Supply chain information sharing in a macro prediction market

Transcription

1 Decision Suppot Systems 42 (2006) Supply chain infomation shaing in a maco pediction maket Zhiling Guo a,, Fang Fang b, Andew B. Whinston c a Depatment of Infomation Systems, UMBC (Univesity of Mayland, Baltimoe County), Baltimoe, MD 2250, USA b Depatment of High Tech Management, College of Business Administation, Cal State Univ San Macos, San Macos, CA 92096, USA c Depatment of Infomation, Risk, and Opeations Management, McCombs School of Business, The Univesity of Texas at Austin, Austin, TX 7872, USA Received 4 Apil 2006; accepted 0 May 2006 Available online 7 July 2006 Abstact This pape aims to addess supply chain patnes' incentives fo infomation shaing fom an infomation systems design pespective. Specifically, we conside a supply chain chaacteized by N geogaphically distibuted etailes who ode a homogeneous poduct fom one manufactue. Each etaile's demand isk consists of two pats: a systematic isk pat that affects all etailes and an idiosyncatic isk pat that only has a local effect. We popose a maco pediction maket to effectively elicit and aggegate useful infomation about systematic demand isk. We show that such infomation can be used to achieve accuate demand foecast shaing and bette channel coodination in the supply chain system. Ou maket-based famewok extends the ange of infomation shaing beyond the supply chain system. It also opens the doo fo othe copoate isk management oppotunities to hedge against aggegate economic isk Elsevie B.V. All ights eseved. Keywods: Supply chain; Infomation shaing; Maco pediction maket; Rational expectations equilibium. Intoduction Coesponding autho. addesses: zguo@umbc.edu (Z. Guo), fangfang@csusm.edu (F. Fang), abw@uts.cc.utexas.edu (A.B. Whinston). Infomation asymmety is a main souce of systems inefficiency in many aeas. Fo example, the well-known bullwhip effect [22,3] efes to the infomation distotion that is caused by misaligned incentives to shae pivate demand infomation tuthfully among self-inteested supply chain patnes, esulting in diect deadweight losses in social welfae. Tuthful infomation shaing has been poposed as a solution to the bullwhip effect. Ove the past few yeas, new business initiatives enabled by emeging technologies such as Electonic Data Intechange (EDI), Radio Fequency Identification (RFID), and XML-steamlined wokflow management have facilitated infomation shaing in decentalized business envionments. Howeve, a technologically effective system does not necessaily esult in impoved decision quality unless it is economically efficient as well. Systems could still be inefficient if uses only stategically epot infomation fo thei own benefit. We seek to investigate the incentive issues fo supply chain infomation shaing. In paticula, we popose a maketbased famewok to undestand how conflicting incentives can be aligned and useful infomation can be elicited in the new supply chain infomation systems design so that a boad scope of benefits can be achieved. In this pape, we conside a simple two-echelon supply chain chaacteized by N geogaphically distibuted /$ - see font matte 2006 Elsevie B.V. All ights eseved. doi:0.06/j.dss

2 Z. Guo et al. / Decision Suppot Systems 42 (2006) etailes who ode a homogeneous poduct fom one manufactue. Each etaile seves he own consume maket whose demand uncetainty can be expessed as the sum of two andom elements a maco isk facto and an idiosyncatic isk facto. The maco facto epesents the systematic isks caused by uncetain macoeconomic events that affect all etailes, such as an economic downtun. The idiosyncatic facto epesents local maket isks unique to individual etailes, such as the effect of weathe on thei local makets. Befoe a selling season each etaile eceives a noisy signal about the maco isk and ode inventoy fom the manufactue based on the infomation available to he. The manufactue, who has no consume demand infomation, is inteested in foecasting expected aggegate odes fom all etailes. The etailes, who bea the uncetainty of the consume makets, ae inteested in effectively foecasting futue demand. Ou goal is to design a new supply chain infomation system that aligns diffeent supply chain patnes' self-inteests and thus enables moe effective infomation shaing and bette decision-making. Some citical questions must be answeed in pusuit of this goal: What infomation could and should be shaed? How do we effectively shae this infomation? In answe to the fist question, we ague that the new infomation system should focus on foecasting element at an appopiate aggegation level. A too boad foecasting goal may seem less elevant and a too naow foecasting goal may not attact sufficient attention, leading to a less effective pediction. In this supply chain context, we should focus on the maco facto that will affect all the etailes instead of extacting individual etailes' oveall foecasts. Thee ae seveal easons. Fist, the manufactue is most inteested in the maco facto foecast since the idiosyncatic isks ae independent. The total idiosyncatic effects fom all the etailes can be cancelled out by the Law of Lage Numbes. Second, individual etailes ae not inteested in shaing thei idiosyncatic facto foecasts because they have the best knowledge and ae not concened with the local isk of othes. They ae, howeve, inteested in maco facto foecast because it affects the foecast accuacy of thei own demand. This common inteest among all supply chain patnes can guaantee maket liquidity and ensue that no individual's pivate inteests can significantly mislead the aggegate opinion. Manipulation of infomation can be potentially educed. Theefoe, a maket designed to foecast the maco facto (i.e., a maco pediction maket) is a viable candidate mechanism to elicit and shae dispesed infomation. As to the mechanism fo effective infomation shaing, using a pediction maket to elicit infomation is an emeging eseach field. A pototype example is the Iowa Electonic Maket (IEM: that pedicts pesidential election outcomes. Othe examples include the Hollywood Stock Exchange Maket ( pimaily used to pedict entetainment events such as movie sales, and Goldman Sachs' Economic Deivatives Maket ( in which likely outcomes of futue economic data eleases (such as etail sales o industy poduction) ae taded. In ou context, the maco pediction maket is designed as a eal money futues maket, in which a etail index with a payoff dependent on the futue ealization of the maco facto is taded. The maco pediction maket has many benefits. Fist, the maket offes a good mechanism to effectively combine beliefs in poducing a eliable foecast. Maket paticipants with heteogeneous beliefs expess thei opinions about the etail index though thei tading behavios. Since tades who make bette pedictions can expect highe payoffs, the pediction maket can effectively attact whoeve have good infomation and aggegate it. Second, the maket aligns tades' incentives to tade because no individual is pivotal in influencing maket pice. Once the numbe of paticipants is lage enough, one etaile's nonpaticipation o misepesentation of infomation deceases only that etaile's own pofitability. It affects neithe maket pice no the accuacy of maket pediction conveyed in the pice. Theefoe, the etaile's dominant stategy is to tade accoding to tue infomation. Thid, the maket is an open system that absobs useful infomation fom souces outside the supply chain system. Speculatos, liquidity tades and othes can paticipate as long as they believe they have elevant infomation. This inceases maket liquidity and impoves foecast effectiveness as the numbe of maket paticipants inceases. Finally, using futues makets in maco vaiables affecting the economy to hedge cuently unhedgeable isks is a maket innovation advocated by Ref. [29]. Ou idea of a maco pediction maket opens the doo fo new oppotunities in copoate isk management. In this pape, we develop a model that shows that the infomation incopoated into the maco pediction maket pice is accuate enough to educe the supply chain's total foecast uncetainty. The infomation also educes the etaile's ode vaiance, which can significantly alleviate the bullwhip effect. We demonstate that demand foecast shaing and channel coodination can be collectively achieved in the maco pediction maket-based supply chain infomation system. Expected supply chain efficiency is impoved unde maket coodination. To the best of ou knowledge, this eseach is the fist to incopoate a pediction maket in a supply chain contactual context. Since ou focus is the infomational content of ceating new maket on supply chain efficiency, we limit ou investigation of the contact fomat to the widely

3 946 Z. Guo et al. / Decision Suppot Systems 42 (2006) used pice-only contact, i.e., the manufactue sets a unit wholesale pice and leaves the ode quantity decisions to the etailes. Othe complicated contact foms such as eode/buy back contacts, non-linea picing/quantity discount policy, and linea tansfe payments ae possible. We choose the simple contact fom in ode to geneate and pesent some clean analytical insights. This pape is oganized as follows. We eview elated liteatue in Section 2. In Section 3, we pesent ou base model unde a supply chain infomation shaing famewok. We analyze the manufactue's and etailes' decision poblems and discuss the constuction of a maco pediction maket. We futhe exploe the value of infomation shaing and popeties such as ode vaiances and supply chain efficiency in Section 4. We extend the maket's ole of infomation aggegation to isk hedging in Section 5. We conclude in Section 6 with an agenda fo futue eseach. 2. Related liteatue The value of infomation shaing has been widely studied in the supply chain liteatue (e.g., [8,9,24]). One solution to alleviate the bullwhip effect was centalizing demand infomation fom supply chain patnes [0]. Howeve, infomation shaing acoss the supply chain is not easily achievable. In geneal, thee is a conflict of incentives in supply chain systems; individuals manipulate infomation solely fo thei own benefit. An effective infomation system should be able to align incentives fom uses with conflicting objectives. Incentive alignment becomes an impotant thid dimension (peceded by softwae engineeing and use acceptance pespectives) fo any sophisticated infomation systems design and evolution [2]. In this pape, following the finance liteatue, we epesent etailes' demand uncetainty in two pats: systematic isk and idiosyncatic isk. Idiosyncatic isk shaing has attacted consideable attention in the supply chain field. Fo example, Risk pooling in inventoy and allocation decisions by etailes facing local stochastic demands was consideed in Ref. []. The impact of a seconday maket was examined by Ref. [23] whee etailes ( eselles in thei pape) can tade thei excess inventoies associated with independent demand isks among each othe. Since systematic isk cannot be educed by isk pooling, it was suggested to use maco economy elated maket instuments to hedge cetain aggegate economic isks [29]. This pape complements pevious wok by investigating the ole of infomation aggegation in dealing with systematic isk. Economic theoy has long ecognized that a popely designed maket efficiently collects and disseminates infomation [6]. New maket efficiency eseach suggests that infomation makets can effectively aggegate infomation and poduce advance foecasts of uncetain outcomes. An infomation maket is pimaily designed fo the pupose of eliciting a paticula piece of infomation. It is an emeging fom of financial makets in which the settling contacts ae futues contacts. It is also called ideas futues, event futues, Intenet-based vitual stock maket, etc. A suvey on eseach in infomation makets was given by Ref.[34]. It was futhe suggested that infomation maket-based foecast could be used fo effective decision suppot [4]. Empiical study also showed evidence that Intenet-based vitual stock maket foecasts outpefom altenative methods such as suveys and opinion polls [30]. It was poposed that oganizing Intenet-based inteactions to bette gathe pedictive infomation. We complement pevious wok by theoetically justifying the eliability of the maket pediction mechanism. Moeove, we integate the pediction function into the decision suppot and theoetically validate both maket pefomance and efficiency impovement in the supply chain application. Rational Expectations Equilibium (REE; see e.g. Refs. [26,4]) is the theoetical suppot fo the infomation evelation and aggegation in maket tansactions. The key to the REE concept is that the act of tading conveys infomation. The leaning in the maket is solved via an application of Bayesian ule [27]. This eseach shows how the maket can povide an incentive to effectively aggegate and eveal pivate infomation and how maket pice is a sufficient statistic fo pedicting the demand maco facto. The concept of REE has been applied to supply chains to study the infomational ole of an industial exchange (see Refs. [25,33]). Pevious wok viewed spot maket tading as an oppotunity to eadjust inventoy positions and shae infomation about demand uncetainty. In contast, we popose a futues maket tading a financial index whose futue payoff depends on ealization of the maco facto. In ou futues maket, demand uncetainty infomation can be evealed ealy and incopoated into the supply chain patnes' decision making. Ou maket has two othe impotant advantages. Fist, the tading infomation indices athe than the physical commodities can educe tansaction costs and so impove maket liquidity. Second, ou pediction maket allows outside tades to pesent thei elevant knowledge, extending the ange of infomation shaing. Ou modeling famewok is distinct fom all pevious wok in infomation economics. By dividing demand uncetainty into a systematic maco facto and an idiosyncatic local facto, we popose tading a etail index epesenting systematic isk in the supply chain in a maco pediction maket, which has stong esemblance to a financial maket. This idea is consistent with the findings that a fim's

4 Z. Guo et al. / Decision Suppot Systems 42 (2006) demand has a stong coelation with some financial index [3]. A numbe of details about the constuction of new makets and a vaiety of new poducts to deal with maco economic uncetainty fom a isk hedging pespective wee povided by Ref. [29]. In contast, we focus on the infomational ole of makets and extend its function to isk hedging in the supply chain infomation system. We study a supply chain in the famewok of newsvendo poblem. The taditional newsvendo model only takes into account a single decision make's ode quantity decision when facing exogenous demand distibution [8]. Stategic inteactions between a manufactue and a etaile wee studied by Ref. [2]. Thei model allowed the manufactue to change the wholesale pice and the uncetain demand distibution can be updated though foecasting. We extend the demand foecast to multiple etailes in a maket famewok. In tems of maket setup, ou model is compaable with the wok in Refs. [9] and [20] in which the infomation was evealed though the tading of a financial asset. As to the maket stuctue, we both assume that odes ae batched togethe to tansact at a single eget-fee, maket-cleaing pice. 3. The model Conside N geogaphically distibuted etailes who ode a homogeneous poduct fom a manufactue. Each etaile faces uncetain maket demand, composed of systematic isks that affect all the makets and idiosyncatic isks that affect only the local maket. We expess the etaile i's demand as D i =a i +b i θ+ε i, i=,, N, whee hf N l; s is a systematic maco economic facto and e i f Nð0; s e Þ is an i.i.d. idiosyncatic andom facto. We assume that a i and b i ae known constants that could diffe among diffeent etailes but these ae common knowledge in the supply chain. We assume that each etaile can pivately deive a foecast (o obtain a pivate signal) θ i fo the maco economic facto θ. Denote θ i=θ+δ i,wheed i fn 0; s d is also i.i.d., indicating the foecast eo. We also assume that τ δ >τ. This condition implies that the foecast is infomative because the foecast vaiance is less than the vaiance of the pio distibution of the maco facto. Suppose the pivate infomation fom individual etailes can be aggegated and define the aggegate signal as Using the ecipocal of pecision τ to denote vaiance is a standad technique in statistics and infomation economics. We use N to denote the nomal distibution when efeing to a distibution, and use Φ and ϕ to epesent the standad nomal cumulative distibution function and the density function, espectively. h u N P N h i h X N d i, which is a sufficient statistic N fo the full infomation eflected in a set of signal ealizations (θ,θ 2,, θ N). θ is the best pedicto compaed with any individual foecast since it has the same mean but the least vaiance. We call this case tuthful foecast shaing. Coesponding to this scenaio is the aggegate infomation supply chain stuctue (Stuctue A). This povides us with a full infomation benchmak solution to which we compae two othe supply chain stuctues: a fully decentalized one (Stuctue D) and a maco pediction maket-coodinated one (Stuctue M). The supply chain patnes' decision poblems ae the same unde all thee supply chain stuctues. The manufactue sets a wholesale pice to maximize the expected pofit based on the expected aggegate etaile ode quantity. Given the manufactue's wholesale pice, each etaile decides on an optimal ode quantity based on he demand distibution foecast. The only diffeence among the thee stuctues is the infomation incopoated in foecasting the demand distibution. In the tuthful foecast shaing scenaio (Stuctue A), the manufactue has access to all the infomation. In the fully decentalized scenaio (Stuctue D), the manufactue cannot obseve any of the etailes' foecasts. Fom a social welfae pespective, full infomation shaing will geneate highe expected supply chain pofits. Howeve, because highe individual etaile's pofit is not guaanteed, it is not clea if a etaile will want to tuthfully shae infomation. To achieve the goal of infomation shaing, we design a maco pediction maket-coodinated supply chain stuctue (Stuctue M) to tade a etail index. The etail index is an aggegate economic measue fo the maco facto θ. Fo simplicity, we assume that the etail index payoff is exactly θ, depending on the futue ealized value of the maco facto. The index maket pice is a public signal that the manufactue and etailes use to update thei beliefs about demand distibution. We call this maket-based foecast shaing. In this case, each etaile can gathe infomation fom a public signal and a pivate one. The etaile decides how much to ely on the public signal based on its pecision. We will compae the supply chain pefomance unde the two types of foecast shaing (Stuctues A and M). In addition, we chaacteize conditions unde which the maket-based foecast shaing will outpefom the full infomation benchmak thus additional benefits can be geneated in the supply chain. In the following, we pesent a maco pediction maket model and chaacteize its equilibium and popeties unde the REE famewok. We then use backwad induction to solve the supply chain decision making poblems unde Stuctues A, D, and M. Fist, we deive the individual etaile's ode decision in the supply chain as a best

5 948 Z. Guo et al. / Decision Suppot Systems 42 (2006) esponse function to the manufactue's wholesale pice. Then we solve the manufactue's optimal picing poblem accoding to the expected aggegate odes fom the etailes. We also chaacteize how the level of infomation shaing affects the supply chain patnes' decision making. 3.. The maco pediction maket The constuction of the maco pediction maket is an impotant maket mechanism design issue that evokes vaious discussions. Fo ou puposes, the tading asset is a futues contact based on a etail index θ, whose payoff depends on the futue likely outcome of maco economic events such as etail sales. Fo simplicity, we assume that one shae of the etail index will pay out monetay units θ. 2 The cuent pice of the futues contact is denoted by p. We assume that the maco pediction maket opeates like an open book call futues maket (see [2] fo a efeence). The maket opens at a pe-specified time, befoe which tades can update thei odes accoding to thei new infomation. Tades take place at an equilibium pice eflecting tades' eget-fee tading decisions. Fo the sake of liquidity, we assume that only the isky asset θ is taded at the initial unning of the maket. Aggegate maket infomation is evealed afte the settlement fo tansaction of θ. At this point, nobody has an infomational advantage to abitage the maket. The maket is complete and efficient unde the REE. Once the index pice is set, the index-based deivatives can be popely piced, and vaious index-based deivatives can be taded. Theefoe, ou maco pediction maket allows fo deivatives tading which can be used fo isk hedging pupose (we will discuss this in Section 5). In the following, we deive the maket equilibium whee only one isky asset, θ, is taded. The way of designing an effective picing mechanism is not unique. In this pape, we focus on a maket stuctue whee the maket make esponds to the aggegate net ode by taking an opposite position. We assume that the maket make doesn't have any pivate infomation. Thus, to pevent economic loss, the maket make sets the index pice as the expected value of the futue payoff given the cuent aggegate net odes in the maket. We assume that thee ae M isk neutal infomed tades in the maket. M=N+N 0,wheeN is the numbe of etailes and N 0 is the numbe of outside tades who have elevant infomation. We don't distinguish among infomed tades' foecast abilities, but this simplification will not affect ou 2 Note that we use θ to efe to eithe the tading asset (the etail index epesenting the maco facto) o its andom payoff intechangeably. Intepetation should take into account the context in which it is used. esults. We assume that each infomed tade i obtains a pivate signal θ i=θ+δ i,wheed i fn 0; sd, and places an ode π i fo i=,, M. 3 Thee ae also some uninfomed tades (also known as noise tades) whose aggegate net ode is andom and exogenously given, i.e. X fn 0; sx. Note that the noise tades' assumption incopoates all the unpedictable elements which may come fom agents' andom liquidation demands o iational behavios. The andom supply povided by noise tades is cucial in poviding the infomed tades with pope incentives to paticipate in the maket. Infomed etailes will ean positive expected pofits at the expense of the noise tades' expected losses in equilibium. The infomed tade i takes the pice infomation into account and stategically odes π i to maximize he expected etun fom the maco pediction maket. max E½ðh pðyþþp i j h i; pš ðiþ p i A REE equilibium is defined by two components. Fist, a tading stategy π i, fo i=,, M, that solves the above maximization poblem given picing function p (y). Second, a picing function p(y) such that given the tading stategy π i, i=,, M, we have " # pðyþ E hjy XM p i X ðiiþ whee y P M p i X is the aggegate demand. The following popositions chaacteize the maket equilibium popeties. Poposition. Fo any given numbe of infomed tades M, thee exists a unique linea REE in which ) An infomed tade i adopts a linea tading stategy π i =β 0 +β θ i+β 2 p,wheeβ 0, β,andβ 2 ae constants; P 2) The equilibium maket pice p A 0 A M h i X L Þ, whee A 0,A, and L ae constants. 4 Fom Poposition, we can see that the symmetic linea tading stategy is evealing since an infomed tade's pivate infomation θ i is indiectly tansfomed into the tade's maket tading volume π i based on any obseved maket pice p. In tun, obseving the index pice 3 Without confusion hee we use the same notation i to denote both etailes and outside infomed tades. 4 Conjectue and pove the existence of a linea REE is a standad technique in financial economics liteatue. Although stuctually simila esults ae obtained, we ae not simply epoducing it since ou infomational assumption is diffeent fom othe available esults. We admit that by focusing on the existence and uniqueness of a linea REE, we do not exclude the possibility of othe non-linea REEs, which is not a geneal inteest fo eseaches.

6 Z. Guo et al. / Decision Suppot Systems 42 (2006) P p is equivalent to obseving the signal M h i X L,whichis an indicato of the available aggegate maket infomation. It's woth mentioning that unde the notion of REE, tades stategically eveal and manipulate thei pivate infomation, although such behavio poves to be self-evealing. The existence of linea REE guaantees that p is also nomally distibuted. This fact allows us to chaacteize the supply chain patnes' belief updates using the Nomal Leaning Theoem (actually a standad Bayesian update fomula fo nomal distibution used in financial maket tading, see Ref. [27]). The uniqueness of the linea REE guaantees one-to-one mapping fom the dispesed maket signals to the aggegate maket pice. L, which often epesents maket liquidity in the REE liteatue, eflects the pecision of the infomation tansfomation. The lage the value of L, the less the influence of X. Theefoe, p is a moe pecise indicato of the useful signals. The accuacy of aggegate foecasts evealed by the maket pice can be inceased when the numbe of infomed tades inceases. We define pice infomativeness as PIu. The uncetainty on θ should be educed Va½hjpŠ based on a good pediction p. In othe wods, the less vaiation of θ conditional on p, the moe infomative the index pice p is. We use the ecipocal to captue this elationship in the definition. Poposition 2. Pice infomativeness PI inceases in M. lim MYl PI l and lim MYl p h. Pice pecision is a function of the numbe of infomed tades. Poposition 2 implies that when the numbe of infomed tades appoaches infinity, the infomation evealed in the maco pediction maket will be accuate enough so that the index pice conveges to the tue value of the maco facto. It's woth noting that one etaile's maco pediction maket ode will have negligible effect on the infomation contained in the index pice because the equilibium pice is detemined by the sum of infomed and uninfomed tades' signals. No individual's ode is pivotal. In the maco pediction maket, etailes can incease pofit by solely taking advantage of thei supeio pivate infomation. They do not pofit by manipulating thei tading odes hoping to mislead the manufactue in he supply chain picing decision. Theefoe, etailes' maco pediction maket decisions and physical supply chain ode decisions ae pefectly sepaable. In the following, we study the etaile's decision poblem unde diffeent supply chain stuctues The etaile's decision poblem Suppose all etailes chage a fixed etail pice in the consume maket. In this pape, we assume the etail pice is exogenously given and cannot be influenced by eithe the etaile o the manufactue. While stategic pice detemination eithe fom the manufactue o the etailes' point of view is an inteesting eseach topic, it is not ou focus hee. Intoducing too much heteogeneity such as diffeent pices in diffeent makets o too much flexibility such as picing decision in the consume maket will damatically complicate ou analysis without futhe incemental value in deiving ou main insights. In the following, we compae etailes' decision poblems unde thee supply chain stuctues A, D, and M. We use supescipt a, d and m to distinguish paametes in the thee supply chain stuctues A, D, and M. Given the wholesale pice s j,foj=a,d,m, the etaile chooses an ode quantity Q j i,foj=a,d,m, tomaximize the expected pofit accoding to the diffeent infomation at each setting. The etaile's decision poblem is (RA) (RD) and (RM). max Q a i z0 E½min½Qa i ; D iš s a Q a i j h Š ðraþ max E½min½Q d Q d i z0 i ; D iš s d Q d i j h iš max Q m i z0 E½min½Qm i ; D iš s m Q m i j h i ; pš ðrdþ ðrmþ whee min [Q j i,d i ], fo j=a,d,m, isetailei's sale in the consume maket. These standad newsvendo poblems have diffeent demand distibution functions epesenting the etaile's uncetainty about futue demand unde diffeent infomation and supply chain stuctues. The optimal ode quantity is offeed by the newsvendo solution; we only need to chaacteize the espective distibution functions. The demand cumulative distibution function is nomal by constuction in (RA) and (RD). In (RM), with the linea pice function we deived in Poposition, the etaile's updated belief, based on the pivate signal and public pice, will emain nomal. We can apply the Nomal Leaning Theoem 5 (see [27] fo a efeence) to deive the analytical expessions fo the distibution functions unde Stuctues A, D, and M. Lemma. Define s v M sd L 2 sx and h i u P jpi h j. Retaile i's optimal ode quantity is detemined by Q j i a i b i l j i q ffiffiffiffiu s j ; fo j a; d; m s j i 5 The Nomal Leaning Theoem gives the following ule fo belief updates: let the pio distibution hfn l;, and let θ =θ+ε, whee s ẽ fn 0 and independent of θ. Then, if θ i is a ealization of θ, the s e posteio distibution hj h i f s N l s e h i;. s s e s s e s s e

7 950 Z. Guo et al. / Decision Suppot Systems 42 (2006) whee l a s i Ns d s l Ns d Ns d s h ; l d i s l s d h i; s s d s s d l m sl s d h i i s s d ðm Þ 2 s v s s d ðm Þ 2 s v ðm Þs v s s d ðm Þ 2 h i X s v L s a b2 i ; i s Ns d s e s d i s m i b 2 i s s d ðm Þ 2 s v s e : b2 i s s d s e ; Lemma 2. lim MYl E X l m i lim NYl l a i, and lim MYl s m i lim NYl s a i. M Lemma 3. If N < ; 2ðM sd sþm qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi M 2sd2 ð Þ then s m i > s a i : ð5m 2 4Þð4M 2ÞM 2sd s s 2 M sd s Lemma 2 implies that when both the numbe of infomed maket paticipants and the numbe of etailes appoach infinity, the maco pediction maket yields a foecast as accuate as the aggegate foecast in tems of the mean and vaiance of the foecasted demand distibution. Lemma 3 gives a condition unde which the etaile's demand pediction is moe pecise using the maco pediction maket than aggegate infomation shaing. Loosely speaking, given N etailes, the moe pecise each etaile's infomation (epesented by τ δ /τ), the moe infomed maket paticipants ae needed befoe the maco pediction maket foecast will outpefom the aggegate foecast. In addition, given the pecision level of each etaile's infomation, the moe etailes in the supply chain, the moe infomed maket paticipants ae needed befoe the maco pediction maket foecast outpefoms the aggegate foecast. This condition is easy to be satisfied. Fo example, given τ=, τ δ =2, if N=4, then M=35; if N=6, then M=77; and if N=20, then M=89. But given τ=,τ δ =4,ifN=4, then M=59; if N=6, then M=37; and if N=20, then M=579. Lemma 3 has impotant implications in the supply chain infomation systems design. In the absence of good incentives, tuthful infomation shaing among etailes is poblematic. In contast, ou poposed maco pediction maket automatically aligns the etailes' incentives to eveal thei pivate infomation. Futhemoe, the maco maket-coodinated infomation shaing can absob useful infomation fom othe maket paticipants. It has the potential to achieve moe accuate foecast than what is available unde tuthful infomation shaing among etailes. Howeve, foecast accuacy alone cannot detemine etaile pofits because the manufactue can use the same infomation to make picing decisions The manufactue's decision poblem The manufactue wants to choose the most pofitable wholesale pice s j, fo j=a,d,m, based on the expected aggegate ode fom the etailes. We assume that thee is no fixed cost and that unit poduction cost is a constant, c. We also assume the manufactue will poduce an amount equal to he expected odes fom etailes. The manufactue's decision poblems unde the thee supply chain stuctues can be expessed as follows: " # max s a z0 ðsa cþ X i max s d z0ðs d cþ X i max s m z0 ðsm cþ X i Q a i j h " # E h i½q d i Š " # E h i½q m i jpš ðmaþ ðmdþ ðmmþ In the tuthful foecast shaing case (MA), the manufactue shaes the etailes' foecasts and so can pecisely update he belief on all the etailes' demand distibutions and infe etailes' ode quantities. A single wholesale pice is set. In (MD), the manufactue does not have any infomation about etailes' odes, yet also sets a single wholesale pice. She takes the expectations ove he pio beliefs about all the etailes' pivate signal distibutions. In the maket-coodinated foecast shaing case (MM) the manufactue sets a contingent wholesale pice based on he ational expectation of the aggegate ode quantity conditional on the cuent index pice p. Since the manufactue does not know each etaile's pivate foecast, she infes it fom the public obseved index pice p. The following poposition compaes the manufactue's picing decisions unde diffeent supply chain infomation stuctues.

8 Z. Guo et al. / Decision Suppot Systems 42 (2006) Poposition 3. The manufactue's wholesale pices unde supply chain stuctues A, D, and M have the following elations: (a) s a is stictly inceasing with θ. If h z a ðns d sþðt d T a Þbl ½ðNs d sþt d st a Š bns d T a ; then s a s d. Othewise, s a <s d. (b) s m is stictly inceasing with p. If pz a T d T m b T m l T d T, then s m s d. Othewise, s m <s d. m (c) If h z T m ða bpþðns d sþ T a ½aNs d sða blþš bns d T a ; then s a s m. Othewise, s a <s m. whee a P N a i; b P N b i; and T j fo j a; d; m: P N p ffiffiffi s j i Poposition 3 details the conditions elated to the manufactue's picing decision. Both 3(a) and 3(b) say that unde tuthful foecast shaing o maco pediction maket-coodinated foecast shaing, thee is a citical factile above which the manufactue will tend to set a highe wholesale pice in supply chain Stuctue A and M than in Stuctue D. Poposition 3(c) futhe chaacteizes the elationship between aggegate signal θ and index maket pice p: a low index maket pice is likely to induce a low s m, and vice vesa. The wholesale pice inceases in both tuthful foecast signal θ and the index pice p since highe values eflect an aggegate peception of a pospeous maco economy in the futue. The manufactue thus expects to eap moe benefits by chaging a high wholesale pice. In the same situation, etailes tend to place lage odes than what they would based on just thei own infomation. This seems to contadict the pactice of quantity discounts, i.e., the highe the ode quantity, the lowe the wholesale pice. The undelying diving foce of this esult is due to the manufactue's confidence that the oveall maket condition is pospeous and he bagaining powe in setting the maket pice. Although in such case the unit ode cost inceases, etailes can be compensated by the likely inceased demand that is accuately pedicted by the maco pediction maket. In contast, without the maket pediction, the etailes will ode accoding to thei decentalized solutions. They face the oppotunity cost of lost sales if demand suges. Theefoe, the etaile will still be able to ean a high total pofit even with a lowe unit pofit magin. On the contay, if the aggegate foecast signal θ o the index maket pice p is low, etailes will geneally believe that the maco economy will wosen and so ode less. The manufactue may set a low pice to encouage moe odes in such an economic downtun. This is also accuately pedicted by the maco pediction maket. In this case, etailes' misfotune will be essentially compensated by the lowe unit odeing pice. The index maket pice ceditably conveys etailes' pivate foecasts about maco economy uncetainty. Demand foecast shaing among the manufactue and etailes is achieved indiectly via the maco pediction maket. The manufactue can contol etailes' ode vaiance by adjusting the pice in a diection that is socially desiable fom the pespective of the supply chain. This adjustment is especially impotant in educing the bullwhip effect. 4. The value of foecast shaing We investigate two aspects of foecast shaing in this section: the impact on etailes' ode vaiance and the expected supply chain efficiency. 4.. The ode vaiance Retailes expeience demand uncetainty fom customes, but the manufactue expeiences it fom the etailes. The manufactue's decision making impoves as etaile aggegate ode vaiance dops. Unde tuthful foecast shaing, thee is no ode vaiance because the manufactue pecisely obseves etailes' demand foecast thus pefectly infes thei ode quantities. When foecast shaing is unavailable, the decentalized ode vaiances vay accoding to the diffeent etaile signals. The maco pediction maket significantly helps the manufactue impove he infeed ode accuacy. Poposition 4. Va(Q m i p)<va(q d i ); Va(Q m i p) deceases in M; lim MYl VaðQ m i jpþ VaðQa i j h Þ 0: Maco pediction maket coodination helps educe ode vaiance because etailes can moe accuately foecast the maco economy and thei own demand uncetainty. The manufactue can also make moe accuate infeences about the maco economy. The maco pediction maket induces less supply chain ode vaiance when moe useful infomation about the maco facto is incopoated. If the maco pediction maket is pecise enough, it can eplicate tuthful foecast shaing as ode vaiance disappeas. This has impotant implications fo the bullwhip effect. This well-known infomational poblem is often epesented by the obseved inceasing ode vaiances fom downsteam patnes in the supply chain. The liteatue has identified potential souces of the bullwhip effect but has not offeed an effective solution to educe the effect by popely managing conflicting incentives among supply chain patnes. Ou maco pediction maket-coodinated supply chain stuctue can alleviate this effect. Note that by imposing a

9 952 Z. Guo et al. / Decision Suppot Systems 42 (2006) coelation acoss the consume makets, potentially thee is anothe dimension of the bullwhip effect the ationing game (see Ref. [22]). We don't deal with this poblem in this pape since we do not assume capacity constaints of the manufactue The expected supply chain pofit A decentalized supply chain solution is geneally suboptimal to an integated, fist-best solution. A fist-best solution, which is usually impossible, equies the manufactue to set the wholesale pice equal to the maginal poduction cost. A numbe of aticles on supply chain coodination discuss the use of moe complex non-linea picing contacts o eal options contacts to achieve the fist-best solution [7]. Howeve, we ae most inteested in detemining the best supply chain stuctue unde the simple pice-only contact, the most common contact fomat in the supply chain pactice. We ae inteested in evaluating the impact of infomation shaing on oveall supply chain efficiency. The total expected supply chain pofit is detemined by the sum of all supply chain patnes' expected pofits. Unde the supply chain stuctues A, D, and M, the expected supply chain pofit can be expessed as EP j XN ð cþe XN whee C i;j ðq j EΠ j R EΠ j M " # Q j i i Þ Z tj pffiffiffiffi s d i l E XN C i;j ðq j i Þ; : UðtÞdt; j a; d; m; and t j U s j Poposition 5. If min(s d, s m, s a ) /2 >c, then the expected supply chain pofit satisfies EΠ a >EΠ d, EΠ m >EΠ d, and lim MYl EP m lim NYl EP a. Poposition 5 shows the value of infomation shaing in the supply chain. Unde the condition min(s d, s m, s a ) /2>c the expected supply chain pofits unde Stuctue A and M ae geate than pofits unde Stuctue D. This condition is not had to be satisfied. Since the manufactue is the Stackelbeg leade in the game, it is not a supise that she will chage a wholesale pice at least half of the etail pice leaving etailes a smalle pofit magin. Most industy poducts have etail pices less than two times the wholesale pice. Compaed to the decentalized supply chain, intoducing the maco pediction maket will impove supply chain efficiency by inceasing the total pie to be divided, and the manufactue's expected pofit will incease since she has all the bagaining powe. Retailes, howeve, may not benefit since the maket condition affects the manufactue's picing decision as well as the division of total supply chain suplus. Retailes' expected positive pofits as a etun of thei pivate knowledge will attact them to tade in the maco pediction maket egadless of the maket condition. Total supply chain efficiency depends on maket liquidity and infomation tanspaency, i.e., how much useful infomation about the maco facto can be foecasted and evealed to the supply chain patnes. In geneal, whethe the maco pediction maket-coodinated supply chain efficiency will outpefom the aggegate supply chain efficiency depends on the tadeoff between the level of infomation asymmety and pediction pecision. On the one hand, the aggegate supply chain has no infomation asymmety and will tend to outpefom the maket pediction. On the othe hand, the maket pediction can incopoate useful outside infomation and so be moe pecise. When both the numbe of infomed tades in the maket and the numbe of etailes appoach infinity, the supply chain stuctues M and A yield the same expected pofits. The taditional supply chain liteatue consides the incentive and coodination issues within a closed system. Ou wok sheds new light on this aea because of the additional benefits geneated outside the supply chain system. Since the maket is an open system, one etaile's non-paticipation decision will not compomise the infomation aggegation. But etailes who believe the maket efficiently pedicts the maco facto will tend to incopoate the maket pice infomation into thei ode decisions. Ou poposed famewok aligns etailes' incentives to shae infomation and exploes the value of useful infomation fom othe souces to incease oveall supply chain efficiency. 5. Extensions and discussions We conside extensions of ou model in this section. Fist, we investigate how etailes' changing isk pefeences influence thei tading stategies. Second, we chaacteize the etaile's Paeto impoving maco pediction maket tading stategy. Thid, we extend the index tading to the index-based deivative tading to demonstate that ou poposed maco pediction maket stuctue can suppot supply chain isk management in copoate pactice. Finally, we discuss the impact of the maco pediction maket constuction on moal hazad poblems. 5.. The isk-avese etaile Retailes' supply chain ode stategy and maco pediction maket tading stategy ae pefectly sepaable

10 Z. Guo et al. / Decision Suppot Systems 42 (2006) when they ae isk-neutal. Thei incentives to tade come fom thei supeio knowledge about futue uncetainty of the economy. No abitage oppotunities exist unde the REE famewok. In equilibium, no contingent claim mattes to the etailes because they expect to pay the aveage value of the contingent claim based on the common maket belief. Consequently, etailes cannot make exta money by tading moe complex financial contacts. Since isk-neutal etailes only cae about the mean effect of thei pofit, thei stategy is simply to tade the index. Retailes pefe to puchase the contingent claim as a type of insuance when they ae isk-avese. A key component in ou model is the etaile's piecewiselinea payoff function, and a kink occus when the demand equals ode quantity. This type of payoff function can be hedged via witing coveed call options on the etail index [7]. Given the etaile's ode quantity Q i, tading the contingent claim is a Paeto impoving stategy because the etaile's expected oveall pofit is the same in both the maco pediction maket and the commodity maket. Howeve, options can cancel off some uncetainty thus educing the pofit vaiance. The contingent claim can be expessed as: f i min½q i ; a i b i hšmax½ Q i ; a i b i hš a i b i h max½ Q i a i b i h; 0Š a i b i h ða i b i h Q i Þ a i b i h b i h Q i a i b i The contingent claim can be geneated by boowing a i shaes of iskless bonds and shot selling b i shaes of the index and long the same shaes of call option with stike pice Ki Q i a i b i. Poposition 6. A isk-avese etaile's Paeto impoving maco pediction maket stategy when odeing Q i in the supply chain is to boow a i shaes of iskless bonds and shot b i shaes of the index θ and long b i shaes of call option with stike pice K i Q i a i. b i This insuance can deal with the supply chain opeation and maco pediction maket uncetainty by smoothing out the total payoff fom both. The futue index pice is positively coelated with the etaile's consume maket demand, so the etaile may face a loss in he consume maket if it goes down. Howeve, the etaile can ean a positive pofit in the maco pediction maket by shot selling. If the futue index pice goes up, the etaile will not have enough inventoy to cove demand and will lose in both the maco pediction maket and the consume maket. Howeve, this loss can be coveed by the call options at hand. In any case, the etaile's isk exposue can be effectively hedged. In the newsvendo model it is clea that isk-avese etailes will ode less than the expected valuemaximizing quantity []. It was shown that, unde vey geneal conditions, the isk-avese etaile's optimal odeing quantity inceases with hedging [3]. Theefoe, oppotunities fo options tading help optimize etailes' inventoy decisions The impact of the maco pediction maket Ou maco pediction maket-coodinated supply chain famewok can bing isk management into copoate business pactice. In the supply chain liteatue, isk shaing and tansfe ae obtained by bilateal contact commitments. Examples of widely used contact foms include eode/buy back contacts [28], nonlinea picing/quantity discount policy [32], and linea tansfe payments [6]. It was shown in [3] that all these contacts can be classified as eal options contacts. Howeve, the question of whethe the options contacts can be popely piced emains unansweed. Followingon wok [5] poposed picing eal options in a bilateal contact using Aow Debeu secuities. We extend the picing of options contact in a maket setting with multiple maket playes. Ou poposed options contacts ae based on a isky secuity (the etail index) with continuous payoffs. This is moe ealistic than using Aow Debeu secuities. Options contacts can povide etailes insuance to deal with opeational isk. Howeve, insuance may cause a moal hazad poblem since the etailes may not take socially conscious actions when they feel economically secue. Moal hazad poblems have been well-undestood in economics [5] but ae geneally ovelooked in the supply chain liteatue. Fo example, when the maket is uncetain, a manufactue may povide etailes with a put option allowing them to sell back unsold poducts at a pespecified salvage value (the stike pice). The etaile may not put much effot into selling poducts if the pomotion cost is highe than its oppotunity loss. All bilateal eal options contacts suffe this poblem. One possible solution is to wite contacts based on maco factos that coelate with the etaile's hedging needs but ae not unde the etaile's contol. Tading indices o index-based deivatives can solve these poblems since they ae simply contingent claims witten on the maco facto (the index). The etailes still incu esidual isk in the maketplace. In addition, options tading can solve the maket paticipation poblem since thee might be expets who ae

11 954 Z. Guo et al. / Decision Suppot Systems 42 (2006) unwilling to tade in the maco pediction maket fo fea of financial losses. Buying o selling options with pefeed stike pices can affod these expets a measue of potection. 6. Conclusion The Intenet has facilitated eal-time infomation access acoss oganizations, making it possible to integate that infomation into decision models. While eseach on supply chain infomation systems design has focused on technological efficiency, such as XML-based wokflow and database integation, ou innovation is to build a maco pediction maket into oganizations' evolutionay infomation systems design to encouage infomation shaing and aid supply chain decision making. We show that the maco pediction maket can be used to educe the bullwhip effect in the supply chain. In addition, the maket allows anyone with infomation to tade. Moe complete infomation makes the supply chain moe efficient. We thus povide impotant insights in designing maket-based infomation systems in guiding the stuctue of supply chain inteactions. We examine the impact of intoducing a new type of maket a maco pediction maket on supply chain infomation shaing and decision making. We also make unique contibutions to the emeging fields of pediction maket and maco hedging maket eseach. Pediction makets ae indiectly influenced by financial makets. The significance of these makets is still limited to pedicting elections, spot tades, and othe utility stocks and no clea esouce allocation issue has yet been studied. In contast to existing eseach, we look at a concete application in the class of supply chain poblems to validate the significance of pediction makets fo decision suppot in business pactice. In the maco hedging maket liteatue, the key to hedging isk is shaing isk. Supply chain patnes tend to act stategically in poviding infomation due to payoff asymmety thus peventing effective isk shaing. The stategy of ceating maco indices to tade instead of tading physical poducts has a numbe of advantages. Fist, the tading asset is boad enough to attact sufficient liquidity in the maket. The liquidity poblem has been identified as an impotant eason fo the failue of many B2B makets. Many industial poducts ae not suitable fo maket tading because of a lack of homogeneity. In addition, contacts specifying diffeent quality, delivey times and othe featues ae usually negotiated between buye and selle, and so geneate high tansaction costs. Index-elated financial contacts, in contast, ae essentially homogeneous poducts that can be taded with sufficient liquidity. Riskpooling can be ealized without costly negotiation and contact enfocement between paties. Theefoe, the ceation of the maco pediction maket makes possible the shaing of economic isks. The maco index-elated financial contacts ae also geneal enough to educe the moal hazad poblems aising fom bilateal insuance contacts. Cetain limitations apply to this pape. We assume the etail pices ae exogenously given and ae the same fo all etailes. Endogenizing the picing decision is an inteesting eseach question that can be studied in the futue. Allowing diffeent etailes to chage diffeent etail pices sounds a moe ealistic elaxation. In the case of heteogeneous etail pices the manufactue can be expected to also set heteogeneous wholesale pices. Futue wok could extend this eseach to cases with multiple manufactues and etailes. The constuction of the index should also be studied. Diffeent indices could be designed to epesent a vaiety of poducts o tangible/ intangible assets in the supply chain netwok. The indices could be futhe distinguished to eflect egional envionmental economic isks. Moe innovative and complex financial instuments, such as index-based deivatives, can also be intoduced fo isk hedging puposes. In addition, futue eseaches can extend ou findings to othe business applications. Acknowledgment This pape was pesented at seveal seminas including those at the Univesity of Texas at Austin, Univesity of Albeta, National Univesity of Singapoe, City Univesity of New Yok Bauch College, and Univesity of Mayland, Baltimoe County. We appeciate valuable feedback fom semina paticipants. We especially thank Anant Balakishnan and Steve Gilbet fo thei helpful comments and suggestions. The authos take esponsibility fo all eos. Appendix A Sketch of Poof of Poposition. We look fo a linea equilibium of the fom 8 < l m i a 0 a h i a 2p p i b 0 b l m i b 2 p ðþ : pðyþ k 0 k y FOC w..t. π i fom Eq. (I) togethe with the equality in Eq. (II) we have the following b 0 0; b k ; b 2 k ð2þ

12 Z. Guo et al. / Decision Suppot Systems 42 (2006) p k 0 Ma 0 a X M M Ma 2 M Ma 2 k X ua 0 A i M Ma 2 X M h i h i X! L ð3þ So L is a uniquely detemined constant fo given M. Define k 0 =β 0 +β 2 p, and k =β, then π i p=k 0 +k θ i. So at the equilibium pice an agent's ode stategy is infomation evealing. Poof of Poposition 2. whee L a. So A 0 k 0 Ma 0 and A, k M Ma 2 M Ma 2 which ae constants fo given M. To ensue that Eq. (I) is a well-behaved concave function of π i,socw..t.π i fom Eq. (I) yields λ >0. To solve the REE, we only need to solve fo constants α 0, α, α 2, λ 0,andλ. Fom Eq. (3) and Nomal Leaning Theoem, h p E hj P i M h i X sl L s M 2 Ms p ðm Ma 2 Þp ðk 0 Ma 0 Þ, s p s M 2 s p a. whee s p M sd L 2 sx Reaanging tems and compaing with p(y)=λ 0 + λ y yields a ðs M 2 s p ÞMs p ðm Ma 2 Þ a sl Ms p ðk 0 Ma 0 Þ a ð4þ ð5þ Belief update by the Nomal Leaning Theoem yields " l m i ue hj h i; h i X # sl s d h i L s s d ðm Þ 2 s v s s d ðm Þ 2 s v ðm Þs v h i s s d ðm Þ 2 X! ; s v L. whee s v M s d L 2 s X Substituting Eq. (3) into μ m i yields a 0 a sl ðm Þðk 0 Ma 0 Þs v a ½s s d ðm Þ 2 s v Š s d ðm Þs v a s s d ðm Þ 2 s v a 2 ðm ÞðM Ma 2Þs v a ½s s d ðm Þ 2 s v Š ð6þ ð7þ ð8þ Since we have 5 unknowns α 0, α, α 2, λ 0, and L in the system of Eqs. (4) (8). So it's solvable. We suppess the expessions fo all othe paametes but L: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi q u t ð5m 2 4Þs 2 ð4m 2ÞM 2 ss d M 2 s 2 d Mðs s d Þ L s d 2ðs Ms d ÞMðM Þs X ð9þ PIu Va½hjpŠ Va hj PM s M 2 L 2 s X s d ML 2 s X s d s M 2 s p h i X L Substituting L 2 fom Eq. (9) and conside N yields lim PI lim s MYl MYl Ms d 2ðsMs d ÞðM Þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi l " XM lim p E hj h i X # MYl L sl s M 2 Ms p s p s M 2 s p ð5m 2 4Þs 2 ð4m 2ÞM 2 ss d M 2 s 2 Mðss d d Þ X M h i X! h L This completes the poof. Poof of Lemma. Since we fomulate the etaile's poblem as the taditional newsvendo poblem, the newsvendo solutions give us Q j i Fi; j s j, j=a,d, m, whee F i,j ( ) denote the foecasted demand distibution by etaile i unde scenaio j. Nomalizing the expession we wite it as Q j i a i b i l j i qffiffiffiffi U s j qffiffiffiffi s j i whee μ j i and s j i ae deived as follows: Recall that h X N h i. It's easy to veify that θ is N nomally distibuted, h fn l; s Nsd. Based on the Nomal Leaning Theoem, the belief update yields l a i s ue½hj h Š Ns d s l Ns d Ns d s h l d i ue½hj h iš s l s d h i s s d s s d " l m i ue hj h i; h i X # sl s d h i L s s d ðm Þ 2 s v s s d ðm Þ 2 s v ðm Þs v s s d ðm Þ 2 h i X! ; s v L

13 956 Z. Guo et al. / Decision Suppot Systems 42 (2006) whee s v M s d L 2 s X Va½D i j h Š b 2 i Va½hj h Š s e Va½D i j h iš b 2 i Va½hj h iš s e Va½D i j h i; pš b 2 i Va½hj h i; pš s e b 2 i s s d ðm Þ 2 u s v s e s m i b2 i s Ns d s e u s a i b2 i s s d s e u s d i This concludes the poof. Poof of Lemma 2 and 3. Results ae diectly obtained by Lemma and Eq. (9). Poof of Poposition 3. Q a i j h s a i b i Ns d s l Ns d Ns d s h pffiffiffiffi U sa ð0þ s a i E h i½q d i Ša i b i E h i½l d i Š pffiffiffiffi U sd s d i a i b i l pffiffiffiffi U sd ðþ E h i½q m i jpš a i b i E h i½l m i jpš pffiffiffiffiffi U sm a s m i b i p i pffiffiffiffiffi U sm s m i s d i ð2þ Note that μ m i =E[θ θ i,p], and E θ i[μ m i p]=e θ i[e[θ θ i,p]]= E[θ p]=p. Substituting Eqs. (0) (2) into (MA), (MD), (MM) and taking FOC w..t. s j,foj=a, d, m, we have U sa T a s a b Ns d s l Ns d Ns d s h sa c /U ð3þ sa U U sd sm T d ða blþ sd c /U sd ð4þ T m ða bpþ sm c /U sm ð5þ whee a P N a i; b P N b i; and T j P N p ffiffi s j i fo j=a,m,d. Let x 0 = c/, x j =s j /, t j =Φ (x j ), fo j=a,d,m. Using the equality Φ ( x j )= Φ (x j ) and, simplifying the expession, we deive T a s a b Ns d s l Ns d Ns d s h Uðt aþ x 0 /ðt a Þ t a T d ða blþ Uðt dþ x 0 /ðt d Þ T m ða bpþ Uðt mþ x 0 /ðt m Þ Let gðtþ UðtÞ x0 /ðtþ 2 tðuðtþ x 0Þ t d t m ð6þ ð7þ ð8þ t. Then g V ðtþ /ðtþ/ðtþ ðuðtþ x 0Þ/ V ðtþ / 2 ðtþ, whee the second equality follows by /ðtþ the fact that / (t)= t/(t). Since Φ(t) is stictly inceasing and /(t) is a stictly deceasing function of t when t 0, g (t)>0 fo t 0. We also know that t j is stictly inceasing with s j. Compaing Eqs. (6), (7) and (8), we deive all the esults fo (a) (c). Poof of Poposition 4. b2 i s2 d VaðQ d i Þb2 i Vaðld i Þ ðs s d Þ 2 Vaðh iþ b2 i s2 d ðs s d Þ 2 d s b2 i s d s d sðs s d Þ VaðQ m i jpþ b2 i Vaðlm i " jpþ # 2 b 2 s d ðm Þs p i s s d ðm Þ 2 s p s s d Compaing equations yields Va(Q d i ) Va(Q m i p) with equality holds when M=. So Va(Q d i )>Va(Q m i p) when M 2. b 2 i s3 dðs sdþ Note that VaðQ m i jpþ, s½ððm ÞL 2 s X s dþðs s dþðm Þ 2 L 2 s X s dš 2 substituting Eq. (9) we can see it is a deceasing function of M. lim MYl VaðQ m i Þ0. Clealy Va(Q i a θ )=0 since full infomation shaing is imposed. Poof of Poposition 5. The expected supply chain pofits unde Stuctue D, A, and M ae " # Z EP d ð cþe XN Q d i XN td p ffiffiffiffi UðtÞdt s d i l ð cþ a bl T d t d Z td T d UðtÞdt l

14 Z. Guo et al. / Decision Suppot Systems 42 (2006) ( " # Z ) EP m E p ð cþe XN Q m i jp XN tm p ffiffiffiffiffi UðtÞdt s m i l ð cþ a bl Z T m Et tm m E p T m UðtÞdt ( " # Z ) EP a E h ð cþe XN Q a i j h XN ta p ffiffiffiffi UðtÞdt s a i l ð cþ a bl Z T a Et ta a E h T a UðtÞdt Theefoe, E½P m P d t d Šð cþ T d Et m T m Z td Z tm T d UðtÞdt E p l T m UðtÞdt l t d > ð cþ T d Et Z m tm T m E p T m UðtÞdt t d t d > ð cþ T d Et m T m 2T m ð Et m t d Þ > 2 c td T d Et m T m whee the next to the last inequality follows fom the condition minðs m ; s d Þ > so that t m U sm 2 < 0 and t d U sd < 0. The last inequality equies that 2 > c. By Eqs. (7) and (8), T d gðt dþa bl a bep T m Egðt mþ > T m gðet mþ. The inequality follows by the stict convexity of g(t) when t 0. Note that g(0) 0. Fo k T d T m <, we have gðt dþ > T d T m gðet mþ > g T d T m Et m. So t d z T d T m Et m. Theefoe, E[Π m Π d ]>0. That is, EΠ m >Π d. E½P a P d t d Šð cþ T d Et a T a Z td Z ta T d UðtÞdt E h l T a UðtÞdt l t d > ð cþ T d Et Z a ta T a E h T a UðtÞdt t d t d > ð cþ T d Et a T a 2T a ð Et a t d Þ > 2 c td T d Et a T a By Eqs. (6) and (7), T d gðt dþa bl T a Egðt aþ > T a gðetaþ. Since τ a i > τ d i, T a >T d. Fo k T d <, we have T a gðt d Þ > T d T a gðet aþ > g T d T a Et a. Theefoe, EΠ a >EΠ d. By Lemma 2, lim MYl E X l m i lim NYl l a i ; and lim MYl s m i lim NYl s a i. The same foecasts yield the same expected supply chain pofits. l l Poof of Poposition 6. Unde REE, tading options neithe inceases etailes' maco pediction maket pofit no affects thei ode quantity; the expected mean of etailes' pofit is the same. Howeve, by smoothing off the uncetain payoff function, the vaiance of wealth is deceased. It is a Paeto impoving stategy fo isk avese etailes. Refeences [] R. Anupindi, Y. Bassok, E. Zemel, A geneal famewok fo the study of decentalized distibution systems, Manufactuing and Sevice Opeations Management 3 (4) (200) [2] S. Ba, J. Stallaet, A.B. Whinston, Reseach commentay: intoducing a thid dimension in infomation systems design - the case fo incentive alignment, Infomation Systems Reseach 2 (3) (200) [3] D. Banes-Schuste, Y. Bassok, R. Anupindi, Coodination and flexibility in supply contacts with options, Manufactuing and Sevice Opeations Management 4 (3) (2002) [4] J.E. Beg, T.A. Rietz, Pediction makets as decision suppot systems, Infomation Systems Fonties 5 () (2003) [5] A. Bunetas, P. Ritchken, Option picing with downwad-sloping demand cuves: the case of supply chain options, Management Science 5 (4) (2005) [6] G.P. Cachon, Competitive supply chain inventoy management, in: S. Tayu, R. Ganeshan, M. Magazine (Eds.), Quantitative Models fo Supply Chain Management, Spinge, 998. [7] G.P. Cachon, Supply chain coodination with contacts, in: S.C. Gaves, A.G. De Kok (Eds.), Handbooks in Opeations Reseach and Management Science: Supply Chain Management: Design, Coodination and Opeation, Elsevie Publishing Company, 2003, Ch. 6. [8] G.P. Cachon, M. Fishe, Supply chain inventoy management and the value of shaed infomation, Management Science 46 (8) (2000) [9] F. Chen, Infomation shaing and supply chain coodination, in: S. C. Gaves, A.G. De Kok (Eds.), Handbooks in Opeations Reseach and Management Science: Supply Chain Management: Design, Coodination and Opeation, Elsevie Publishing Company, 2003, Ch. 7. [0] F. Chen, Z. Dezne, J.K. Ryan, D. Simchi-Levi, Quantifying the bullwhip effect in a simple supply chain: the impact of foecasting, lead times and infomation, Management Science 46 (3) (2000) [] L. Eeckhoudt, C. Gollie, H. Schlesinge, The isk-avese (and pudent) newsboy, Management Science 4 (5) (995) [2] M. Fan, S. Sinivasan, J. Stallaet, A.B. Whinston, Electonic Commece and the Revolution in Financial Makets, Thomson Leaning, [3] V. Gau, S. Seshadi, Hedging inventoy isk though maket instuments, Manufactuing and Sevice Opeations Management 7 (2) (2005) [4] S.J. Gossman, On the efficiency of competitive stock makets when tades have divese infomation, Jounal of Finance 3 (976) [5] S.J. Gossman, O.D. Hat, An analysis of the pincipal-agent poblem, Econometica 5 (983) [6] F. Hayek, The use of knowledge in society, Ameican Economic Review 35 (4) (945)

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