section 5 consides the ipact of shaing infoation unde a two-pat taiff egie instead of a wholesale pice echanis. Section 6 concludes.. Assuptions and odel set-up The distibution channel we conside consists of a anufactue and a downstea etaile; both fis ae isk neutal and axiize thei expected pofits. Given that p epesents the etail pice, end- b custoe deand is given by D ( p) = y( p), whee y( p) = ap (defined fo a> 0, b> 1) is a pice dependent deteinistic function, and is a unifoly distibuted ando vaiable with ean of 1. Moe pecisely, U[1 L,1+L] fo 0 L 1, with f (.) and F(.) denoting its pdf and cdf. Hence, endcustoe deand is deteined by a ando daw fo the distibution U[1 L,1+L], whee natue 6

9 deteines the extent of uncetainty L. The deand is intinsically stochastic with an aveage of y ( p), a standad deviation of y ( p )L 3, and a volatility which deceases (inceases) as L tends to 0 (1). It follows that the aveage deand y( p) tends to 0 as p gows vey lage, and goes to infinity as p appoaches 0. This popety is innocuous and is equivalent to the usual assuption that the deand eaches the aket potential (usually a constant) when the poduct is fee. The paaete b easues pice sensitivity. We assue that the pice elasticity of the aveage deand b is coon knowledge and that b > 1 so that the deand is sufficiently elastic. In ou odel, the ando vaiable captues deand uncetainty, the functional fo of its distibution (unifo) and its ean ae coon knowledge. The only unknown is the vaiance of, which is chaacteized by the lowe and uppe bounds of the distibution 1 L and 1+L. As such, the anufactue and the etaile need to fo estiates of L independently. The steps in ou odel ae as follows. Fist, the anufactue deteines the wholesale pice w, using its pivate deand estiate,, to pedict the etaile s eaction. We assue that the anufactue has a constant aginal cost, c, unknown to the etaile, and does not have any capacity constaints. (The assuption that c is pivate infoation is otivated by the fact that the aginal costs ae highly dependent upon the anufactue s oganizational capabilities, which in geneal ae unknown to the etaile.) Subsequently, the etaile, with the wholesale pice w at hand, sets the etail pice, p, and places an ode, q, using its own deand estiate. Finally, the deand D(p) is ealized. If D( p) > q, the etaile expeiences a shotage and incus an oppotunity cost in tes of pofits lost, ( ) ; if D( p) ( p w) D p q ( ) < q, the etaile has leftove poducts ove which it incus a loss, w q D p. We assue that neithe the etaile no the anufactue incus any goodwill cost in the event of shotage, and that any leftove poducts have zeo salvage value. Howeve, it would be possible to extend ou odel to incopoate these. 7

10 The esulting faewok can be viewed as a one-peiod gae of incoplete infoation, and the appopiate solution concept in this setting would be the Bayesian-Nash equilibiu. Specifically, the fis optial stategies need to be consistent with thei beliefs deived fo Bayes ule. In ou faewok, howeve, the beliefs do not ipact ou esults. This is because (i) as we will show in Section 3., the optial wholesale pice w is independent of L and does not convey any useful infoation about the anufactue s estiate to the etaile, and (ii) even though the anufactue ay deduce the etaile estiate L, this has no consequence on the optial wholesale pice, and the equilibiu solution eains unchanged. Theefoe, it is ational fo a fi to use its own estiate. Foally, the non-bayesian natue of the gae is illustated by the following clais: Clai 1: The anufactue and the etaile fo point estiates of L. Poof: All poofs ae in the Appendix. Clai : The anufactue s wholesale pice w is uninfoative. Clai 3: Without infoation shaing ( L is unknown to the etaile), it is ational fo the etaile to use he own estiate update. L ; with infoation shaing, a known L tigges an all-o-nothing Now suppose that the anufactue and the etaile each fo a point estiate of L, thei beliefs on ae then given by U[ 1 L, 1+ L ] and U[ 1 L, 1 L ] possible that L i L o Li +, espectively. Note that it is L, whee i =,. In wods, the anufactue and the etaile can eithe oveestiate o undeestiate L. Since the ean of the deand distibution is known, a fi s deand estiate is supeio if its estiated vaiance is close to the tue state. Accoding to ou definition, L i is supeio to L j if L Li < L Lj. At the sae tie, the anufactue and the etaile each eceive a signalσ that eveals the type of the othe playe. Fo siplicity, we assue that each playe can be of i thee types{ h,, l}, whee h type is supeio, type is the sae as the othe playe o unknown, l 8

11 natue L 0 1 M R L, σ L, σ Figue 1: The infoation set of each playe type is infeio. In su, the infoation set of each playe is given by{ L, σ } (see Figue 1). While infoation about the fi s own deand volatility estiate (L o L ) is always pivate, infoation about which estiate is supeio (if it exists) can be eithe pivate o coon knowledge. Put diffeently, a fi s deand estiate is only known to itself, but the quality of this estiate ay be known to the othe fi. Fo exaple, when foecasting the sales of a new novel, a national book stoe such as Aazon ay have a deand estiate of n ± x units, while a egional publishe s deand estiate is n ± y units. This infoation is stictly pivate unless puposely evealed. On aveage, one would expect Aazon s estiate to be supeio because of its sophisticated CRM (custoe elationship anageent) solutions and national pesence (thus σ = h, σ = l). Howeve, the egional publishe can geneate a supeio estiate though popietay aketing eseach (this ay o ay not be known to Aazon, thus σ = l, σ = h o ). If the egional publishe deals with a local bookstoe that has siila aketing capability as itself, σ dictates that the anufactue is of type and vice vesa, etc. Note that the cases whee σ = σ = l, σ = σ = h ae equivalent to σ = σ =. We suaize the altenative infoation stuctue iplied by the signal geneating pocess of σ i in Table 1. i i 9

12 Table 1: Altenative infoation stuctues Fi's knowledge of the quality of the deand estiate Whose estiate of deand volatility is supeio M R Only M knows Only R knows Neithe fi knows Both fis know σ Scenaio 1a Scenaio a = l, σ = σ =, σ = Scenaio 1b σ = h, σ = h Scenaio b σ =, σ = l i Scenaio 3 σ = σ = j Quality is coon knowledge σ i = h σ = l j When the quality of the deand estiates is pivate infoation, thee ae thee possible scenaios (see Table 1): (1) the anufactue knows whose estiate is supeio but the etaile does not, () the etaile knows whose infoation is supeio but the anufactue does not, and (3) neithe fi knows who has bette deand estiate. As the odel unfolds, we shall see that these altenative infoation stuctues geneate vaious incentive and cedibility issues and hence ipact the feasibility of infoation shaing. We will exploe these iplications in details in Section The Basic Model The basic odel exained in this section focuses on situations whee the anufactue and the etaile inteact using a wholesale pice only egie. Situations in which the anufactue and the etaile inteact using a two-pat taiff echanis ae analyzed in Section 5. The wholesale pice only contact iplies that the only inteaction between the etaile and the anufactue occus when the anufactue posts its wholesale pice and when the etaile places its ode. As such, ou basic odel consides the ipact of deand volatility and asyetic infoation when infoation shaing does not occu. The esults obtained hee seve as the basis fo analyzing the value and feasibility of infoation shaing in Section 4. To analyze the faewok and deteine the equilibiu decisions we use backwad induction. To illustate the ipact of deand volatility, we fist conside the case in which both the etaile and the 10

13 anufactue have syetic and accuate infoation, that is, L = L = L. Section 3.1 deives the etaile s pofit axiizing stategy fo this case, given the wholesale pice deteined by the anufactue. Based on these esults, the anufactue s decision poble is analyzed in Section 3.. Subsequently, section 3.3 povides insights as to the ipact of deand volatility on the equilibiu stategies. Finally, section 3.4 discusses the ipact of infoation asyety on the equilibiu stategies. Although Sections 3.1 and 3. ae integal coponents of ou analysis, they focus on the technical aspects of the odel and ae elatively self-contained. Reades who ae not inteested in the undelying atheatics of the odel developent can go diectly to Sections 3.3 and 3.4 to obtain the key insights fo the odel. 3.1 Syetic Infoation: Retaile Pofit Maxiizing Stategy The etaile pofit fo the peiod, π, is the diffeence between its sales evenues and puchase costs. Assuing a wholesale pice w, a etail pice, p, an ode quantity, q, and the deand D(p), π can be expessed as follows: pd( p) wq fo D( p) q π ( q, p, w) = (1) ( p w) q fo D( p) > q Following the appoach outlined, fo exaple, in Petuzzi and Dada (1999), we expess all quantities elative to the deteinistic pice-dependent coponent y ( p) by defining what we efe to as the ean-adjusted ode quantity z = q/y(p). This esults in an altenative ean-adjusted epesentation, which claifies the ipact of deand uncetainty and siplifies the analysis to coe. ( p w ) w( z ) fo z π ( z, p,w ) = y( p ) () ( p w ) ( p w )( z ) fo > z If the etaile has accuate infoation ( axiize when deciding p and z (o equivalently q) can be expessed as L = L), the expected pofit that the etaile attepts to 11

14 1+ L E { π (, z p, w) } = y( p) ( p w) xf() x dx 1 L z 1+ L w ( z x) f( x) dx ( p w) ( x z) f( x) dx 1 L z (3) Defining Ψ ( p,w ) = y( p )( p w ) and z 1+ L Λ ( z, p, w) = y( p) w ( z x) f( x) dx+ ( p w) ( x z) f( x) dx 1 L z = y( p) LpF ( z) + ( p w)(1 z) we can also wite { } E π (, z pw, ) =Ψ( pw, ) Λ (, z pw, ). (4) Hence, the expected pofit can be expessed as the iskless pofit, Ψ(p,w), which epesents the pofit obtained by the etaile in the deteinistic poble (e.g. L = 0 ), less the expected loss that esults fo the pesence of uncetainty, expessed by the loss function Λ ( z, p, w). Note that the expected loss equals the su of the expected cost of odeing too uch and the expected oppotunity cost of odeing too little. To deteine the optial pice p ( w ) and ean-adjusted ode quantity z ( w ) that axiize (3) and (4) fo a given w, we conside the fist-ode optiality conditions and poceed by taking the fist patial deivatives of E { (, z p, w) } { π } π with espect to z and p: E (, z p, w) Λ (, z p, w) = = y( p) ( p w) pf( z) z z [ ] { π (,, )} E z p w p w = y( p) z(1 b ) + ( b 1) LF ( z) p p Obseve that fo any given p the optial ean-adjusted ode quantity z ( p,w ) coesponds to the standad newsvendo esult, that is, 1

15 1 p w p w z ( p, w) = F ( ) = 1 L+ L. (5) p p It is easy to see fo (5) that z ( p,w ) is inceasing in p. Intuitively, the explanation fo this is that the oppotunity cost fo evey unsatisfied deand (p w) inceases with p, while the cost of evey suplus ite eains constant at w. Siilaly, fo any given z we can deteine the optial pice p (, zw: ) b z (, ) = 1 ( ) p z w w b z LF z (6) Obseve that wheneve deand is deteinistic (e.g. L = 0 ), the optial iskless pice p ( w ) b = w. b 1 Moeove, we note that z LF ( z) < z since both L and F( z ) ae non-negative, and that z LF ( z) > 0 since L 1 and F ( z) F( z) z. Thus, equation (6) illustates the well-known esult (Kalin and Ca, 196) that the intoduction of uncetainty will yield a pice that is lage than the optial iskless pice, i.e. p ( w ) b w. b 1 Using (5) (o (6)), the etaile s pofit axiization poble can be educed to an optiization poble ove a single vaiable. Substituting the expession fo z ( p, w ) into the expected pofit function (4) endes the expession w E { π ( z( pw, ), pw, )} = yp ( ) ( p w) 1 L, p which is deceasing in the deand volatility L. Using the fist ode optiality condition with espect to p, endes p ( w ) as specified in Lea 1. Lea 1: Fo any given w, the optial etail pice b p ( w) = w H( b, L), (7) b 1 13

16 whee 1+ L 1 L L HbL (, ) = + + > 1. (8) b Note that [b/(b 1)]H(b,L) can be viewed as a genealized double aginalization facto, which is iniized fo the special case of deteinistic deand (i.e., L = 0) whee it degeneates to b/(b-1). Fo Lea 1 it is easy to deteine the optial ean adjusted ode quantity z ( w ) by substituting p ( w ) fo p in (5). 1 b 1 b 1 z ( w) F 1 1 L L = = + 1 bh ( b, L) bh ( b, L) (9) The coesponding actual ode quantity, q ( w ), follows diectly as q ( w ) = z ( w )y( p ( w )). 3. Syetic Infoation: Manufactue Pofit Maxiizing Stategy The anufactue has to deteine an optial wholesale pice w. Given that, in the cuent case, the etaile and anufactue have syetic and accuate infoation, the anufactue can pedict the etaile s esponse to any given ode quantity he chooses. Consequently, the etaile s pofit function, as a function of the wholesale pice, can be expessed as π ( w) = ( w c) q( p( w), w) b 1 1 b = ( w c) 1+ L L H( b, L) y( w) b H(, b L) b 1 b (10) Note that π (w) is a deteinistic function, that is, the anufactue s pofit is deteined by how uch the etaile odes instead of actual sales duing the peiod. This iplies that the anufactue does not expose itself to any isk associated with deand uncetainty. To deteine the anufactue s optial wholesale pice w, we use the fist ode optiality condition fo π (w) with espect to w, π ( w ) 1 1 w c 1 b b L L b = + H( b, L) y( w) = 0. w w bh(, b L) b 1 14 b

17 Solving fo w yields w b = c b 1, (11) It is inteesting to note that w is in fact independent of the deand volatility L, and woth pointing out that this is unlikely to hold if the anufactue faces constained capacity, which typically ceates a coplex elationship between c and the quantity odeed. Finally, we also note that in the case of deteinistic deand (L = 0), (11) togethe with (6) illustates the well-known double-aginalization pinciple. 3.3 Ipact of Deand Volatility Fo the above, we conclude that fo given estiates of the deand volatility L, the pofit axiizing stategy fo the anufactue is to set a wholesale pice w and the optial esponse fo the etaile is to ode q ( w ) units which ae sold at a etail pice of p ( w ). To analyze the value of infoation shaing, an ipotant question is how changes in the deand volatility estiates ipact these decisions and the associated pofits. In the eainde of this section we povide soe stuctual popeties that help answe these questions. Fist, howeve, we obseve that since the anufactue s optial wholesale pice w is independent of L (see (11)), the pofit axiizing stategies ae unaffected by changes in the anufactue s estiate of the deand volatility. We theefoe concentate on the ipact of deand volatility changes on the etaile s stategy. In the pesence of deand volatility, the ode quantity q ( ) deand ovestocking. ( ( )) w geneally diffes fo the aveage y p w due to the asyety between the costs associated with undestocking and Lea : Fo any given L, ( ) q w > y( p ( w)) if and only if 1 HbL (, ) b > b. 15

18 z q 1 y( p ) L 0 1 L 0 1 Figue : Ipact of deand volatility on ode quantity. This is illustated in Figue, which shows both the ean-adjusted and the absolute ode quantity as a function of L. Clealy, ( ) q w = y( p ( w)) when L = 0. Howeve, as L inceases decease below 1 (and theefoe ( ) z ( w ) will initially q w < y( p ( w)) ), until we each the value of L fo which 1 HbL (, ) b = b. Fo lage values of L, z ( w ) will be lage than 1. In addition, the etaile can fine-tune the costs of ovestocking and undestocking since it has the ability to set pices, which will cause the etail pice p ( w ) to diffe fo the optial iskless pice p ( w ) b = w. As discussed in the intoduction of this pape, the conventional appoach to deand b 1 uncetainty focuses on the ean, but fails to account fo these additional tade-offs that ae caused by the intoduction of deand volatility. This ay becoe pobleatic when deand volatility is an ipotant facto. We note that while a two-point distibution can also account fo the effect of deand volatility, it is ipossible to disentangle the effect of the ean fo that of vaiance in such distibutions, since any change in the vaiance will also iply a change in the ean. To illustate the ipact of deand volatility, we fist conside its ipact on the optial etail pice. Poposition 1: The pofit axiizing etail pice p ( w ) is stictly inceasing in L. 16

19 Intuitively, by inceasing the etail pice, the etaile can educe the deand vaiability (ecall that its standad deviation is y ( p )L 3 and that y(p) is deceasing in p) and counte the effect of an incease in L on the loss te Λ ( z, p, w). Of couse, an incease in the etail pice also educes the ean deand, y(p), which iplies a eduction in the iskless pofit Ψ ( p, w). To illustate how deand volatility ipacts the optial ode quantity q ( w ) we fist obseve that, while the ean-adjusted ode quantity z ( p,w ) is inceasing in p, the actual ode quantity q ( p,w ) = y( p )z ( p,w ) will have a axiu. Intuitively, this follows since any incease in z ( p,w ) ae counteed by a decease in the ean deand y ( p) = ap -b as p inceases. Lea 3: Fo any given w, q ( p,w ) stictly inceases with espect to p when b L p w b L and stictly deceases with espect to p when b L p w b L. Coollay 1: The pofit axiizing ode quantity q ( w ) is stictly deceasing in L. Obseve that coollay 1 iediately follows fo Poposition 1 and Lea 3, since b b L p ( w) w > w b 1 b L. 3.4 Ipact of Infoation Asyety Let us now conside the situation whee the etaile and the anufactue have asyetic deand estiates, which ay both be diffeent fo the tue deand volatility L. Thus, the etaile s estiate L ay be diffeent fo the anufactue s estiate L. In this case, the basic odel is again deived fo backwad induction. Howeve, when the etaile akes its decisions egading etail pice and ode quantity to axiize its expected pofits (given w), it does so ex ante without knowing D(p). Instead, it has to ely on its best deand estiate D (p). The associated pofit function, and consequently the expected pofit, ae equivalent to () and (3) afte 17

20 substituting D (p) fo D(p) and fo, espectively. In the asyetic case, the optial etail pice is given by b p ( w) = w H( b, L) b 1 wheeas the optial ean adjusted ode quantity b 1 ( ) = bh b L z w L L (, ). In Section 3., we showed that the anufactue s optial stategy is in fact independent of its deand estiate. Thus, even with asyetic infoation the optial wholesale pice w b = c b 1. To analyze the ipact of infoation asyety, we fist obseve that Poposition 1 and Coollay 1 iply that wheneve the etaile undeestiates deand volatility, the esult will be a etail pice that is too low and an ode quantity that is too high. Convesely, if the etaile oveestiates the deand volatility, the etail pice will be too high and the ode quantity too low. The ipact on channel pofits, howeve, is soewhat oe coplicated. Afte the pofit axiizing stategies ( w, q ) and ( w ( ) p w ) ae evealed, the anufactue s pofit, π ( w ) = ( w c) q ( w ), is unabiguously defined. Note that π ) depends on L via q ), but that it is independent of L and L. The ( w ( w etaile s expected pofit, on the othe hand, is a bit oe abiguous. Fo the etaile s pespective, the deand estiate,, is coect. Unde this deand estiate, its peceived expected pofit is E { π z ( w ), p ( w ), w )} ( as defined in (3) and (4). Howeve, objectively, the tue deand uncetainty is (unknown to the etaile). Unde the tue deand distibution the etaile s actual ( expected pofit is E { π z ( w ), p ( w ), w )} E whee. In analogy with (4) we have { π ( z ( w ), p ( w ),w )} Ψ ( p ( w ),w )) Λ ( z ( w ), p ( w ), w ) 18 = (1) G( L,z) 1+ L Λ ( z, p,w) = y( p) w ( z x) f ( x) dx + ( p w) ( x z) f ( x) dx, (13) 1 L G( L,z)

21 and 1 L if z < 1 L G ( L,z ) = z if 1 L z 1 + L (14) 1 + L if z > 1 + L Clealy, if the etaile s estiate is coect, i.e., = and L = L, the etaile s peceived expected pofit coincides with its actual expected pofit. Poposition : Unde the equilibiu stategies w, q ) and p ) : ( w ( w (i) The anufactue s pofit, π ( ), and the etaile s peceived expected pofit, E { π z ( w ), p ( w ), w )} ( w, ae deceasing in L. ( (ii) The etaile s actual expected pofit, E { π z ( w ), p ( w ), w )}, is axiized when the etaile s estiate of the deand distibution is coect, i.e., when L =L. (iii) When L =L and the etaile s deand estiate is coect, the etaile s actual expected pofit is deceasing in the deand volatility L. Fo Poposition we conclude that if the etaile oveestiates the deand volatility (L > L), it has a negative ipact on the pofits of both the etaile and the anufactue. On the othe hand, an undeestiation (L < L), will benefit the anufactue. Poposition also assets that inceased volatility, even when coectly estiated, educes pofits of both the etaile and anufactue. The iplications of this poposition on the potential benefits fo the channel to shae infoation about deand volatility ae futhe discussed in Section Infoation Shaing in a Wholesale Pice Only Regie In the infoation shaing scenaios we conside, each fi knows its own estiate of deand volatility (L o L ). In addition it ay also have infoation about the quality of the othe fi s estiate elative to its own. Moe pecisely, a fi ight know which estiate is supeio, that is, 19

22 whethe L o L is close to the tue state L. Howeve, as discussed in Section, L as well as the coelation between the estiates ae unknown. Unde this infoation asyety, the fi with a supeio estiate needs a echanis to convey its infoation (about L o L ) to the othe fi when it is pofitable to do so. The tansission of this infoation can only be successful if the othe fi finds itself bette off, o at least no wose off, to use such infoation. Thoughout this pape, we say that infoation shaing occus when such tansission is successful, that is, when the fis shae thei pivate infoation about deand volatility (L o L ). An ipotant obsevation explained in Sections is that belief updating is oot fo the situation we conside. To bette undestand the incentive and cedibility pobles in infoation shaing, we outline the taxonoy of altenative infoation stuctues, suaized in Table 1 (on p. 10). We discuss each of these scenaios in tun. In Scenaio 1, if the anufactue s estiate is supeio (Scenaio 1a), he needs to cedibly convey this infoation to the etaile when doing so ipoves his pofit. The incentive poble aises since the anufactue only wants to shae his bette infoation if the etaile s ode quantity is too low and hence huts his pofit. Howeve, the anufactue ay also have an incentive to induce the etaile to ode too uch. Thus, the cedibility poble also aises as the etaile does not know whose estiate is supeio and would suffe fo a lowe pofit if he odes too uch. If the etaile s estiate is supeio (Scenaio 1b), no action is necessay. The anufactue siply coplies with the etaile s ode and the etaile s infoation is tansfeed to the anufactue costlessly. Neithe cedibility no incentive pobles ae pesent since the etaile has no incentive to anipulate the ode quantity given his lack of knowledge on whose deand estiate is supeio. In Scenaio, cedibility and incentive pobles aise when the anufactue possesses a bette deand estiate (Scenaio a), but no action is necessay if the etaile s deand estiate is supeio (Scenaio b). The undelying logic is siila to that discussed in Scenaio 1. In Scenaio 3, it is not clea that infoation shaing is at all feasible. At least one fi should be able to evaluate the expected ipoveent in pofits when 0

23 infoation shaing occus, but such judgent cannot be ade if neithe fi knows whose deand estiate is supeio. In su, infoation shaing is feasible when at least one fi knows the quality of the deand estiates and when the fis can ovecoe the incentive and cedibility pobles. In a coodinated channel, the two fis act as if they wee a single entity, which iplies the absence of double aginalization and a etail pice and ode quantity that axiize the channel pofits. As we deonstate in Section 3, the wholesale pice by itself neithe coodinates the channel no achieves infoation shaing. Iye and Villas-Boas (003) show that, unde deteinistic deand and coplete infoation, a wholesale pice only contact coodinates the channel when the etaile s bagaining powe is sufficiently lage. A bagaining faewok, howeve, is beyond the scope of this pape. An altenative picing schee, the two-pat taiff consisting of a fixed fee and a vaiable fee, coodinates the channel unde syetic infoation. Howeve, it is not clea whethe a two-pat taiff achieves infoation shaing in the pesence of infoation asyety. In this section, we exaine the potential value of infoation shaing unde a wholesale pice egie, and exploe how infoation can be shaed in a utually beneficial anne using pofit shaing and buy back contacts. A paallel analysis unde a two-pat taiff egie is povided in Section The Value of Infoation Shaing In Section 3 we analyze the ipact of the anufactue and etaile having asyetic estiates of the deand volatility unde a wholesale pice only egie without infoation shaing. In this section we exaine the potential value of shaing such infoation in tes of inceased channel pofits. We also conside the consequences fo the pofit axiizing stategies in tes of picing and ode quantities. The fundaental question is whethe infoation shaing always has a potential to ipove channel pofits and how infoation shaing ipacts each fi s expected pofit. To siplify the analysis without sacificing any insights, we hencefoth conside a situation whee the anufactue s estiate of deand volatility is pefect (i.e., L = L), but the etaile s estiate deviates fo the tue 1

24 state. The potential value of infoation shaing is obtained by copaing the situation of no infoation shaing (analyzed in Section 3) with the situation of pefect infoation shaing. The latte efeing to the situation whee both fis use the best available estiate L. (Recall that wheneve L is supeio, infoation shaing takes cae of itself and is of little inteest to analyze futhe.) Poposition 3: Suppose L = L and let L = L + δ, whee δ denotes the deviation fo the tue state, L, and satisfies the egulaity condition 0 L + δ 1. Unde a wholesale pice only egie, infoation shaing ipoves expected channel pofits when δ > 0, but ay eithe incease o decease channel pofits when δ < 0. Moe pecisely, when δ < 0 infoation shaing inceases expected channel pofits if and only if the infoation shaing condition (ISC) is satisfied: HbL ˆ(,, ) ˆ δ bhbl (,, δ) Ω ( L, δ, b) + 1 b 1 4 L HbL (, ) Ω ( L,0, b) H( b, L + δ ) b+ 1 1 (ISC) whee HbL ˆ (,, δ ) and Ω (, bl, δ ) only depend on b, L and δ. To appeciate the above poposition, we identify the souces of distotion in the channel. Copaed to a coodinated channel with coplete infoation, the cuent channel suffes fo thee types of distotion: double aginalization, deand uncetainty, and iscalculation of deand uncetainty. While the fist two types of distotion is detiental to both fis (the effect of deand uncetainty on fis pofits is delineated in Poposition ), the effect of the thid type of distotion on the two fis can be asyetic. As asseted in Poposition 1, both the pofit axiizing etail pice, p ), and ( w ( w ode quantity, q ), ae distoted by uncetainty. By contast, the wholesale pice is unaffected by the deand volatility. In the absence of infoation shaing, the anufactue takes the etaile s ode quantity as given and poduces exactly that aount. Hence, the anufactue does not bea any isk associated with deand volatility. When δ > 0, which eans that the etaile oveestiates the deand uncetainty, it leads to a highe etail pice and a lowe ode quantity than what would othewise be

25 Δπ Δπ 1 δ 0 1 Δπ Figue 3: The value of infoation shaing unde a wholesale pice only egie. the case (see discussion in Section 3). The opposite is tue when δ < 0. An inteesting conclusion fo Poposition 3 is that wheneve the etaile undeestiates the deand volatility (i.e., δ < 0) it is only the pice elasticity, b, and the anufactues estiate, L, that deteines whethe infoation shaing causes channel pofits to incease o decease (see (ISC)). Hence, using Poposition 3, the anufactue can assess fo which δ (o equivalently L estiates) shaing its supeio infoation about the deand volatility would incease channel pofits and when it would educe the. Futheoe, ISC can help deteine when infoation shaing is beneficial to the anufactue. To illustate the above points, Figue 3 shows the diffeence in the anufactue s and the etaile s expected pofits when pefect shaing takes place (L = L = L) copaed to when no infoation shaing occus. We use the notation: ( z ( w ), p ( w ), w ) ( z ( w ), p ( w ), w ) Δ π = π π, and { ( ( ), ( ), )} { ( ( ), ( ), )} Δ π = E π z w p w w E π z w p w w, whee E { ( z( w), p( w), w) } π is the etaile s actual expected pofit when the optial stategies ae based on the supeio estiate L (which in ou case happens to coincide with the tue state, L). 3

26 { ( ( ), ( ), ) } E π z w p w w is the actual expected etaile pofit when no infoation shaing takes place. A positive Δ π (o Δ π ) iplies that the fi s expected pofit inceases when infoation is shaed, while a negative value eans it deceases. Fo Figue 3 we can see that infoation shaing inceases both the etaile s and the anufactue s pofits when the etaile oveestiates the deand uncetainty ( Δ π > 0 when δ > 0), a esult that follows fo Poposition. In this case, infoation shaing is incentive copatible and ipoves channel pofits (Poposition 3). That is, both paties ae bette off with espect to thei expected pofits when using L. On the othe hand, when the etaile undeestiates the deand uncetainty (δ < 0), we can see that infoation shaing deceases the anufactue s pofit while it still benefits the etaile ( Δ π < 0 and Δ π > 0 when δ < 0). This esult also follows fo Poposition. Moeove, as asseted in Poposition 3, Figue 3 indicates that the loss in the anufactue s pofit of shaing the infoation on deand volatility can exceed the gain in the etaile s pofit ( Δ π >Δ π when δ < 0), i.e., condition (ISC) is not satisfied. This causes a conflict of inteest and infoation shaing educes channel pofits. Thus, we conclude that infoation shaing ay o ay not be valuable in an uncoodinated channel, and it depends in a coplicated way on the pice elasticity b, and the deand estiates L and L. An ipotant insight is that befoe the fis actually shae thei infoation, they do not know with cetainty whethe they ae facing a situation whee it is beneficial to do so. This iplies incentive issues fo the anufactue to shae its supeio infoation. To explain this futhe, conside the anufactue befoe infoation shaing. Given that it has no pio knowledge of the etaile s estiate L (beyond the fact that it deviates fo the tue volatility L, ), one can ague that fo the anufactue s pespective, L is a stochastic vaiable with equal (ex ante) pobability fo 0 L 1 (o equivalently 0 L + δ 1). Using Poposition 3 and (ISC), the anufactue can easily deteine the 4

27 ange of δ whee infoation shaing inceases and deceases expected channel pofits, espectively, and thus the pobability fo infoation shaing to be beneficial. Fo exaple, if L < 0.5 we know without using condition (ISC) that thee is at least a 50% chance infoation shaing will incease the expected channel pofits (the pobability that δ>0 is 1 L ). One can theefoe ague that in this case it is ational fo the anufactue to shae its infoation. (Note that this aguent is not contingent on L = L, since the L is unknown and L is the best estiate available when the anufactue akes its decision.) Howeve, fo cetain values of L and b shaing is bound to not take place because the anufactue concludes that thee is a lage chance pofits will decease than incease. As an altenative, befoe shaing the anufactue can also copute the expected gain in channel pofits acoss the entie ange of feasible δ values (fo exaple using the expessions specified in the poof of Poposition 3 and integate nueically). If this gain is positive it would be ational fo the anufactue to shae infoation, othewise not. To conclude, it is not obvious that the anufactue is always willing to shae its supeio infoation since doing so ay ipove the etaile s pofit at the expense of educing its own pofit. Although infoation shaing educe/eliinate the distotion caused by the iscalculation of deand uncetainty, its ipact on the pofits of the anufactue and the etaile is asyetic. In paticula, infoation shaing is not incentive copatible when the etaile undeestiates deand volatility. In su, infoation shaing is feasible only when it benefits both fis, i.e., when the infoation shaing condition illustated in Poposition 3 holds. 4. Infoation Shaing Contacts As discussed ealie, fis need to ovecoe incentive and cedibility pobles to achieve infoation shaing. In what follows, we investigate two altenative contactual aangeents that help achieve infoation shaing. In paticula, these contacts ae elatively easy to ipleent. We fist analyze the pofit shaing contact when the quality of the deand estiates is coon knowledge; 5

28 we then exaine the buy back contact when only one fi knows whose deand estiate is supeio. In addition, we study the effect of infoation shaing on picing, fis pofits, and channel pofits The pofit shaing contact When both the anufactue and the etaile know which deand estiate is supeio, cedibility is not an issue but the incentive poble eains. A pofit shaing contact is a siple echanis to facilitate infoation shaing unde such cicustances. Since infoation shaing takes cae of itself when the etaile s estiate is supeio, we only conside the case when the anufactue s estiate is supeio. Ou analysis pesues that the anufactue has an inteest in shaing. (As explained in Section 3.1., this is not always the case since the anufactue ay conclude befoe the fact that the isk of educing the expected channel pofit is too high.) The sequence of actions is as follows. Fist, the anufactue and the etaile negotiate fo a division of the cobined gain in pofits when infoation shaing occus. The gain (loss) in pofit fo each fi is elative to the no infoation shaing case, whee the fis use thei own deand estiates. Although the division can be abitay depending on each fi s bagaining powe, we assue without loss of geneality that both fis split the gain equally. If the negotiation is successful, both fis subit thei deand estiates siultaneously. Othewise, the fis do not eveal thei deand estiates and the gae poceeds as in the no-infoation-shaing case descibed in Section 3. The solution concept in the pofit shaing contact is one of Nash bagaining. Without infoation shaing, the equilibiu stategy z ( w ), p ( w ), w ) is based on the etailes deand estiate. With infoation shaing, both fis ( use the supeio estiate L when deteining the optial stategy ( z ( w ), p ( w ), w ). Afte the 6 deand estiates ae evealed both paties agee that L is the best available estiate of the tue deand volatility. Unde this estiate the etaile s expected pofit with and without infoation shaing ae E { ( ( ), ( ), π z w p w w )} and E { ( z ( w ), p ( w ), w )} π espectively. Siilaly the anufactue s pofit with and without infoation shaing ae ( z( w), p( w), w) π and

29 π ( z ( w ), p ( w ), w ). Hence, afte the contact is signed (in ou case afte the fifty-fifty split is ageed on), the fis peceived change in the expected total channel pofits is ΔΠ = ( E { π ( ( ), ( ), )} { ( ( ), ( ), )}) z w p w w E π z w p w w + π( z( w), p( w), w) π( z( w), p( w), w) ( ) (15) and the pofit shaing contact dictates that the anufactue and the etaile each eceives 1 ΔΠ in equilibiu. A poinent featue of the pofit shaing contact is that although the ageeent on how to split the gain in channel pofits is eached ex ante, befoe the deand is ealized, the actual pofit shaing occus ex post, afte the deand ealization. Note that ΔΠ in (15) epesents the expected actual gain in pofits if L = L. Given the intinsic stochasticity of the deand, a pofit shaing contact can lead to eithe an incease o a decease of the pofits of both fis in ealization. This eans that unde this contact the anufactue and the etaile shae the isk associated with the deand uncetainty. (Unde a wholesale pice only contact the etaile beas this isk on his own.). As outlined in Poposition 1, the optial etail pice and ode quantity can eithe incease o decease depending on whethe infoation shaing educes the etaile s oveestiation o undeestiation. Futheoe, fo Poposition 3 and Figue 3, we can conclude that the sign of ΔΠ as defined in (15) is abiguous (note that ΔΠ is equivalent to Δ π +Δ π unde the pesuption that the anufactue s estiate is coect). This suggests that afte signing the contact the fis ay ealize that the peceived change in expected pofits due to infoation shaing, ΔΠ, is negative. Pofit shaing in this case eans that the etaile has to give up pofits to the anufactue and both paties end up being wose off. Consequently, the etaile has incentives to beak the contact, to use the anufactue s estiate, which it now knows, and leave the anufactue to take the entie pofit loss. Hence, soe kind of enfocing echaniss ay be equied in ode to secue the contact. 7