confidentiality and information sharing in supply chain coordination

MANAGEMENT SCIENCEVol. 54, No. 8, August 2008, pp. 1467–1481issn 0025-1909 �eissn 1526-5501 �08 �5408 �1467

informs ®

doi 10.1287/mnsc.1070.0851©2008 INFORMS

Confidentiality and Information Sharing inSupply Chain Coordination

Lode LiYale School of Management, New Haven, Connecticut 06520, and Cheung Kong Graduate School of Business,

100738 Beijing, China, [email protected]

Hongtao ZhangDepartment of Information and Systems Management, The Hong Kong University

of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, [email protected]

We consider information sharing in a decentralized supply chain where one manufacturer supplies to mul-tiple retailers competing in price. Each retailer has some private information about the uncertain demand

function which he may choose to disclose to the manufacturer. The manufacturer then sets a wholesale pricebased on the information received. The information exchange is said to be confidential if the manufacturerkeeps the received information to herself, or nonconfidential if she discloses the information to some or allother retailers. Without confidentiality, information sharing is not possible because it benefits the manufacturerbut hurts the retailers. With confidentiality, all parties have incentive to engage in information sharing if retailcompetition is intense. Under confidentiality, the retailers infer the shared information from the wholesale priceand this gives rise to a signaling effect that makes the manufacturer’s demand more price elastic, resulting in alower equilibrium wholesale price and a higher supply chain profit. When all retailers share their informationconfidentially, they will truthfully report the information and the supply chain profit will achieve its maximumin equilibrium.

Key words : information sharing; confidentiality; signaling; supply chain coordination; truth tellingHistory : Accepted by Gérard P. Cachon, operations and supply chain management; received November 21,2005. This paper was with the authors 1 year and 4 months for 3 revisions. Published online in Articles inAdvance May 19, 2008.

1. IntroductionThis paper is concerned with vertical informationsharing in a supply chain consisting of one manu-facturer and two or more competing retailers. Eachretailer has some private information about marketdemand and may choose to reveal it to the manufac-turer. We refer to information sharing here as beingvertical because it is between a retailer and the man-ufacturer, in contrast to situations where informationsharing is horizontal, i.e., between oligopolists in thesame level of a supply chain.The above setting is similar to that of our previ-

ous work (Li 2002, Zhang 2002), which addressedthe incentives for sharing information between retail-ers and the manufacturer. One impetus of this ear-lier work was the notion of “information leakage,”whereby demand information transmitted from a cer-tain retailer to the manufacturer is leaked to, or in-ferred by, other retailers through the wholesale price,which is a function of the shared information. How-ever, both papers had implicitly assumed that theeffect of information leakage through the wholesaleprice would be the same as if the information weredirectly given to all retailers. By doing so, we ignoredthe signaling effect. The signaling effect occurs when

a change in the wholesale price changes the retailers’inference about the shared information.In a supply chain environment, information trans-

mitted from a retailer to the manufacturer can be“leaked” to other retailers in two distinct ways:direct and indirect. The manufacturer may reveal theinformation by means of direct communication orthe information may be inferred through the manu-facturer’s action such as setting a wholesale price.A nondisclosure legal agreement may prevent directdisclosure but often allows the recipient of the infor-mation to use it in business decisions1 (such as whole-sale pricing) and therefore is not able to preventrevealing the information indirectly. Although thetwo manners of leakage may reveal the same infor-mation to the retailers, their economic consequencesare very different.In essence, confidentiality in vertical information

sharing creates a situation of information asymme-try: the manufacturer has aggregate information, andthe retailers have dispersed information but take the

1 Many confidentiality agreements do limit the use of the exchangedinformation but rarely disallow the recipient to use the informationin dealing with the original information owner.

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Li and Zhang: Confidentiality and Information Sharing in Supply Chain Coordination1468 Management Science 54(8), pp. 1467–1481, © 2008 INFORMS

wholesale price as a signal of the aggregate infor-mation. It is through signaling that confidentialitymanifests its economic consequences. We study con-fidentiality by investigating the signaling effect andits impact on the manufacturer, the retailers, and thesupply chain as a whole. The setting of our previ-ous work, which in effect assumes direct leakage, istreated as a special case with low confidentiality.We refer to a retailer who chooses to reveal his

demand signal as a participating retailer and describevarious degrees of confidentiality through three dis-closure scenarios:

Scenario 1 (S1). Disclosure to the manufacturer andall retailers. A participating retailer transmits his sig-nal to a depository that is accessible to the manufac-turer and all retailers.

Scenario 2 (S2). Disclosure to the manufacturer andall participating retailers. A participating retailertransmits his signal to a depository that is accessibleto the manufacturer and all participating retailers, butnot to any of the nonparticipating retailers.

Scenario 3 (S3). Disclosure to the manufactureronly. A participating retailer transmits his signal to adepository that is accessible to the manufacturer, butnot to any of the retailers.2

In S1, information sharing is least confidential. Thisis a case of public disclosure where the manufacturerand all retailers, participating or not, have access tothe shared information. This is essentially what drivesthe results in Li (2002) and Zhang (2002). The whole-sale price in this case is simply a marginal cost to theretailers.In S3, information sharing is the most confidential

and the manufacturer ends up with more informationthan each of the participating retailers. Because retail-ers do not observe the shared information directly,they will infer it from the wholesale price which isobservable. Now the wholesale price is not only amarginal cost to retailers but also a source of demandinformation. Hence the signaling effect occurs.Scenario 2 has an intermediate degree of confiden-

tiality. This is a case of exclusionary disclosure wherethe manufacturer and only participating retailers havedirect access to the shared information. The wholesaleprice signals demand information to nonparticipatingretailers.In general, we can define the degree of confidential-

ity in the sense of nondisclosure as follows. A scenariohas a higher degree of confidentiality if there is asmaller set of retailers who, besides the manufacturer,also have direct access to the shared information. This

2 Although we assume at the outset that each participating retailerwill report his demand signal truthfully, we shall come back to theissue of incentive compatibility under this scenario and show thatthis assumption can be relaxed.

set is empty in S3 and includes all retailers in S1. Sce-nario 2 is a special yet interesting case of intermediateconfidentiality between the two extremes.We use a three-stage game to analyze each sce-

nario. In the first stage, and before any private infor-mation is available, each retailer commits to sharinginformation or to keeping it private, and the manu-facturer commits to receiving the information.3 In thesecond stage, after retailers have received their privateinformation and the signals have been sent, the man-ufacturer sets a wholesale price. In the third stage,retailers set retail prices competitively in a Bayesianfashion. In most sectors, retailers compete in pricein the short run, and therefore our assumption ofBertrand retailers seems reasonable.The game solution then allows us to examine the

incentives for information sharing in each scenario,i.e., for a fixed degree of confidentiality. Informationsharing will occur only if it benefits both the informa-tion owner (retailer) and the recipient (manufacturer).In S1, information sharing benefits the manufacturerbut harms the retailers. In S3, all parties have incen-tive to engage in information sharing if retail compe-tition is intense.We then compare the three scenarios to examine

the impact of confidentiality. For any given set of par-ticipating retailers, higher confidentiality results in alower equilibrium wholesale price. With confidential-ity, a higher wholesale price signals a more favor-able market condition and the retailers respond bysetting higher retail prices, which will reduce retailsales. Thus, the signaling effect makes the manufac-turer’s demand more price elastic and prompts herto set a lower wholesale price. A lower wholesaleprice alleviates double marginalization and benefitsthe supply chain as a whole. When all retailers sharetheir information confidentially, we show that thedecentralized decisions achieve the centralized opti-mal solution. We further demonstrate that truthfulreporting by all retailers is a Nash equilibrium wheninformation sharing is confidential, that is, no retailerhas incentive to misreport his demand signal if allother retailers truthfully report theirs. In other words,confidentiality induces truth telling and coordinatesthe supply chain.Lee and Whang (2000) point out that lack of con-

fidentiality is one of the greatest obstacles to supplychain information sharing. In outlining the precau-tions that data-sharing partners should keep in mind,Lee and Whang (2000) claim that confidentialityshould be a top priority. In fact, confidentiality must

3 Although public information disclosure could be a unilateralaction of the information owner, confidential information exchangerequires bilateral agreements, i.e., the recipient’s incentive for infor-mation should also be considered.

Li and Zhang: Confidentiality and Information Sharing in Supply Chain CoordinationManagement Science 54(8), pp. 1467–1481, © 2008 INFORMS 1469

often be agreed upon at the early stage of forminga supply chain partnership. For example, prior toimplementing a VMI (vendor managed inventory)system in which the supplier will receive demandinformation (point of sales data) from a retailer, thelatter often requires that the data be kept confidentialto other retailers who may or may not be suppliedby the same vendor. Besides using the demand infor-mation for production and inventory planning, thesupplier will conceivably also use the information inher future wholesale pricing decision or negotiation.A critical question is: In what ways does the confiden-tiality agreement impact the supply chain members?Confidentiality is crucial to the implementation

of CPFR (collaborative planning, forecasting, andreplenishment). CPFR is a nine-step guideline sup-ported and published by the Voluntary InterindustryCommerce Solutions Association (http://www.vics.org/) with the goal of improving the performance ofall companies throughout the supply chain. Confiden-tiality is part of the front-end agreement in the veryfirst step of the CPFR process, where “participatingcompanies identify executive sponsors, agree to con-fidentiality and dispute resolution processes, developa scorecard to track key supply chain metrics rel-ative to success criteria, and establish any financialincentives or penalties” (http://www.techexchange.com/thelibrary/introduction_to_cpfr.html).On the other hand, there is a lack of academic

research on the issue of confidentiality. Accord-ing to neoclassical economic theory, the informationasymmetry caused by confidentiality often makes acompetitive market less efficient. Economists havetended to see information asymmetry as undesir-able and undervalue the possible damages causedby unwanted disclosures of information. However,Swire (2003) calls for more attention from researchers,economists in particular, to the importance of privacyprotection and confidentiality. This paper sheds lighton the impact of confidentiality in the context of asupply chain. We demonstrate that confidentiality hasvalue to the information owners (retailers) and makesthe supply chain more efficient as a whole.In our model, the ultimate determinant of the sup-

ply chain performance is retail prices, which arethe result of interplay of three factors: retail com-petition, double marginalization (wholesale pricing),and information asymmetry (confidential informa-tion sharing). Retail competition lowers retail prices,double marginalization raises them, and informationasymmetry lowers them through lowering the whole-sale price. Although each factor is often perceived toharm the supply chain, their interplay may balanceout one another’s effect and even result in overalloptimality. The wholesale price arrangement is some-times criticized as being “too simplistic” yet, coupled

with confidentiality, it may be all that is needed tocoordinate the supply chain partners.The plan for this article is as follows. Section 2

reviews the related literature. Section 3 specifies themodel and its information structure. Section 4 solvesthe three-stage game for each scenario, comparesthe firms’ payoffs across the scenarios, and demon-strates the impact of confidentiality. Section 4 dis-cusses extensions and further research.

2. Literature ReviewThe survey by Chen (2003) points out three areasconcerning information sharing in supply chains. Thefirst takes the perspective of a central planner whoacquires information to improve the supply chain’sperformance, assuming no competition among sup-ply chain members. The second regards supply chainswhere not all players have the same information.Information asymmetry prompts members of the sup-ply chain to engage in screening and signaling. Theresearch in this part mostly assumes a channel struc-ture with one supplier and one retailer. The third area,to which this paper belongs, investigates informationsharing in a channel structure that has one supplierand many competing retailers.Of the supply chain literature that deals with in-

formation asymmetry, the stream of work concern-ing asymmetric demand information is more closelyrelated to this paper. That includes Porteus andWhang (1999), Cachon and Lariviere (2001), andOzer and Wei (2006). Porteus and Whang (1999)develop a model where the buyer faces one of twodemand distributions but the supplier only knowsthe probability of either distribution. They derive andcharacterize the optimal contractual form from thesupplier’s perspective. Cachon and Lariviere (2001)prescribe a mechanism for credible sharing of demandinformation between a supplier and a downstreamfirm. Their mechanism coordinates the channel witha capacity reservation contract under forced compli-ance. Ozer and Wei (2006) shows that a combinationof buyback agreement and advance purchase contractcoordinates the channel even when the parties act ontheir own will.Our work differs from the above in several impor-

tant ways. First, the information allocation in theaforementioned work is fixed, i.e., the more informedparty stays more informed and the less informedstays less informed. In our model, the allocationof information in a supply chain may change viainformation-sharing activities and the informationasymmetry may get inverted: each retailer is initiallymore informed than the manufacturer but the latterbecomes more informed after receiving informationfrom all retailers.


Second, the above papers consider a one-supplier,one-retailer supply chain where confidentiality is notan issue. Information asymmetry is usually seen asa deficiency that hinders the supply chain coordi-nation and needs to be overcome using remedialmechanisms. In our multiretailer supply chain model,the information asymmetry arising from confidentialinformation sharing is a device that promotes supplychain coordination.Third, the above papers all use a newsvendor

model and focus on inventory or capacity decisionswhile we focus on pricing decisions. Our model bearsresemblance to the case of competing retailers consid-ered in Cachon and Lariviere (2005) in that the rev-enue earned by retailer i depends on a single actionby each retailer. Their model, however, assumed sym-metric information.Lastly, while in our model the wholesale price cred-

ibly signals the information that the manufacturer hasreceived from the retailers, a separate issue is whetherthe retailers would have disclosed the true demandinformation to the manufacturer in the first place.Under the assumptions of our model, we show thatthe retailers have no incentive to distort their infor-mation if information exchange is confidential.Many supply chain transactions are governed by

simple contracts defined only by a per-unit wholesaleprice (Lariviere and Porteus 2001). This is arguablythe simplest form of interaction but usually failsto achieve channel coordination because of dou-ble marginalization. For remedies, more sophisti-cated contracts were proposed, e.g., revenue sharing(Cachon and Lariviere 2005), buy back (Pasternack1985), quantity flexibility (Tsay 1999), and sales rebate(Taylor 2002). Bernstein and Federgruen (2005) studya price-discount contract that coordinates a supplychain with competing newsvendors who choose bothprice and order quantity. We demonstrate in this paperthat confidentiality may provide another remedy forcountering double marginalization and enable thesimple wholesale price to coordinate the supply chain.Other (wholesale) price-setting mechanisms may

also perform very well. Mendelson and Tunca (2007)consider a supply chain with one supplier and manyCournot-competing manufacturers and show that aspot-market mechanism improves the supply chainefficiency while aggregating different pieces of infor-mation dispersed among competing participants. Ourpaper differs from theirs in the following three areas:First, their model allows supply chain participantsto have two trading opportunities. The first roundof trading, with no private information, occurs in astandard monopoly market in which the supplier setsthe wholesale price, and the second round of trad-ing, with private information, occurs in a spot mar-ket (in the sense of Kyle 1989), where firms move

simultaneously to submit their demand or supplycurves and a third party sets the price to clearthe market. On the other hand, our model assumesthat supply chain participants have only one trad-ing opportunity in a standard monopoly market,where the upstream firm sets the wholesale price firstand then downstream Bertrand retailers react accord-ingly. Second, unlike Mendelson and Tunca (2007),we allow the supply chain participants to share theirprivate information prior to trading. Hence, there isinformation asymmetry and strategic signaling in themonopolistic wholesale price-setting process wheninformation exchanges are confidential. Third, thespot-market outcome approaches the first-best solu-tion as the number of downstream firms goes toinfinity; our paper shows that a standard monopolywholesale price-setting mechanism coupled with con-fidentiality in information sharing is sufficient toobtain the exact first-best solution for any given num-ber of retailers.There is a literature in industrial organization

that concerns horizontal information sharing. Researchalong this line includes Novshek and Sonnenschein(1982), Clarke (1983), Vives (1984), Gal-Or (1985,1986), Li (1985), Shapiro (1986), and Raith (1996), etc.In a stereotypical model with demand uncertainty,an oligopoly of firms produce either differentiatedproducts or a homogeneous product, facing a lin-ear demand function with a common but a prioriunknown intercept. Before deciding its selling priceor output quantity, each individual firm privatelyobserves a noisy signal of the true value of the inter-cept. Information-sharing decisions are usually mod-eled as a two-stage game. Each firm decides whetherto report its own signal to an information club beforeobserving it and then, after signals are observedand reported, firms compete in a Bayesian fashionwith incomplete information. It is well-known that allfirms will reveal their private demand information ifthe competition is in price but none will do so if thecompetition is in quantity. In our model, the directinformation exchange is vertical, between a manufac-turer and oligopolistic retailers, and there is indirectstrategic information transmission when the whole-sale price signals aggregate demand information.4 Wealso address the issue of truthful reporting, which issimply assumed in the literature.There is quite a large literature in legal studies

that addresses various issues related to confidential-ity, ranging from privacy of personal financial dataand health records and drafting of confidentiality

4 Signaling also arises in horizontal information sharing. For exam-ple, Mailath (1989) uses a two-period, n-firm model and considershow each firm’s pricing decision in the first period signals its unitcost to its competitors, thereby influencing their beliefs and hencetheir decisions in the second period.


agreements to confidentiality in settlements and arbi-tration. However, only a small part of that liter-ature employs quantitative modeling to assess theimpact of confidentiality. Yang (1996) and Daughetyand Reinganum (1999, 2002) address the impact ofconfidential settlement on sequential bargaining by adefendant facing a series of plaintiffs. Daughety andReinganum (2007) consider the effects of confidential-ity on prices and profits using a signaling model oftwo competing firms and two customers where theprice signals a firm’s product quality.Finally, confidentiality is not the same as transac-

tion security. Clifton et al. (2008) propose using cryp-tographic techniques to let trucking companies sharedelivery information without revealing the identityof the individual firm. It is not inconceivable thatthe same techniques could be used to share demandinformation. Security requires not revealing an indi-vidual retailer’s identity; confidentiality, as addressedin this paper, requires not revealing the retailer’sdemand information.

3. The ModelIn a two-echelon supply chain of one manufacturerand n retailers, the manufacturer provides a commonbase product at a wholesale price of P per unit, andthe retailers further process it to make similar but non-identical products through different processes of cus-tomization. For convenience, we refer to the manu-facturer as she and a retailer as he. All firms are riskneutral. We use N = �1�2� � � � �n� to denote the set ofretailers and refer to retailer i’s product as product i.The retailers are symmetric and compete in price in theend market for which the demand function is given by

qi = a+ �− �1+ �pi +

n− 1∑j �=i

pj� (1)

where qi is the realized demand for product i, pi isthe retail price set by retailer i, and � is a randomvariable representing demand uncertainty, E�� = 0and Var�� = �2 > 0. The products are assumed tobe imperfect substitutes and so > 0. A larger indicates a higher degree of substitution and greaterintensity of retail competition. Note that the totaldemand

∑ni=1 qi = na+ n� −∑n

i=1 pi does not dependon directly. This is intended to keep the marketpotential unchanged for different values of . Theretailers incur a constant and identical marginal cost,on top of the wholesale price P , for customizationand retailing, which we normalize to zero withoutloss of generality. The manufacturer incurs a constantmarginal production cost c. All model parameters arecommon knowledge.

3.1. Information StructureEach retailer i observes a private signal Yi about �and may choose to share it with other firms. The

joint probability distribution of ��Y1� � � � �Yn�, whichis common knowledge, satisfies the following condi-tions: (C1) E�Yi � ��= � for all i; (C2) E�� Y1� � � � �Yn�=∑

i∈N �iYi, where �i are constants; and (C3) Y1� � � � �Yn

are i.i.d. conditional on �. The expected conditionalprecision of the signal is 1/E�Var�Yi � ��. An extremecase is perfect demand signal with Var�Yi � �� = 0 sothat Yi = �. We exclude this uninteresting case fromconsideration and assume E�Var�Yi � �� > 0. Defines � E�Var�Yi � ��/�2. The reciprocal 1/s is an indicatorof signal accuracy—it is proportional to the samplesize if each Yi is a sample mean from independentsampling.Let K denote the set of retailers who commit to

reveal their information, with k ≡ �K� ≤ n, and letYK � �Yl�l∈K be the set of disclosed signals. ByLemma 1 of Li (1985), conditions (C1)–(C3) imply that

E�� YK�=1

k+ s

∑l∈K

Yl�

It can be shown that

E�Yj �YK�= E�� YK� for j K�

and

E�Yj � Yi�YK� = E�� Yi�YK�

= �k+ s�E�� YK�+Yi

k+ 1+ sfor i� j K� j �= i�

The information structure implied by condi-tions (C1)–(C3) is general enough to include a varietyof prior-posterior distribution pairs such as normal-normal, gamma-Poisson, and beta-binomial. There isan issue about the nonnegativity of the uncertainintercept of the demand function, a+ �, and whethera firm’s optimization problem results in an interior-point solution. For the last two of the aforementionedconjugate pairs, it is easy to find a condition for theequilibrium solutions to be interior points for almostall realizations of the uncertainty, i.e., a− c+ � ≥ 0almost surely. One way to state such a condition isa− c+ � ≥ 0, where � is the lower limit of the sup-port of �’s probability distribution. However, for thenormal-normal case, which is unbounded on the neg-ative side, no such condition exists. On the otherhand, from a practical standpoint, if � (the standarddeviation of �) is small relative to a− c, the equilib-rium outcome will be an interior-point solution formost realizations of demand uncertainty and signals(i.e., with a probability close to one).5

5 For a small � , our solution will violate the boundary constraintonly with a small probability. Because expected values are lit-tle affected by events of small probability, we obtain a good


Table 1 Information Available to Firms

Participating NonparticipatingScenario Manufacturer retailer i ∈ K retailer i K

S1 YK YK and P �YK � Yi , YK , and P �YK �

S2 YK YK and P �YK � Yi and P �YK �

S3 YK Yi and P �YK � Yi and P �YK �

3.2. Three-Stage GameWe study a three-stage game for which the sequenceof events and decisions are as follows:1. Each retailer commits to either disclose his infor-

mation or not. After that, retailer i observes a signal Yi

and, if he is a participating retailer, Yi is made knownto the manufacturer and other retailers according tothe specified disclosure scenario.2. The manufacturer sets a wholesale price P .3. Upon learning P , each retailer chooses a retail

price pi. Finally, demand is realized and production iscompleted to meet the demand.We assume that in each stage, each player observes

all other players’ decisions in previous stages. In par-ticular, K is known to all retailers after the first stagebut before the firms make their price decisions, i.e.,all retailers know who among them is sharing infor-mation with the manufacturer although they may notobserve the transmitted signals. We believe this is areasonable assumption because, in practice, informa-tion sharing is a long-term decision and the existenceof an information link (say, for transmitting point-of-sales data) will, in time, become known to other firms.Table 1 summarizes the information available to the

manufacturer or a retailer at the time of decision mak-ing in different disclosure scenarios.In S3, although shared information YK is directly

available only to the manufacturer, the retailers caninfer it (or part of it) from the wholesale price, whichis a function of YK . Similarly, in S2, the shared infor-mation is directly available only to the manufacturerand participating retailers, but the nonparticipatingretailers can infer it from the wholesale price.

4. Analysis of the GameWe solve the game by backward deduction for eachof the three scenarios. We find it easier to work withthe retail margin, wi � pi − P , rather than pi directly.Using pi = P +wi, we rewrite the demand function forretailer i as

qi = a− P + �− �1+ �wi +

n− 1∑j �=i

wj�

approximation by allowing such violations. Various models inaccounting, economics, and operations management literature uselinear demand and normal distribution without even mentioningthe boundary constraint. We follow this precedent of sidesteppingthe issue and assume that the equilibrium for the firms’ pric-ing decisions is always an interior-point solution to the first-ordercondition.

and express the total demand as D = ∑ni=1 qi = na −

nP +n�−∑ni=1wi.

4.1. Scenario 1—Disclosure to All FirmsIn the third stage, knowing the disclosed informa-tion YK � �Yl�l∈K and the wholesale price P , retailer ichooses wi to maximize

wiE�qi � Yi�YK� = wi

(a− P +E�� Yi�YK�− �1+ �wi

+

n− 1∑j �=iE�wj � Yi�YK�

)�

The first-order condition (FOC) for a Nash equilib-rium is

�1+ �w∗i = a− P +E�� Yi�YK�− �1+ �w∗

i

+

n− 1∑j �=iE�w∗

j � Yi�YK�� (2)

The unique solution to the FOC is given by

w∗i �P �=

12+

�a− P +E�� YK�� for i ∈K� (3)

w∗i �P �=

12+

�a− P + �1−Bk�E�� YK�+BkYi�

for i K� (4)

where

Bk =�2+ ��n− 1�

2�1+ ��n− 1��k+ 1+ s�− �n− k− 1� �

It is straightforward to verify that (3) and (4) sat-isfy the FOC. Proof of the uniqueness is in OnlineAppendix EC.1 (provided in the e-companion).6 Notethat the retail margins w∗

i �P � are increasing in E�� YK�, i.e., retailers set higher margins if the market con-dition is more favorable. Also note that Bk is strictlydecreasing in k.In the second stage, the expected demand for the

manufacturer, conditional on YK , is

E�D∗ �YK� = na−nP +nE�� YK�−n∑i=1E�w∗

i �P � �YK�

= n�1+ �

2+ �a− P +E�� YK��

To maximize �P − c�E�D∗ � YK�, the manufacturer setsthe wholesale price to

P ∗ = P �1��YK�� c+!�1��a− c+E�� YK�� (5)

6 An electronic companion to this paper is available as part ofthe online version that can be found at http://mansci.journal.informs.org/.


where the superscript denotes the scenario and thecoefficient for the markup (above the marginal cost) is

!�1� = 12 �

As a special case, if no information is shared (k= 0),we have YK =� and P �1� = �a+ c�/2.In Online Appendix EC.2, we derive the firms’

expected profits given the equilibrium wholesaleprice and retail margins in (3), (4), and (5):

"�1�M �k�= $M

[�a− c�2+

(k

k+ s

)�2

]for 0≤ k≤ n�

"�1�R �k�= $R

[�a− c�2+

(k

k+ s

)�2

]for k > 0�

"�1�R �k�= $R

[�a− c�2+

(k

k+ s

)�2

]+Ck�

2 for k < n�

where "�1�R �k� is the payoff of a participating retailer,

"�1�R �k� is the payoff of a nonparticipating retailer, and

$M = n�1+ �

4�2+ �� $R =

1+

4�2+ �2� and

Ck =�1+ ��Bk�

2�k+ 1+ s�s

�2+ �2�k+ s��

(6)

The payoff of each firm in S1 can be expressed asthe sum of two terms. The �a− c�2 term is indepen-dent of information sharing and is, in fact, the solu-tion for the case of deterministic demand. The �2 termis a measure of informational gain depending on theinformation available to each firm. The payoff to anonparticipating retailer, "�1�

R �k�, has an extra �2 term(with Ck), which is the gain due to his undisclosedprivate information.

Proposition 1. (a) "�1�M �k + 1� > "

�1�M �k� for k =

0� � � � �n − 1, the manufacturer is always better off asmore retailers disclose their information; (b) "�1�

R �k+ 1� < "�1�R �k� for k= 0� � � � �n− 1, each retailer is always worse

off by disclosing his information.

The proof is in Online Appendix EC.2. Thus, noretailer has an incentive to publicly disclose his infor-mation. Similar conclusions are obtained in Li (2002)for Cournot retail competition with a homogeneousproduct and in Zhang (2002) for duopoly retailerscompeting in price or quantity. Their models implic-itly assume public disclosure as in S1. Our develop-ment in this subsection, although similar to theirs, isneeded for comparison with S2 and S3 to assess theimpact of confidentiality.

4.2. Scenario 3—Disclosure to Manufacturer OnlyIn this scenario, K is the set of retailers who transmittheir signals to the manufacturer. The manufactureruses YK = �Yl�l∈K in setting a wholesale price P .

Although a retailer cannot observe YK (or all of it)directly, he will try to infer it from P . How heinfers information from P depends on his beliefas to the functional form of P�YK�. We restrict thesearch for equilibria to the subspace where P�YK� isa strictly increasing function of E�� YK�; namely, P isrelated to YK only through a monotone relationshipwith E�� YK�. Specifically, we assume that in equilib-rium each retailer conjectures that the wholesale pric-ing policy takes the form of

P = f �E�� YK�� that is, E�� YK�= f −1�P��

for some strictly increasing and differentiable functionf �·�. The function f �·� is then found through the stepsdescribed below.In equilibrium, each retailer takes E�� YK� to be

equal to f −1�P� and acts on his conjecture (or belief)by substituting f −1�P� for E�� YK� in his first-ordercondition (2), which we solve to obtain the following(see the appendix for details): if exactly one retailershares information, K = �l�, the retail margins are

w∗l �P �=

12+

�a− P + �1−A1�f−1�P�+A1E�� Yl��

w∗i �P �=

12+

�a−P+�1−B1�f−1�P�+B1Yi� for i �= l�

where A1 = �2+ + B1�/�2�1+ ��* if two or moreretailers share information, �K� = k≥ 2, the retail mar-gins are

w∗i �P �=

12+

�a− P + f −1�P�� for i ∈K� (7)

w∗i �P �=

12+

�a− P + �1−Bk�f−1�P�+BkYi�

for i K� (8)

From these, we derive E�D � YK� =∑n

i=1 E�q∗i �P � � YK�,

the conditional expected demand for the manufac-turer, in terms of E�� YK�, P , and f −1�P�. The whole-sale price P = f �E�� YK�� is an equilibrium if andonly if

f �E�� YK��= argmaxP

�P − c�E�D �YK��

That is, the retailers’ conjecture must be fulfilled inequilibrium: as long as all retailers believe that thewholesale price will be set to f �� YK�� such that theyuse f −1�P� for E�� YK� in their retail margin deci-sions, it is optimal for the manufacturer to set thewholesale price to f �E�� YK��. This condition yieldsa differential equation from which we obtain f �·�.In the appendix, we show that the equilibrium

wholesale price is

P ∗ = P �3��YK�� c+!�3�k �a− c+E�� YK�� (9)


where the coefficient for the markup (above themarginal cost) is

!�3�0 = 1

2� !

�3�1 = n + �n− 1�B1+A1

2n�1+ �� and

!�3�k = n + �n− k�Bk

2n�1+ �for k > 1�

Although the equilibrium in (9) is not the unique one,it gives the manufacturer, the Stackelberg leader ofthe game, higher profit than all other equilibria. Thus,the manufacturer will set the wholesale price to P ∗. Ifno information is shared (k= 0), we have YK =� andP �3� = P �1� = �a+ c�/2.Because Bk is strictly decreasing in k, so is !

�3�k .

It then follows that !�3�k < !�1� for k ≥ 1. From (5)

and (9), we see that P �3��YK� < P�1��YK�, i.e., con-fidentiality lowers the equilibrium wholesale price.The wholesale price in S1 is simply a unit cost tothe retailers, but in S3 it plays an additional role ofsignaling demand information. A higher P signalsto retailers a more favorable market condition andinduces them to set higher retail margins. Therefore,the signaling effect of an increase in wholesale priceresults in higher retail prices and, consequently, lowerretail quantities. This implies that the demand for themanufacturer becomes more elastic to the wholesaleprice. It is this added price elasticity for the manufac-turer, when information is shared confidentially, thatprompts her to set a lower P .As !�3�

k is decreasing in k, so is E�P ∗�= c+!�3�k �a−c�,

the expected equilibrium wholesale price. Because aparticipating retailer bases his retail pricing decisionsolely on what the wholesale price signals, as in (7),more participating retailers implies a stronger sig-naling effect and greater demand elasticity for themanufacturer.

Proposition 2. The manufacturer lowers the wholesaleprice on average when receiving information confidentiallyfrom more retailers.

In the appendix, we derive the firms’ ex ante pay-offs in the first stage:

"�3�M �k�= $

�3�M �k�

[�a− c�2+

(k

k+ s

)�2

]for 0≤ k≤ n�

"�3�R �k�= $

�3�R �k�

[�a− c�2+

(k

k+ s

)�2

]for k > 0�

"�3�R �k�=$

�3�R �k�

[�a−c�2+

(k

k+s

)�2

]+Ck�

2 for k<n�

where $�3�M �k� = 4!�3�

k �1 − !�3�k �$M and $

�3�R �k� =

4�1−!�3�k �2$R with $M and $R given in (6).

The payoff of each firm is again expressed as thesum of two terms. However, the �a− c�2 term is now

dependent on information sharing (and is no longerthe solution for the case of deterministic demand).The second �2 term (with Ck) in "�3�

R �k� is the same asin S1, thus the gain from private information to a non-participating retailer is not affected by confidentiality.Because !

�3�k is below 1

2 and is strictly decreasing,we have

Lemma 1. $�3�M �k� is strictly decreasing and $�3�R �k� is

strictly increasing in k.

As more retailers transmit their information to themanufacturer, the �a − c�2 term becomes smaller forthe manufacturer but greater for all retailers. In partic-ular, if � is small, the �a− c�2 term dominates and themanufacturer would become worse off by receivinginformation. In this case she would have no incentiveto engage in confidential information sharing.Now we address the question whether individ-

ual firms have incentives to voluntarily engage inconfidential information sharing. Let us first con-sider the manufacturer’s incentive. Recall the param-eter in the demand function (1) which indicates theintensity of retail competition. It is easy to show that"

�3�M �k+1� >"

�3�M �k� if is large; i.e., the manufacturer

becomes better off with information from more retail-ers if retail competition is intense. Intuitively, underintense retail competition, retail margins are close tozero and the wholesale price is nearly equal to theretail price, thus the manufacturer essentially “runs”the supply chain all by herself and so benefits frommore information.We next consider the retailers’ incentive. We can

show that "�3�R �n� − "�3�

R �n − 1� > 0, i.e., each retailerwants to disclose his information confidentially if allother retailers do so. Combining this with the lastparagraph, we see that if retail competition is intense,all retailers sharing information confidentially withthe manufacturer is an equilibrium. However, it is notthe only equilibrium. Online Appendix EC.3 showsthat if is large, "�3�

R �k + 1� < "�3�R �k� for k < n − 1.

Therefore, if retail competition is intense, no informa-tion sharing is an equilibrium and k retailers sharinginformation is not an equilibrium for any 1≤ k≤ n−1.Given that the only possible equilibria involve all

sharing or none sharing, the question is which equi-librium is more likely to occur. Online Appendix EC.3shows that "�3�

R �n� > "�3�R �0� if both and s are large.

A large s means less accurate demand informationand greater benefit of information aggregation.

Proposition 3. When retail competition is intense andthe demand information is less accurate, each retailer andthe manufacturer have incentives to engage in confidentialinformation sharing, and complete information sharing isa Pareto-dominant equilibrium outcome.


When is large but s is small, the retailers willbe worse off by sharing information, "�3�

R �n� < "�3�R �0�,

while the manufacturer will be better off, "�3�M �n� >

"�3�M �0�. One possible arrangement is for the manufac-

turer to pay the retailers for their information. In thefirst stage the manufacturer offers a payment $ to eachretailer for sharing his information. The payment $has to be large enough for retailers to be better off,$ > "�3�

R �0�−"�3�R �n�, and the total payment n$ has to

be small enough for the manufacturer to be better off,n$ < "

�3�M �n�− "�3�

M �0�. For a $ satisfying both condi-tions to exist, we need "

�3�M �n�− "�3�

M �0� > n� "�3�R �0�−

"�3�R �n��. We show in Online Appendix EC.3 that this

inequality holds if is large.

Proposition 4. When retail competition is intense,each retailer and the manufacturer have incentives to engagein confidential information sharing through a payment $,satisfying

"�3�R �0�−"

�3�R �n� < $<

["

�3�M �n�− "�3�

M �0�]/n�

and with such $, complete information sharing is a Pareto-dominant equilibrium outcome.

We have assumed so far that the manufactureroffers the same wholesale price to all retailers. A ques-tion is whether the manufacturer has an incentive tooffer differentiated wholesale prices to the retailers.Suppose that the manufacturer can offer a differentwholesale price to each retailer and that confiden-tiality agreements prevent disclosure of the shareddemand information. Furthermore, each retailer doesnot observe the wholesale prices other than hisown when making the retail price decision. We canshow under these conditions that when all retailersshare information, offering the same wholesale priceP �3��YN � to all retailers is an equilibrium outcome.

4.3. Scenario 2—Disclosure to Manufacturer andParticipating Retailers

Nonparticipating retailers conjecture that

P ∗ = f �E�� YK�� that is, E�� YK�= f −1�P��

In equilibrium, each nonparticipating retailer takesE�� YK� to be equal to f −1�P� and acts on his conjec-ture (or belief) by substituting f −1�P� for E�� YK� inhis first-order condition (2), which we solve to obtainthe following:

w∗i �P �=

12+

�a− P + �1−Ak�f−1�P�+AkE�� YK��

for i ∈K�

w∗i �P �=

12+

�a−P+�1−Bk�f−1�P�+BkYi� for iK�

where Ak = ��2 + ��n − 1� + �n − k�Bk�/�2�1 + � ·�n−1�− �k−1��. Note that An = 1 and 0<Ak < 1 for

1≤ k < n. We can show that the equilibrium wholesaleprice is

P ∗ = P �2��YK�� c+!�2�k �a− c+E�� YK�� (10)

where the coefficient for the markup (above the mar-ginal cost) is

!�2�0 = 1

2� and !

�2�k = n +�n−k�Bk+kAk

2n�1+ �for k≥1�

Note that !�2�1 = !

�3�1 and !

�2�n = !�1�—S2 is the same as

S3 if k= 1 and as S1 if k= n.The firms’ ex ante payoffs are

"�2�M �k�= $

�2�M �k�

[�a− c�2+

(k

k+ s

)�2

]for 0≤ k≤ n�

"�2�R �k�= $

�2�R �k�

[�a− c�2+

(k

k+ s

)�2

]for k > 0�

"�2�R �k�=$

�2�R �k�

[�a−c�2+

(k

k+s

)�2

]+Ck�

2 for k<n�

where$�2�M �k�= 4!�2�

k �1−!�2�k �$M

and$�2�R �k�= 4�1−!

�2�k �2$R

with $M and $R given in (6).

4.4. Confidentiality, Supply Chain Coordination,and Incentive Compatibility

Confidentiality in information sharing implies thatonly the designated parties and no one else willreceive the information directly. Scenario 3 representsa situation in which the manufacturer and each par-ticipating retailer keep the shared information secretto other retailers. We say that information is sharedconfidentially in this case, although each retailermay infer participating retailers’ aggregate informa-tion from the wholesale price. In contrast, S1 can bethought of as a situation where someone (the manu-facturer or the retailer himself) leaks each participat-ing retailer’s information to all retailers. Scenario 2has an intermediate degree of confidentiality and canbe viewed as a situation where someone leaks eachparticipating retailer’s information to all participatingretailers.To compare the three scenarios, we start with

!�1� > !�2�k > !

�3�k for 1< k< n�

!�1� > !�2�1 = !

�3�1 and !�1� = !

�2�n > !

�3�n �

(11)

From these, we can show that $M ≥ $�2�M �k� ≥ $

�3�M �k�

and $R ≤ $�2�R �k�≤ $

�3�R �k�, and then that

"�1�M �k�≥"

�2�M �k�≥"

�3�M �k�� "

�1�R �k�≤"

�2�R �k�≤"

�3�R �k��

and "�1�R �k�≤ "�2�

R �k�≤ "�3�R �k��

where the inequalities are strict for 1< k< n.


Proposition 5. For any given set of participatingretailers, a higher degree of confidentiality harms the man-ufacturer and benefits all retailers.

Therefore, the manufacturer has an incentive tobreak confidentiality while each participating retailerhas an incentive to keep it. To ensure confidentiality,a retailer can sign a binding confidentiality agreementwith the manufacturer. From Propositions 3 and 4,all parties have incentive to sign such an agreementwhen retail competition is intense.We now examine the effect of confidentiality on

the profitability of the supply chain. Suppose YK isknown to the manufacturer and all retailers as in S1.Denote by "�P�YK� the expected total supply chainprofit conditional on YK for any given wholesaleprice P . Let P I �YK�= argmaxP "�P�YK� and "I�YK�="�P I �YK��YK�. Online Appendix EC.4 shows that

P I �YK�= c+!I�a− c+E�� YK��

where !I = /�2�1+ ��. Note that !I < !�3�k for k < n

and !I = !�3�n . It then follows from (11) that

P �1��YK� > P�2��YK�= P �3��YK� > P I �YK� for �K� = 1�

P �1��YK�>P�2��YK�>P�3��YK�>P I �YK� for 1< �K�<n�

P �1��YN �= P �2��YN � > P�3��YN �= P I �YN ��

Denote by "�m��YK� the expected total equilibriumsupply chain profit conditional on the disclosed infor-mation YK in scenario m, m= 1�2�3. The equilibriumsupply chain profit can be obtained by substitutingthe equilibrium wholesale price P �m��YK� into the sup-ply chain profit function:

"�m��YK�="�P�m��YK��YK� for m= 1�2�3�

This obviously holds for S1. It also holds for S2 andS3 because the retailers’ expectations are fulfilled inequilibrium and the disclosed information is correctlyanticipated, E�� YK�= f −1�P ∗�. We then have that

"�1��YK� <"�2��YK�="�3��YK� <"I�YK� for �K� = 1�

"�1��YK�<"�2��YK�<"�3��YK�<"I�YK� for 1< �K�<n�

"�1��YN �="�2��YN � <"�3��YN �="I�YN ��

Summarizing the above, we have

Proposition 6. For any given set of participatingretailers, a higher degree of confidentiality results in a lowerequilibrium wholesale price and a higher expected supplychain profit for (almost) every realization of the disclosedinformation YK .

Therefore, confidential information sharing and theconcomitant information asymmetry improve supplychain efficiency. Most strikingly, when all retailersshare their information with the manufacturer and

the shared information is kept strictly confidential,P �3��YN � = P I �YN �, the confidentiality perfectly alignsthe manufacturer’s self-interest with that of the entiresupply chain.Actually, an even stronger result holds. Suppose a

central planner owns the supply chain, has all thedemand information YN , and wants to choose retailprices pi to maximize the supply chain’s expectedprofit conditional on YN :n∑i=1�pi − c�E�qi �YN �

=n∑i=1�pi − c�

{a+E�� YN �− �1+ �pi +

n− 1∑j �=i

pj

}�

Because pi = wi + P , this is equivalent to choosingmargins wi for any given wholesale price to maximizen∑i=1�wi+P−c�

{a−P+E�� YN �−�1+ �wi+

n−1∑j �=iwj

}�

We obtain the optimality condition by setting the par-tial derivative of the above w.r.t. wi to zero for all i,

a− P +E�� YN �+

n− 1∑j �=i

wj − 2�1+ �wi

− �P − c�+

n− 1∑j �=i

wj = 0� (12)

We next see whether the above optimality conditionfor the centralized supply chain would be satisfied bydecentralized decisions. Recall the first-order condi-tion (2), which holds in equilibrium for all scenariosof confidentiality. Applying (2) with K =N , we obtain

a− P ∗ +E�� YN �+

n− 1∑j �=i

w∗j − 2�1+ �w∗

i = 0�

We then rewrite condition (12) as, for all i ∈N ,−�P ∗ − c�+

n− 1∑j �=i

w∗j = 0� (13)

Lemma 2. In any scenario of confidentiality, when allretailers share their information with the manufacturer, theequilibrium wholesale price and retail margins (decentral-ized decisions) maximize the supply chain profit if and onlyif they satisfy (13).

By (9) and (7), the equilibrium wholesale price andretail margins in S3 are

P �3��YN � = c+!�3�n �a− c+E�� YN ��

= c+

2�1+ ��a− c+E�� YN �� and

w∗i �P

�3��YN �� =1

2+ �a− P �3��YN �+E�� YN ��

= 12�1+ �

�a− c+E�� YN �� i ∈N�

It is easy to check that they satisfy (13).


Proposition 7. When all retailers share their informa-tion confidentially with the manufacturer, the supply chainis coordinated, i.e., the decentralized decisions implementthe centralized optimal solution.

All our results thus far are based on the assumptionthat the retailers who commit to share informationwould later do so truthfully. We next investigate theissue of compatibility and show that truth telling isan equilibrium behavior under confidentiality.For K = N , suppose that a certain retailer l trans-

mits a signal �Yl, which may or may not be the same ashis true signal Yl, but all other retailers transmit theirtrue demand signals and all other firms, including themanufacturer, believe that all retailers transmit theirtrue demand signals. Let �YN = ��Yl*Yj� j �= l�. Becausethe manufacturer and other retailers follow their equi-librium strategies in response to the reported signals�YN , the wholesale price �P = P �3��YN �, and other retailmargins, �wj =w∗

j �P�3��YN �� for j �= l still satisfy (13) for

i= l, i.e.,−� �P − c�+

n− 1∑j �=l

�wj = 0�

Given the other firms’ decisions, �P and �wj ’s, j �= l,retailer l’s demand is

q̃l = a− �P + �− �1+ �wl +

n− 1∑j �=l

�wj

= a− c+ �− �1+ �wl +[−� �P − c�+

n− 1∑j �=l

�wj

]�

Note that the last term in the square brackets isthe part of demand that might be influenced by thereported signal. As shown above, the equilibriumresponses of the manufacturer and other retailers toany signal reported by retailer l are such that thebracketed term in q̃l always equals zero, and thisreduces his demand to

q̃l = a− c+ �− �1+ �wl�

Because the reported signal �Yl has no impact on hisdemand at all, retailer l has no incentive to misreport.In general, retailer l might benefit from a higher

demand q̃l if a falsely reported signal couldinduce a lower wholesale price �P and/or higher otherretail margins �wj , j �= l. A deflated report �Yl < Yl,which lowers other firms’ estimation of E�� YN �,induces a lower wholesale price but also lowers otherretail margins. An inflated report �Yl > Yl, which raisesother firms’ estimation of E�� YN �, increases otherretail margins but also induces a higher wholesaleprice. Thus, a false report �Yl �= Yl always has twoopposite effects on q̃l (through the wholesale priceand through other retail margins). Under confidential-ity, these two effects exactly cancel out each other anda falsely reported signal will not increase retailer l’sdemand or profit.

Proposition 8. When all retailers share their informa-tion confidentially with the manufacturer, no retailer hasincentive to report his demand signal falsely, given that allother retailers truthfully report their demand signals.

Note that Proposition 8 is a corollary of Propo-sition 7 as it follows directly from the optimalitycondition (13), so incentive compatibility and supplychain coordination are closely connected. In S1, condi-tion (13) does not hold because of a higher wholesaleprice,

−�P �1��YN �− c�+

n− 1∑j �=i

w∗j �P

�1��YN ��

=− 12+

�a− c+E�� YN �� < 0�

Given that all other retailers report their true demandsignals, retailer l could increase his demand by low-ering other firms’ estimation of E�� YN � through adeflated report and, thus, he has incentive to give amore pessimistic report of his demand information.That is, without confidentiality, truth telling is not aNash equilibrium.Finally, note that in the absence of confidential-

ity (S1), the supply chain may achieve a lower totalprofit with vertical information sharing than with noinformation sharing. Hence, lack of confidentialitydestroys the incentive for (otherwise beneficial) infor-mation sharing in the supply chain.

5. Concluding RemarksDouble marginalization, competition, and informa-tion asymmetry are often cited as causes of supplychain inefficiency because they allegedly distort firms’incentives and drive individual decisions away fromoverall optimality. However, these three factors do notalways distort incentives in the same direction. Onthe contrary, their interplay may sometimes balanceout such that the supply chain performs optimallyor nearly so. The wholesale price arrangement, some-times criticized as being “too simplistic,” may be allthat is needed to coordinate the supply chain partnerswhen coupled with confidentiality.It is well-known that the supply chain suffers from

“double-marginalization.” When each player maxi-mizes its own profit, the manufacturer will chargea wholesale price that is too high from the perspec-tive of the supply chain. We have shown that confi-dentiality alleviates the double marginalization whenretailers are Bertrand oligopolists. Confidential verti-cal information sharing centralizes each retailer’s dis-persed information at the manufacturer level withoutdirect disclosure to other retailers. The wholesaleprice therefore aggregates the information and is used


by retailers to form expectations of the market condi-tion. It is this strategic signaling that effectively low-ers the equilibrium wholesale price and improves thetotal supply chain profits. In a perfectly competitivemarket, rational expectation under asymmetric infor-mation improves market efficiency (see Grossman1981 and references therein). We have shown thatrational expectation under asymmetric informationcreated by confidential information sharing may alsoimprove the efficiency of a monopoly/oligopoly sup-ply chain.The question is: How general is this result? With-

out confidentiality, the wholesale price is simply aunit cost to retailers and a unit revenue to the man-ufacturer. In the presence of confidentiality, it playsan additional role of signaling demand information.A higher (lower) wholesale price signals to retail-ers a more (less) favorable market condition, induc-ing them to set higher (lower) retail margins whichin turn reduce (increase) retailers’ orders from themanufacturer. Hence, the signaling effect renders themanufacturer’s demand more elastic to the wholesaleprice. It is this added price elasticity for the manufac-turer, when information is shared confidentially, thatprompts her to lower the wholesale price, improvingthe supply chain efficiency.This intuitive argument seems to point to a con-

dition under which confidentiality improves the sup-ply chain efficiency, namely, the signaling effect of anincrease (decrease) in the wholesale price has to resultin smaller (greater) retail quantities. We believe thatour efficiency result can be extended, by exploringthis condition, to more general situations such asmore general demand functions, heterogeneous infor-mation (different signal precision for different retail-ers), convex production cost functions, uncertainty inthe slope of the demand function, etc.On the other hand, if the signaling effect of an

increase in the wholesale price results in greater retailquantities, the efficiency result may not hold. Forexample, if the retailers compete in quantity, the sig-naling effect works against the supply chain effi-ciency. A higher wholesale price signals to retailersa more favorable market condition, inducing them toset greater quantities which increase retailers’ ordersfrom the manufacturer. That is, contrary to the caseof Bertrand retail competition, the signaling effectrenders the manufacturer’s demand less elastic tothe wholesale price and prompts her to raise thewholesale price. Hence, under Cournot retail competi-tion, confidentiality makes the wholesale price higher,impairing the supply chain efficiency.We have assumed a make-to-order manufacturer

and left out one of the most important gains frominformation sharing, the reduced inventory costs of

leftovers and shortages. One would expect that incor-porating these costs would provide increased incen-tives for firms in a supply chain to share information.One way to address these incentives is to assume thatthe manufacturer, after the wholesale price decisionbut before the demand realization, can produce aninitial quantity (make to stock) at marginal cost co.If the demand exceeds the initial production, addi-tional units are made at a marginal cost of c > co.In the appendix, we show that the make-to-stockoption lowers the wholesale price, and that moreintense retail competition increases—while informa-tion sharing reduces—the demand variability facingthe manufacturer, to which her inventory-related costis proportional. Furthermore, confidentiality of infor-mation sharing does not affect the manufacturer’sinventory-related cost. Hence, the results in this paperregarding confidentiality still hold in the make-to-stock setting, i.e., a higher degree of confidentialitybenefits the manufacturer but hurts the retailers, andconfidentiality improves supply chain profitability.Some of the results in the paper suggest testable

predictions about relationships among vertical infor-mation sharing, supply chain performance, andfactors such as degree of confidentiality, intensity ofmarket competition, and precision of demand infor-mation. We shall leave empirical and experimentaltesting of these predictions to future research.

6. Electronic CompanionAn electronic companion to this paper is available aspart of the online version that can be found at http://mansci.journal.informs.org/.

AcknowledgmentsThe authors thank the area editor, the associate editor, andtwo reviewers for their comments and constructive sugges-tions. This work was supported by the Research GrantsCouncil of Hong Kong, project HKUST6056/01H, CheungKong Graduate School of Business, and the Yale School ofManagement Faculty Research Funds.

Appendix

Equilibrium Wholesale Price and Ex Ante Payoffs inScenario 3We consider three cases separately: K = �, �K� > 1, or�K� = 1.

No Retailer Sharing Information. This is the same asK =� in S1.

More Than One Retailer Sharing Information. With�K� = k > 1, each retailer conjectures that

P = f �E�� YK�� that is, E�� YK�= f −1�P�


for some strictly increasing function f �·�. Retailer i’sresponse to P satisfies the first-order condition (2) withE�� YK� replaced by f −1�P�,

�1+ �w∗i = a− P +E�� Yi�P�− �1+ �w∗

i

+

n− 1∑j �=iE�w∗

j � Yi�P�� (14)

where it is believed by the retailers that

E�Yj � Yi�P�= E�� Yi�P�= f −1�P� for i ∈K� j �= i�

E�Yj � Yi�YK�= E�� Yi�P�=�k+ s�f −1�P�+Yi

k+ 1+ s

for i K� j �= i�

The solution to (14) is given by

w∗i �P �=

12+

�a− P + f −1�P�� for i ∈K�

w∗i �P �=

12+

�a− P + �1−Bk�f−1�P�+BkYi� for i K�

The above is the same as (3) and (4) but with E�� YK�replaced by f −1�P�. Using E�Yi � YK� = E�� YK� for i K,we can write E�D � YK�=

∑ni=1 E�q

∗i �P � � YK�, the conditional

expected demand for the manufacturer, as

na−nP +nE�� YK�−∑i∈KE�w∗

i �P � �YK�−∑iKE�w∗

i �P � �YK�

= n�1+ �

2+ �a− P�+nE�� YK�−

k

2+ f −1�P�

− n− k

2+ ��1−Bk�f

−1�P�+BkE�� YK��

= n�1+ ��a− P�− �n− �n− k�Bk�f−1�P�

2+

+ �n�2+ �− �n− k�Bk�E�� YK�2+

�

The expected profit, �P − c�E�D � YK�, for the manufacturerconditional on YK is

12+

�P − c�{n�1+ ��a− P�− �n− �n− k�Bk�f

−1�P�

+ �n�2+ �− �n− k�Bk�E�� YK�}�

To maximize �P −c�E�D �YK� over P , we set the first deriva-tive to zero, i.e.,

d

dP�P − c��n�1+ ��a− P�− �n− �n− k�Bk�f

−1�P��

+ �n�2+ �− �n− k�Bk�E�� YK�= 0�

For P = f �E�� YK�� to be an equilibrium, the above equalitymust hold if we replace E�� YK� by f −1�P�, i.e.,

d

dP

{�P − c��n�1+ ��a− P�− �n− �n− k�Bk�f

−1�P��}

+ �n�2+ �− �n− k�Bk�f−1�P�= 0�

This is a differential equation in f −1�P� and can be writ-ten as

−�n− �n− k�Bk��P − c�df −1�P�dP

+n�1+ �f −1�P�

+n�1+ ��a+ c− 2P�= 0� (15)

The general solution is given by

f −1�P�= P − c

!�3�k

�1+ �P − c�/kZ�− �a− c��

where Z is an arbitrary constant, and

!�3�k = n + �n− k�Bk

2n�1+ �� /k =

n + �n− k�Bkn− �n− k�Bk

�

Because we want f �·� to be strictly increasing, we must haveZ ≥ 0. Given any Z ≥ 0, an equilibrium wholesale price P�Z�solves f −1�P�= E�� YK�, that is,

!�3�k �a− c+E�� YK��= �P − c��1+ �P − c�/kZ��

The highest equilibrium wholesale price is obtained withZ= 0, i.e.,

P ∗ = f ∗�E�� YK��= c+!�3�k �a− c+E�� YK��

This P ∗ gives the manufacturer higher profit than any otherequilibrium and, therefore, as a Stackelberg leader, she willset the wholesale price to P ∗.At equilibrium, the retailers’ conjecture, E�� YK� =

f ∗−1�P�, is fulfilled and the manufacturer’s conditionalexpected demand equals

E�D �YK� =n�1+ �

2+ �a− P +E�� YK��

= n�1+ �

2+ �1−!

�3�k ��a− c+E�� YK��

and thus her conditional expected profit at equilibrium is

E�1∗M �YK� = �P ∗ − c�E�D �YK�

= n�1+ �

2+ !�3�k �1−!

�3�k ��a− c+E�� YK��2�

The retail margins at equilibrium are

w∗i = 1

2+ �a− P ∗ +E�� YK��

= 1−!�3�k

2+ �a− c+E�� YK�� for i ∈K�

w∗i = 1

2+ �a− P ∗ + �1−Bk�E�� YK�+BkYi�

= 1−!�3�k

2+ �a−c+E�� YK��+

Bk�Yi−E�� YK��2+

for iK�

The retailers’ conditional expected profits at equilibriumare given by E�1i � Yi�YK�= �1+ ��w∗

i �2. Finally, the firms’

ex ante payoffs in the first stage are obtained by takingexpectation over �Yi�YK�.

Exactly One Retailer Sharing Information. SupposeK = �l�. The difference between this case and the case ofk > 1 is that retailer l knows YK = �Yl� and does not infer it


from P . While Equation (14) is the first-order condition forany retailer i �= l, retailer l’s first-order condition is given by

�1+ �w∗l = a− P +E�� Yl�− �1+ �w∗

l +

n− 1∑j �=lE�w∗

j � Yl��

The solution to these first-order conditions is

w∗l �P �=

12+

�a− P + �1−A1�f−1�P�+A1E�� Yl��

w∗i �P �=

12+

�a− P + �1−B1�f−1�P�+B1Yi� for i �= l�

where A1 = �2+ + B1�/2�1+ �. We can then show thatf −1�P� satisfies the differential equation

−�n−A1− �n− 1�B1��P − c�df −1�P�dP

+n�1+ �f −1�P�

+n�1+ ��a+ c− 2P�= 0�

This differs from (15) only in the coefficient of the derivativeterm. The rest of the proof follows the same steps as in theprevious case (k > 1) and is omitted.

Make-to-Stock ManufacturerIn any scenario—S1, S2, or S3—the sequence of decisionsand events is as follows:1. Each retailer commits to either disclose his informa-

tion or not. After that, retailer i observes a signal Yi and,if he is a participating retailer, Yi is made known to themanufacturer and other retailers according to the specifieddisclosure scenario.2. The manufacturer sets a wholesale price P and makes

an initial production amount Q.3. Upon learning P , each retailer chooses a retail price pi.

Finally, demand is realized and additional production, ifneeded, is completed to meet the demand.The manufacturer now has the option of making to stock.She has an opportunity to produce an initial lot Q at thesame time that she selects a wholesale price P . We assumethat the manufacturer is obliged to meet the demand from theretailers. This is a reasonable assumption when the manu-facturer wants to maintain her reputation and resolves toalways satisfy downstream orders. The marginal cost forproducing the initial Q units is co. If D =∑n

i=1 qi > Q, thenD − Q additional units are made at a cost of c per unit,c > co. If D < Q, the leftover Q −D is sold at the salvagevalue of v per unit, v < co. If the manufacturer does not usethe make-to-stock option, then Q≡ 0 and we return to themake-to-order setting as before with unit production cost c.In the third stage, the retailers’ margin decisions w∗

i �P �in response to an announced wholesale price P is the sameas before. The retailers are not concerned with Q, knowingthat their orders, whatever they are, will be filled.In the second stage, with a given information-sharing

arrangement, the manufacturer chooses her strategy, P�YK�and Q�YK�. Anticipating the retailers’ margin decisionsw∗

i �P �, the manufacturer faces demand

D=n∑i=1

qi = na−nP +n�−n∑i=1

w∗i �P ��

which does not depend on the initial production deci-sion Q. The manufacturer’s expected profit conditional on

her information YK , as a function of P and Q, can be writ-ten as

E�1M �YK� = E�PD− coQ− c�D−Q�+ + v�Q−D�+ �YK�= �P − co�E�D �YK�

−E��co − v��Q−D�+ + �c− co��D−Q�+ �YK��The first term, independent of Q, is the expected profit atthe make-to-stock marginal cost, and the second term is theinventory cost accounting for possible overproduction andexpedition.Knowing w∗

i �P �, the manufacturer chooses P and Q tomaximize her expected profit. The maximization can bedone in two logical steps:

maxP�Q

E�1M �YK�=maxP

{maxQ

E�1M �YK�}� (16)

Because �P − co�E�D � YK� does not depend on Q, the innermaximization is equivalent to minimizing the inventorycost for a given P ,

argmaxQ

E�1M �YK�

= argminQ

E��co − v��Q−D�+

+�c− co��D−Q�+ �YK�� (17)

This is a newsvendor problem. Note that in each scenarioand for any given P , we can write the residual demand, thedifference between the demand realization and its expectedvalue, as

�D = D−E�D �YK�

= n�− Bk2+

∑iK

Yi −(n− �n− k�Bk

2+

)E�� YK�� (18)

We see that �D is independent of the choice of P , i.e., Ddepends on P only via its conditional expectation E�D �YK�.Let �Q∗�YK� be the solution to a newsvendor problem withdemand �D,

�Q∗�YK�= argmin �Q E��co − v�� Q− �D�+

+�c− co�� D− �Q�+ �YK�� (19)

The solution to (17) is given by Q∗�P�YK� = �Q∗�YK� +E�D � YK�. By D−Q∗ = �D− �Q∗, the two problems, (17) and(19), have the same optimal value (the minimum inven-tory cost),

Vk � E��co − v�� Q∗ − �D�+ + �c− co�� D− �Q∗�+ �YK�≡ E��co − v��Q∗ −D�+ + �c− co��D−Q∗�+ �YK��

Because the residual demand �D is the same for all scenarios,so is Vk. Therefore, inventory costs are not affected by confiden-tiality of vertical information sharing.The optimal wholesale price in the solution to (16) can be

found by ignoring the inventory cost,

argmaxP

{maxQ

E�1M �YK�}= argmax

P

��P − co�E�D �YK�−Vk�

= argmaxP

�P − co�E�D �YK��The right-hand side is precisely the optimization problemthat the manufacturer solves in earlier sections except that cis now replaced by co. Thus, the equilibrium wholesale


price P ∗ is the same as in the make-to-order case except thatwe need to replace c with co. As a consequence, the retailers’ex ante payoffs, "R�k� and "R�k�, remain the same as beforeexcept c is replaced with co. Note that P ∗ is now lower thanbefore because co < c. The manufacturer’s payoff in the firststage is given by

"�1�M �k�= $M

[�a− co�

2+(

k

k+ s

)�2

]−Vk�

"�2�M �k�= $

�2�M �k�

[�a− co�

2+(

k

k+ s

)�2

]−Vk�

"�3�M �k�= $

�3�M �k�

[�a− co�

2+(

k

k+ s

)�2

]−Vk�

where the first term is the payoff as before except using cofor c.To examine the demand variability experienced by the

manufacturer, we impose a more restrictive informationstructure.

Normal Conjugate Information Structure. The demandsignals, Yi, i ∈N , are independent draws from a normal dis-tribution with an unknown mean � and a known varianceand � itself is a priori normally distributed with zero meanand variance �2. In other words, �Yi� i ∈ N� and � form anormally distributed conjugate pair (DeGroot 1986).From (18), the variance of D conditional on YK for any

given P equals

�2k �Var�D �YK�=Var� �D �YK�=Var

[n�− Bk

2+

∑iK

Yi �YK]�

We can show, assuming the normal conjugate informationstructure, that

�2k =

[1

k+ s

(n− Bk�n− k�

2+

)2+(

Bk2+

)2�n− k�

]s�2�

When all retailers share information, the demand vari-ance is �2

n = n2s�2/�n+ s�, which is not dependent on .For k < n, we can show that �2

k is increasing . While ahigher intensity of downstream competition increases theaverage demand facing the manufacturer, it also increasesthe demand variability and thus her inventory-related costs.This may result in a net loss to the manufacturer.We can show that �2

k is decreasing in k. Thus, the manu-facturer faces less demand uncertainty as she receives infor-mation from more retailers.

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confidentiality and information sharing in supply chain coordination

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