information sharing in a channel with partially informed retailers

Vol. 27, No. 4, July–August 2008, pp. 642–658issn 0732-2399 �eissn 1526-548X �08 �2704 �0642

informs ®

doi 10.1287/mksc.1070.0316©2008 INFORMS

Information Sharing in a Channel withPartially Informed Retailers

Esther Gal-Or, Tansev GeylaniKatz Graduate School of Business, University of Pittsburgh, Pittsburgh, Pennsylvania 15260

{[email protected], [email protected]}

Anthony J. DukesMarshall School of Business, University of Southern California, Los Angeles, California 90089,

[email protected]

While retailers have sales data to forecast demand, manufacturers have a broad understanding of the mar-ket and the coming trends. It is well known that pooling such demand information within a distribution

channel improves supply chain logistics. However, little is known about how information-sharing affects whole-sale pricing incentives. In this paper, we investigate a channel structure where a manufacturer and two retailershave private signals of the state of the demand. Our model identifies the presence of a pricing distortion, whichwe term the inference effect, when a manufacturer sets price to an uninformed retailer. Because of this inferenceeffect, the manufacturer would like to set a low wholesale price to signal to the retailer that the demand islow. On the other hand, the manufacturer would like to set a high wholesale price so that he earns the optimalmargin on each unit sold. Vertical information sharing benefits the manufacturer by eliminating the distortioncaused by the inference effect, which is more profound in a channel whose retailer has a noisier signal. Thisresult implies that when there is a cost associated with transmitting information, the manufacturer may chooseto share information with only the less-informed retailer rather than with both.

Key words : channels of distribution; information sharing; retailing; game theoryHistory : This paper was received August 7, 2006, and was with the authors 5 months for 2 revisions.Published online in Articles in Advance March 31, 2008.

1. IntroductionThere has been a great deal of attention in supplychain management on information-sharing initiatives.Initiatives, such as Collaborative Planning, Forecast-ing, and Replenishment (CPFR), involve the exchangeof information among members of the distributionchannel to improve supply chain efficiency. Much ofthe data that is shared concerns the state of con-sumer demand and is used by suppliers and retailersto improve forecasts and distribution planning. Whilemuch has been written about the logistic benefits forvertical information sharing, little attention has beenpaid to the strategic benefits. In this paper, we exam-ine how pricing strategies are affected by the sharingof demand information within a distribution channel.In an early application of CPFR, Warner-Lambert,

makers of Listerine mouthwash, and Wal-Mart agreedto share demand forecasts six months in advanceof the expected retail sale date with the intent toimprove order accuracy and production planning(Seifert 2003, Småros 2003). The benefit commonlyattributed to this and other similar initiatives1 is a

1 Others include Continuous Replenishment Program and EfficientConsumer Response.

more streamlined supply chain, which reduces inven-tories and lowers operating costs for all membersof the supply chain.2 In this case, Listerine’s pro-duction scheduling was considerably smoother whileWal-Mart improved its in-stock position from 85% to98% (Seifert 2003).Such logistic benefits are now well known for pool-

ing demand forecasts in a supply chain (Lee et al.1997). In this research, we acknowledge these moti-vations and ask the next question: How does shar-ing information within a distribution channel affect amanufacturer’s pricing incentives? We take as giventhat a smoother supply chain can lower operationalcosts and allow a manufacturer to price more compet-itively. However, when controlling for these cost savings,our research shows that by sharing demand informa-tion with a retailer, a manufacturer may benefit addi-tionally from higher wholesale prices.The magnitude of this benefit for the manufacturer

depends greatly on the characteristics of the distri-bution channel. Given that Warner-Lambert entered

2 Manufacturers, for instance, enjoy smoother production sched-ules while retailers reduce inventories and avoid stockouts. See, forexample, the 2002 CPFR Baseline Study from the Grocery Manufac-turers of America.

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Gal-Or, Geylani, and Dukes: Information Sharing in a Channel with Partially Informed RetailersMarketing Science 27(4), pp. 642–658, © 2008 INFORMS 643

into a sharing arrangement with the largest retailer inthe world, it may also be tempting to reason that thispotential benefit is largest with large retailers. Ourmodel, however, indicates that this reasoning may notalways hold. To illustrate, consider the following.Apparel manufacturer VF, snack producer Nabisco,

and Delta Faucet are other examples of supplierswho have benefited by implementing informationexchange systems with the retailers who distributetheir products. But, contrary to the example above,these suppliers did not initiate their information-sharing arrangements with dominant, power retailerslike Wal-Mart, Target or Home Depot. Rather, theystarted exclusively with the smaller specialty retail-ers ShopKo, Wegmans, and TrueValue Hardware,respectively.3 This research investigates reasons whya manufacturer may, in some cases, find it optimal toexchange demand information with its low-volumeretailer instead of sharing with a large-scale big-boxretailer.Our results rely on the notion that manufactur-

ers and retailers all have different kinds of demandinformation. Retailers, for instance, have point-of-sale(POS) data, knowledge of their own merchandisingefforts, and aggregate store measures. Moreover, theprecision of this information may differ across retail-ers depending on the retailers’ size and location.Manufacturers, on the other hand, often have broaderinformation about the market, consumer motivations,demographic patterns (Desrochers et al. 2003), andstudy the factors that affect sales of their own prod-ucts (Blattberg and Fox 1995).We interpret these data sources as providing the

respective channel member a private signal about thestate of demand. When information-sharing arrange-ments have been implemented, these signals can bepooled, yielding more accurate demand forecasts. Buteven when information-sharing arrangements havenot been established, strategic choices permit infer-ences about other channel members’ signals. Weillustrate, specifically, that a retailer may infer themanufacturer’s knowledge about demand throughwholesale prices. A high wholesale price, for instance,tells the retailer that the manufacturer expects highdemand.4 The retailer’s ability to use wholesale priceto infer the manufacturer’s signal complicates thepricing problem facing the manufacturer. In particu-lar, the retailer is more sensitive to (wholesale) price

3 See Hill (2000), JDA Enterprise (2002), and VICS (1999) for accountsof these information-sharing initiatives.4 A high wholesale price could imply many other things in additionto high demand, including competitive positioning, differences incosts, or differences in profit targets. However, when the retailer isupdating its belief about demand, a high wholesale price increasesthe likelihood in a probabilistic manner that demand is higher.

in the absence of information sharing. Thus the man-ufacturer, faced with the familiar channel inefficien-cies of double marginalization, is induced to distortits wholesale price downward relative to the casewith no demand uncertainty. We refer to the phe-nomenon that induces this distortion as the inferenceeffect. The distortion is alleviated, however, when themanufacturer can directly communicate its signal tothe retailer. We conclude that alleviating the adverseconsequences of the inference effect is an incentivefor a manufacturer to implement information-sharingarrangements with a retailer.The magnitude of the inference effect, and, conse-

quently, the benefit of vertical information sharing,depends on several factors. The degree of retail com-petition, the relative precision of a retailer’s stochasticsignal, and whether competing retailers are alreadysharing demand signals are three important factorsdetermining the benefits of vertical information shar-ing, which are explored in this research.First, we investigate how the general competitive

environment in which a retailer operates affects theimpact of the inference effect. We might expect, forexample, the inference effect to differ between acompetitive discounter and a specialty niche retailer.As mentioned above, the inference effect stemsfrom channel inefficiencies associated with doublemarginalization, and such inefficiencies are known tobe less severe when retailers face strong competition.Consequently, our results suggest that a manufacturermay benefit more by sharing its information withretailers in less competitive environments.Second, the relative precision of retailers’ demand

signal directly affects the size of the inference effect.Volume of sales plays an important role in the accu-racy of retailer information. Some retailers, becauseof their larger market share, have access to largeramounts of POS data than the others.5 In addition, aretailer’s investment in information technologies (ITs)is an important factor in determining the precision ofthat information. This paper shows that the adverseconsequences of the inference effect are more pro-nounced for a channel in which the retailer has lessprecise information because the retailer is likely torely more heavily on wholesale price for inferencesabout the state of demand. Thus, sharing informationin these channels offers relatively more benefits thanin channels with more accurate information.Finally, we evaluate how the information possessed

by one retailer affects the magnitude of the infer-ence effect in a competing retail channel. We ask, for

5 For example, Wal-Mart holds 500 terabytes of data in its datawarehouse (Beckham 2002). This database is second only to that ofthe U.S. government in size (Nelson 1998).

Gal-Or, Geylani, and Dukes: Information Sharing in a Channel with Partially Informed Retailers644 Marketing Science 27(4), pp. 642–658, © 2008 INFORMS

example, what is the manufacturer’s benefit of shar-ing information with Wal-Mart given that it is alreadysharing information with Wal-Mart’s competitor. Ourmodel suggests that there may be diminishing returnsto developing information-sharing arrangements withadditional retailers. The implication of this result isthat even if the cost of developing an information-sharing network stays constant, the payoff from thisinvestment may depend on the number of channelswith such a network already installed.There are significant costs associated with imple-

menting information-sharing arrangements in a givendistribution channel. Despite the fact that themarginal cost of information transmission is virtu-ally zero, there may also be large setup costs inbuilding and developing communication technolo-gies, solving incompatibility of IT systems betweenpartners, buying forecast software, and training per-sonnel. This implies that, despite the noted benefitsof vertical information sharing, implementing a shar-ing arrangement in a given channel is not optimalunless the benefits exceed costs. While the investmentin one channel may have spillover benefits in another,many of these costs are channel specific. Therefore,just because a manufacturer finds information sharingoptimal in one channel, does not automatically meanit is optimal in a second. This cost structure impliesthat it is possible to see a manufacturer exchangedemand information in selected retail channels, butnot in all.6

Though the initial analysis focuses on one-sidedinformation sharing—from the manufacturer to aretailer—supply chain collaboration in practice usu-ally involves sharing information in both directions(Min et al. 2005). The lessons from the one-sided anal-ysis serve as a benchmark for the subsequent analysisof two-sided sharing in which information is transmit-ted not only from a manufacturer to a retailer, butalso from a retailer to a manufacturer. As indicatedabove, alleviation of the inference effect is most bene-ficial when a retailer has a relatively imprecise signalof demand. With two-sided sharing, the manufacturerwould receive poorer information in return than ifit had shared with the better-informed retailer. Weprovide conditions indicating when and with whichretailer(s) the manufacturer gains the most benefitfrom a two-sided information-sharing arrangement.Then, we use the results of this analysis to derivetestable hypotheses to determine whether alleviatingthe adverse consequences of the inference effect may

6 Of course, market conditions are constantly changing throughtime, and the manufacturer-retailer collaborations mentioned ear-lier later evolve to include other retailers. What is relevant for ourobjective is to explain why manufacturers might make exclusiveinformation-sharing arrangements with less-informed retailers insome, but not all, instances.

provide an incentive for the manufacturers to sharetheir information.The subject of information sharing has attracted the

interest of many academics in different fields. In mar-keting, Villas-Boas (1994) examines whether compet-ing firms should share the same advertising agency,which can make a firm’s private information avail-able to competitors.7 In accounting, Radhakrishnanand Srinidhi (2005) study the implication of chan-nel members’ bargaining power on the implemen-tation of information exchange (IE) arrangements.In economics, there is a literature on informationsharing in oligopoly. This research (e.g., Novshekand Sonnenschein 1982, Vives 1984, Gal-Or 1985, Li1985) investigates information-sharing incentives offirms engaged in horizontal competition. We dis-tinguish our work from these by the fact that weinvestigate the incentive for information sharing in adistribution channel that involves vertical relations.Another strand of literature in economics that isdirectly related to our analysis is the literature onsignaling (e.g., Spence 1973, Milgrom and Roberts1982, Gal-Or 1987). Similar to the inference effect thatarises in our analysis, in this literature, as well, theabsence of direct communication among asymmetri-cally informed parties leads to distortions in theirbehavior.As mentioned previously, there have been a num-

ber of studies on information sharing in the supplychain management literature, which identify benefitsrelating to improving logistics, alleviating orderbatching, and inventory shortages (e.g., Gavirneniet al. 1999, Cachon and Fisher 2000, Lee et al. 2000,Raghunathan 2001). However, these papers primarilyuse channel structures, in which there is no horizon-tal competition between the retailers, and informationtransmission is only from the retailer to the manu-facturer. In addition, we focus on the role demanduncertainty plays in the pricing decisions of themanufacturer.A relevant paper, Li (2002), incorporates horizontal

competition to a vertical information-sharing modelto examine the leakage effect of information sharing.This effect is caused by the reaction of competitorsthat are not involved in information sharing. How-ever, in Li’s (2002) research as well, the downstreamretailer transmits its information to the upstream sup-plier. He et al. (2007) and Niraj and Narasimhan(2002), on the other hand, investigate informationtransmission not only from the retailer to the manu-facturer, but also from the manufacturer to the retailer.However, He et al. (2007) and Niraj and Narasimhan

7 In a work related to ours, Raju and Roy (2000) show that althoughfirms do not share information, they obtain forecasts that canreduce uncertainty about industry demand.


(2002) do not allow the retailers to infer the manufac-turer’s private information from the wholesale price,and are thus unable to detect the channel distortionscaused by the inference effect.Our work is also similar in spirit to the growing lit-

erature on asymmetric channel structures. For exam-ple, Dukes et al. (2006) consider retailers that areasymmetric in terms of their retailing costs. In Geylaniet al. (2007), the asymmetry is in retailers’ differentialability to dictate their terms to the upstream supplier,and in Raju and Zhang (2005), it is in price leadership.In the channel structure analyzed here, on the otherhand, retailers differ in the quality of their demandsignals.As with much of the marketing literature on chan-

nels, our research relates to the manufacturer’s useof strategies to coordinate channel efforts. Caldieraroand Coughlan (2007) and Jeuland and Shugan (1983),for instance, examine the use of sales force incen-tives and wholesale pricing contracts, respectively, asa means to reduce channel inefficiencies, while Luoet al. (2007) proposes an approach to new productdevelopment that aligns channel interests. The man-ufacturer in our setting, by contrast, is concernedwith the impact of demand information on channeldecisions.Subsequent sections are organized as follows.

Section 2 provides the basic modeling framework.Section 3 characterizes the equilibrium in a chan-nel where a manufacturer considers transmitting hisdemand information to two asymmetrically informedretailers. Section 4 extends this model to incorpo-rate bilateral information exchange. Section 5 pro-poses two hypotheses to test whether alleviationof the inference effect is a benefit from verticalinformation sharing, and §6 includes concludingremarks and extensions. Finally, most of the techni-cal details are provided in the appendix to this paper.The remaining details are contained in a TechnicalAppendix available on the Marketing Science websiteat http://mktsci.pubs.informs.org.

2. Modeling FrameworkConsider a channel with two retailers who competein the sale of a single product that is supplied bya manufacturer. Without loss of generality, assumethat marginal costs for both the manufacturer andthe retailers are zero. The retailers are symmetricin every aspect except the accuracy of their privateinformation about the state of the demand. We makethis assumption to focus solely on the implicationof asymmetry in the accuracy of information of theretailers on the manufacturer’s incentives to shareinformation. Similar to the retailers, the manufac-turer also has access to private information about the

Figure 1 Information Structure

Manufacturer: x0x0 = u + ε0, ε0 ~ N(0, s0)

Retailer 1: x1x1 = u + ε1, ε1~ N(0, s1)

pw

Retailer 2: x2x2 = u + ε2, ε2 ~ N(0, s2)

cov(ε0, ε1) = cov(ε1, ε2) = cov(ε0, ε2) = 0

cov(ε0, u) = cov(ε1, u) = cov(ε0, u) = 0

pw

state of the demand. This information may be sharedwithin the channel and this decision is strategicallymade by the manufacturer.We further assume that the manufacturer offers a

uniform wholesale price pw to both retailers. Follow-ing the manufacturer’s wholesale pricing decision,the retailers i = 1�2 compete on retail prices pi. Eachretailer faces the following linear stochastic demand:

qi = a

b+ d− bpi

b2− d2+ dpj

b2− d2+u�

i �= j� a > 0 and b > d > 0� (1)

where u is normally distributed with mean 0 and vari-ance .8 All the channel members observe noisy sig-nals of u. The signal observed by the manufacturer isx0 and by the retailers are x1 and x2. Specifically, fori = 0�1�2, we assume xi = u + �i, (u��0��1��2� ∼N�0��), where � = diag� � s0� s1� s2�. Notice that inthis formulation, the noise in a signal is capturedby si. The better-informed i is the smaller si is. Weassume si i = 0�1�2 and to be known by all thechannel members. The model’s information structureis illustrated in Figure 1.9

8 This is an equivalent form of qi = � − �pi + �pj + u, with � > 0and � > � > 0. We use the demand function given in (1) because ofits nice boundary cases of no differentiation and local monopolieswhen d = b and d = 0, respectively. The direct demand functionsqi = a/�b+ d�−bpi/�b2− d2�+dpj/�b2− d2� are equivalent to the sys-tem of inverse demand functions pi = a− bqi − dqj i� j = 1�2� i �= j .Note that when d = 0, the inverse demand reduces to pi = a− bqi,which is the schedule facing a monopolist. Hence, d = 0 can beinterpreted as maximum differentiation between retailers. In con-trast, when d = b, the inverse demand reduces to pi = a− b�qi + qj �,implying that the price of i declines at the same rate irrespectiveof whether retailer i or j expands its physical sales. Hence, d = bcorresponds to no differentiation between the retailers.9 Notice that we assume perfectly correlated disturbances for theretailers (u1 = u2 = u). It is also possible to assume market-specificdisturbances ui for retailers i = 1�2, and an overall market demandsignal that is observed by the manufacturer in the form of the aver-age of these signals: �u1+u2�/2. For simplicity, our analysis is basedon the perfectly correlated disturbances assumption, but the readermay bear in mind that incentives for information sharing revealed


Figure 2 Timing of the Model

Manufacturer makesinformation sharing

decision

Manufacturer andretailers observedemand signals

Manufacturer setswholesale price

Retailers setretail prices

The sequence of events and decisions are as fol-lows. First, the manufacturer decides whether andwith which retailer to share information. This deci-sion involves investment in the infrastructure neces-sary to support the sharing of information with theselected retailers. This infrastructure may include ITsand personnel dedicated to the interaction with theretailers. Subsequent to the information-sharing deci-sion, nature determines the demand signals x0, x1, andx2 and channel members observe a subset of theserealizations. Second, the manufacturer and retailersobserve their private signals and any signals whichthey are privy to as determined by the information-sharing arrangement made in the first stage. Third,after signal realizations have been observed, the man-ufacturer sets the wholesale price. Last, the retailerschoose their prices. The timing of this game is graph-ically depicted as a four-stage process in Figure 2.We distinguish between two types of information-

sharing arrangements: one sided and two sided. Withone-sided sharing, information is transmitted onlyfrom the manufacturer to the retailer. Specifically, one-sided information sharing implies that a retailer isinformed of the manufacturer’s private signal x0. In§3, we develop the model in the case of one-sidedinformation. Later, in §4, we extend the analysis totwo-sided information sharing where information istransmitted not only from the manufacturer to theretailer, but also from the retailer to the manufacturer.Thus, in the two-sided case, a decision to share infor-mation with retailer i implies that the manufacturerand retailer i both observe x0 and xi in stage 2.The timing depicted in Figure 2 reflects the fact

that the installation of communication infrastructureis a long-term decision, relative to pricing. The man-ufacturer must, therefore, commit to its information-sharing policy before observing its own signal.10 Inaddition, the assumed timing implies the manufac-turer can adjust its wholesale price pw contingent onthe demand signal x0 that it observes. It follows thata retailer can draw inferences about the realization ofthe demand signal based on the observation of pw,

by our model will be present as long as there is positive correlationbetween the individual market disturbances (0< ��u1�u2� < 1). Seethe Technical Appendix at http://mktsci.pubs.informs.org.10 An alternative timing, in which the manufacturer’s sharing deci-sion is made after it observes his signal, yields the same basicresults. See the Technical Appendix at http://mktsci.pubs.informs.org.

even when the manufacturer chooses not to com-municate directly with the retailer. In our analysis,we demonstrate that such indirect inferences hurt themanufacturer in comparison to an environment wherehe can commit to directly communicate in a truthfulmanner with the retailer.Each agent in the model bases its pricing decision

on its own observed signal, those learned throughinformation sharing, and in the case of the retailers,on the manufacturer’s wholesale price. We thus definea decision rule for each agent as a mapping fi i =0�1�2 from the space of possible signal values and, inthe case of retailers, possible wholesale prices. Specif-ically, the manufacturer’s decision rule specifies thewholesale price using pw = f0�x0�, where x0 = �x0� � � ��is a vector of observed signals, which always includesthe signal x0. In the case of two-sided informationsharing, x0 possibly includes retailers’ signals. Retaileri’s decision rule specifies a retail price pi = fi�xi� pw�,i = 1�2, where xi = �xi� � � �� is a vector of observed sig-nals, which always includes the signal xi and possiblyx0 in the case of information sharing.As we show in the Technical Appendix at http://

mktsci.pubs.informs.org, normality of the randomvariables combined with the assumption of lineardemand implies that we can restrict our attention tolinear decision rules, without loss of generality.11 Thatis, in our analysis, we assume that each agent’s deci-sion rule f �·� is a linear function of its arguments andreflects optimal choices. The exact form of this linearfunction is then determined matching it with equilib-rium conditions of the particular game under consid-eration. Furthermore, we are assured that this processleads to the unique Bayesian-Nash equilibrium.

3. One-Sided Information SharingIn this section, we investigate one-sided communi-cation. When the manufacturer decides to share itsinformation, it is transmitted from the manufacturerto one or both of the retailers. Two-sided informationsharing is considered later in §4. The analysis can bebroken up by considering the four possible scenar-ios, or subgames, that are possible after the manu-facturer’s information-sharing decision in stage 1. In

11 Previous literature has demonstrated that this environment leadsto a unique Bayesian-Nash equilibrium with all parties followinglinear decision rules when decisions are simultaneous (see Radner1962, Theorem 5; Basar and Ho 1974; Vives 1999, Ch. 8). Our chan-nel setting, however, requires us to extend this result to a sequentialsetting.


the No-Sharing (NS) game, the manufacturer does notreveal its private signal to either retailer. If the manu-facturer decides to share this signal with retailer i = 1or 2, exclusively, then the parties play a Partial Shar-ing (PSi) game. Finally, it may share the signal withboth retailers in which case we are in the Full Sharing(FS) game.As will be shown, an uninformed retailer’s use

of wholesale price to infer the manufacturer’s pri-vate signal on demand plays an important role in thechoice of wholesale price, and, consequently, for theincentives to share information. The role this infer-ence plays can be illustrated by a careful analysis ofthe NS scenario. Consider the subgame following themanufacturer’s decision in stage 1 not to reveal hisprivate signal to either retailer. We analyze this sub-game by solving the pricing decisions of the retail-ers (fourth stage) first and then the wholesale pricingdecision of the manufacturer (third stage), given thatthe manufacturer decides not to share its informationin the first stage. As discussed above, we can restrictattention to linear decision rules.At the fourth stage, retailer i, i = 1�2 knows its own

signal and is able to use the manufacturer’s wholesaleprice to infer something about the state of demand.Thus the retailer uses its decision rule

pi = fi�xi� pw�=Di0+Di

1xi +Di2p

w (2)

to set the price. The coefficients Dik, k = 0�1�2 must be

consistent with equilibrium in the NS. Thus the pricepi must maximize

E !i � xi� pw"

=(

a

b+ d− bpi

b2− d2+ dE pj � xi� pw"

b2− d2

+E u � xi� pw"

)�pi − pw�� (3)

where retailer i’s expectations of its rival retailer’sprice and of the demand parameter u have beeninserted in the expression for expected demand.Retailer i’s first-order condition (FOC) with respect topi implies

pi = a�b−d�+dE pj �xi�pw"+�b2−d2�E u �xi�p

w"+bpw

2b�

i = 1�2� i �= j� (4)

Retailer i uses retailer j’s decision rule to form expec-tation about its price

E pj � xi� pw"=Dj0+D

j1E xj � xi� pw"+D

j2p

w� (5)

To make an inference on the stochastic demand term,recall that retailer i uses not only its own signal, but

the manufacturer’s signal as inferred by his price pw.That is, retailer i can, itself, evaluate the manufac-turer’s decision rule, which has the assumed form

pw = f0�x0�= �0+�x0� (6)

by solving for x0 if � �= 0.12 Equation (6) implies thatthe retailers can perfectly infer x0 from the wholesaleprice pw, since it is only the manufacturer’s demandsignal that affects its pricing. When the pricing ofthe manufacturer depends on additional supply-sideuncertainties, the retailers would not be able to drawperfect inferences about x0 based on the observationof pw.13 We make the simplifying assumption thatonly demand uncertainties lead to fluctuations in pw

to highlight the above-mentioned inference effect.We discuss the implications of relaxing this assump-tion in §6.Knowledge of the realizations of both x0 and xi

imply (DeGroot 1970, pp. 51–55)

E�u � xi� x0�= E�xj � xi� x0�= s0xi + six0

si + s0+ sis0� (7)

Inserting (6) into (7), we have

E�u � xi� pw�= E�xj � xi� pw�= s0xi + si��pw −�0�/��

si + s0+ sis0�

(8)

Equation (8) accounts for the fact that despite noinformation sharing, retailers can perfectly infer themanufacturer’s private signal by inverting the man-ufacturer’s optimization problem. In addition, it saysthat the manufacturer can influence retailers’ assess-ment of the demand parameter u in its choice of pw.In particular, if � > 0, then the statistical updatingrule in (8) implies that retailers infer a higher state ofdemand the higher wholesale price is.Equations (2), (4), and (5) yield six equations, which

can be solved for the six unknown parameters �Dik,

k = 0�1�2 for i = 1�2, where the hatted notationcorresponds to the retailer’s optimal decision rule.

12 The condition � �= 0 ensures that the manufacturer’s decision ruleis an invertible function of its private signal. In fact, it is intuitivethat � > 0, since the manufacturer will respond to a higher demandparameter with a higher price. As we show in Lemma 1, this isindeed the case in equilibrium.13 Wholesale prices may depend on many other factors, includingdifferent production costs, competitive positioning, and profit tar-gets. If all of these factors are deterministic, drawing perfect infer-ences about the stochastic demand signal x0 is still possible. Theadditional factors are simply reflected in this case in the values ofthe coefficients �0 and �. However, if there is some stochastic ele-ment in determining the value of additional factors, retailers willbe able to draw only imperfect inferences from pw . In particular,a higher value of pw would imply that demand was likely to behigher only in a probabilistic sense (provided that � > 0).


The optimal �D’s are functions of exogenous demandparameters a� b�d, the distribution parameters s0, s1,s2, and , and the coefficients �0 and � of the manu-facturer’s pricing decision rule. The algebraic detailsof this solution offer little insight and are thus rele-gated to the appendix (in proof of Lemma A.1).At the second stage, the manufacturer chooses its

pricing decision rule using the decision rules of the re-tailers derived above to maximize expected profitsconditional on its own signal

E !m � x0"= E �qi + qj�pw � x0"�which can be rewritten as follows:

E !m � x0" =(2a−E pi � x0"−E pj � x0"

b+ d+ 2E u � x0"

)pw

= (�2a− �Di

0+Di1E xi � x0"+Di

2pw�

− �Dj0+D

j1E xj � x0"+D

j2p

w�� · �b+ d�−1

+ 2E u � x0")pw� (9)

The manufacturer’s expectations of retailers’ decisionrules for prices have been substituted into the respec-tive demand Equations (1). The expected profit func-tion, expressed above, reveals an adverse incentivefor manufacturer’s wholesale pricing decision. To seethis, first note that because the manufacturer cannotuse nonlinear pricing rules, it is faced with the famil-iar channel distortions of double marginalization. Sec-ond, each retailer uses wholesale price to statisticallyassess the state of demand. As previously discussed, ahigher pw indicates a higher state of demand (throughretailers’ inference on u).14 Therefore, because of aninference effect, the marginal effect of wholesale priceon output (retail sales) is exaggerated. In this sense,asymmetric information exacerbates channel ineffi-ciencies associated with double marginalization.To see this mathematically, observe in (9) each

retailer’s reaction to pw. The coefficients D12, D

22 reflect

the sensitivity of output with respect to wholesaleprice. In a model of no uncertainty, these coeffi-cients are easily computed to be b/�2b− d�. However,with uncertainty and private information, �D1

2� �D22 > b/

�2b− d�, which reflects greater retailer sensitivity towholesale price. Therefore the manufacturer’s optimalwholesale price is lower than with full information.To put it differently, the manufacturer must distort pw

downward to convey a lower state of demand andinduce retailers to set lower retail prices. Note thatin spite of the attempt of the manufacturer to conveyinformation about a low state of demand, the retail-ers are never deceived. When the schedule of pw is

14 If there are additional cost uncertainties affecting pw , a higher pw

implies a higher probability that demand is higher instead of thedefinite deterministic inferences arising in our model.

strictly increasing, a separating equilibrium prevails,and there is a one-to-one mapping from x0 to pw.Hence the retailers can perfectly infer the value ofx0 from the observation of pw. This suggests that themanufacturer may benefit if it could credibly committo truthfully15 revealing its private signal by meansother than through the unit price, pw.To determine the equilibrium wholesale price, we

evaluate the optimization problem of the manufac-turer. The FOC for the maximization of (9) withrespect to pw leads to

pw = 1

2�Di2+D

j2�

·(2a− � �Di0+ �Di

1E xi � x0"�− � �Dj0+ �Dj

1E xj � x0"�+ 2�b+ d�E u � x0"

)� (10)

where the manufacturer’s expectations of retailers’signals can be expressed as follows (DeGroot 1970,pp. 51–55):

E xi � x0"= E xj � x0"= E u � x0"= x0

+ s0� (11)

Intuitively, (11) expresses the manufacturer’s poste-rior expectation of the retailers’ signals. As the preci-sion of its own signal improves (a decrease in s0), itsexpectation of xi gets closer to its own signal.Using (10) to match the coefficients in (6) leads to

two equations, which can be solved for the optimal� and �0 in terms of exogenous demand and distri-bution parameters, details of which are omitted fromthe main text, but found in the appendix. The solu-tion ( �, �0), presented in Lemma 1, characterizes themanufacturer’s optimal wholesale price conditionalon the realization of x0 in the NS game. Lemma 1 alsopresents the manufacturer’s optimal wholesale pricein the other information-sharing regimes.In the partial information-sharing game, the man-

ufacturer informs retailer i of its demand signal x0,but does not inform retailer j . In the third stage, themanufacturer chooses its decision rule pw using deci-sion rules of the retailers and given his own signalto maximize E !m � x0". The main differences betweenthe solution of this game and that of the NS gameare in the conditional expectations and the linear deci-sion rule retailer i uses. Instead of the conditional

15 To make this commitment credible, the manufacturer may investup front in costly infrastructure or personnel training that supportsthe collaboration with the retailers. However, this up front commit-ment is not necessarily monetary. It can be any action that bindsthe manufacturer to truthfully transmit its information. If, however,such credibility is not established, there is an incentive for the man-ufacturer to report untruthfully a signal lower than the true realiza-tion to further mitigate inefficiencies from double marginalization.(See Technical Appendix at http://mktsci.pubs.informs.org.)


expectations given in (8), retailer i estimates u directlyfrom the manufacturer’s signal using (7) rather thaninferring it from the wholesale price pw. This soft-ens the inference effect since retailer i’s expectationE xj � xi� x0" does not depend on wholesale price pw

as in (9). Retailer j , on the other hand, has not beeninformed of x0 and infers it from pw by inverting themanufacturer’s decision rule as in (9). Hence the infer-ence effect is present in the PSi game, but not to theextent as in the NS game.Finally, in the FS game, the manufacturer shares x0

with both retailers, so that retailers’ inference aboutu are independent of pw. Therefore the inferenceeffect is not present in the FS game. The followinglemma summarizes the derivation of the manufac-turer’s decision rules in each NS, PSi, and FS gamesand illustrates the impact of information sharing onwholesale pricing.

Lemma 1. The wholesale price selected by the manufac-turer in the first stage is given as

pw = yk

(a+ �b+ d�

+ s0x0

)� for k =NS�PSi� F S�

where

yNS ≡

{4bd� +s0�

2sisj + s0� +s0��si+sj �

·�2b2+bd+d2�+ 2s20�4b2−d2�

}

2�4b2(i(j −d2 2s20��

yPSi ≡

[�4b2−d2� 2s20+� +s0�

2sisj �2b2+bd+d2�]

+ 12b s0� +s0� �8b3−2b2d+bd2+d3�si

+�4b3+2b2d+2bd2�sj "

2�4b2(i(j −d2 2s20��

yF S = 12� (i≡ � +s0�si+ s0�

It is directly shown that yFS > yPSi > yNS , imply-ing that as the manufacturer increases the extentof information sharing with the retailers, it raisesalso the overall level of the wholesale prices that itcharges. Hence the inference effect has adverse con-sequences for the manufacturer’s ability to set a highprice. In fact, the expected wholesale price is highest,E pw" = a/2, when the manufacturer shares informa-tion with both retailers. Otherwise, whenever bothor one of the retailers does not have access to x0,expected wholesale price is lower: E pw" < a/2 (sinceyPSi� yNS < 1/2 when d < b�. Therefore the asymme-try of information that arises in our model forcesthe manufacturer to cut its wholesale price, on aver-age.16 Whenever the manufacturer does not reveal

16 It is interesting to note as well that in all regimes E pw"→ a/2 as�s1� s2� → 0. This is driven by the reduced value of the wholesaleprice as a signal and suggests the manufacturer has an incentive tohelp the retailer acquire more precise information.

directly its private demand signal, retailers draw indi-rect inferences about this signal from the wholesaleprice charged by the manufacturers. Specifically, ahigher price is interpreted as a signal of an improvedstate of demand. Such inferences have the poten-tial to exacerbate the problem of double marginal-ization that arises in the channel. To alleviate thisproblem, the manufacturer ends up cutting its whole-sale price below the full information optimum. Theextent of price cut depends, however, on the extent ofcompetition between the retailers. When the compe-tition between the retailers intensifies, which, in ourmodel implies that the retailers become less differen-tiated, and the difference (b − d) declines, the man-ufacturer does not have to cut the price to a verylarge extent. With a more competitive retailing mar-ket, the problem of double marginalization in thechannel diminishes, thus reducing the adverse con-sequences of the inference effect. In particular, when(b − d) is 0, which implies that the retailers are per-fectly homogenous, the adverse consequences disap-pear completely, and E pw"= a/2 for all informationalregimes, including NS and PSi. In contrast, the prob-lem of double marginalization is most severe whenthere is no competition between the retailers at all;namely, when d = 0. In this case, the adverse conse-quences of the inference effect are maximized, thusleading to a significant cut in the wholesale pricebelow the full information level (E pw" � a/2, in thiscase, for the NS and PSi regimes).We summarize the above insights in Corollary 1.

Corollary 1. The adverse consequences of the infer-ence effect:(i) are mitigated as the manufacturer raises the extent

of information sharing with the retailers; namely,

pwFS > pw

PSi > pwNS�

(ii) are more severe the more highly differentiated theretailers are �the larger the difference b− d�.

The adverse consequences of the inference effect17

on the manufacturer’s pricing decision are similarto those derived in the signaling literature in eco-nomics. In this literature, similar distortions arisewhenever asymmetrically informed parties interactwithout being able to credibly and directly share theirprivate information. In Spence (1973), the distortionsare characterized in the context of the interaction

17 It is interesting to note that the inference effect would have sim-ilar adverse consequences on the manufacturer if the uncertaintywere about the slope of the demand rather than its intercept. Hencethe manufacturer would be inclined to directly communicate withthe retailer information about price sensitivity of the consumersinstead of allowing the retailer to infer this sensitivity via pw . (Seethe Technical Appendix at http://mktsci.pubs.informs.org.)


between an employer and potential job applicants. InMilgrom and Roberts (1980), the distortions arise inthe context of the interaction between an incumbentmonopolist and a potential entrant, and in Gal-Or(1987), the distortions are derived in the context ofsequential play of firms in the marketplace.Note that we have referred to the adverse conse-

quence of the inference effect on wholesale price only.However, to evaluate the manufacturer’s expectedbenefit from the information sharing, we put the equi-librium pricing decision rules back into the objectivefunction of the manufacturer for each of the informa-tional regimes the manufacturer may choose in thefirst stage of the game. In Lemma 2, we state theexpressions for those expected profits.

Lemma 2. The maximized first-stage expected profits ofthe manufacturer are

E�!NSm � = V

{2b�yNS�2

+

{2b�b−d�� +s0�y

NS

·[4b� +s0�sisj +�2b+d�� s0��si+sj �]}

�4b2(i(j −d2 2s20�

}�

E�!PSim � = V

{2b�yPSi�2

+

{�2b+d��b−d�� +s0�y

PS

·[2b� +s0�sisj +�2bsj +dsi� s0]}

�4b2(i(j −d2 2s20�

}�

E�!FSm � = V 2b�yFS�2�

where V ≡[a2+ �b+d�2 2

+s0

] �2b−d��b+d�"−1�

Using the expressions of Lemma 2, we can now estab-lish our first proposition.

Proposition 1.(i) E�!FS

m � > E�!PSim � > E�!NS

m �.(ii) Let E�!PS1

m � and E�!PS2m � denote the expected manu-

facturer profits when sharing with retailers 1 and 2, respec-tively. Then, E�!PS1

m � > E�!PS2m � if s1 > s2.

Proposition 1 states that if the manufacturer choosesto transmit information to exactly one of the retailers,it will choose the less-informed one. To understandwhy, recall that it is the reduction of the inferenceeffect that benefits the manufacturer when sharinginformation. When the manufacturer is in the no-information-sharing regime and considers revealingx0 to exactly one retailer, it evaluates in which channelthe inference effect is most severe. Equation (8) indi-cates that inferences on the demand component u aremore sensitive to wholesale price pw for the retailer

with lower signal precision (i.e., larger si). Thus, lossesbecause of the inference effect on wholesale price aregreatest with retailer 1. If we interpret s1 > s2 as say-ing retailer 1 is less informed than retailer 2, then themanufacturer has greater benefit from informing theless-informed channel member.However, according to part (i) of the proposition,

even if the manufacturer shares information withthe less-informed retailer, it can further benefit fromrevealing its demand signal to the better-informedretailer as well. The question that remains, however,is whether this benefit is greater or smaller now thatthe competing retailer has been informed. This ques-tion is relevant in view of our earlier assertion thatsustaining information sharing with each retailer maybe costly, given the investment in physical and humancapital it requires. If the benefit from informationsharing with the second retailer increases after thefirst retailer is informed, it would imply that the man-ufacturer always chooses to inform both retailers if itis optimal to inform one. We show, however, in Propo-sition 2 that this may not be the case.

Proposition 2.(i) E�!FS

m �−E�!PSim �" > 0 i = 1�2.

(ii) E�!PSim �−E�!NS

m �" − E�!FSm �−E�!PSi

m �" > 0 i =1�2, if �2b+d� s0/b" si�b−d�−bsj "−2dsisj � + s0� > 0.Hence, if si sj and d is sufficiently small, there are dimin-ishing returns to information sharing.

Under the condition of Proposition 2(ii), the man-ufacturer may transmit its information exclusivelyto the less-informed retailer if the cost associatedwith sharing information is sufficiently high. Let cdenote the cost of sharing information with any givenretailer. The manufacturer will share its informationwith exactly one retailer if

E�!PSim �−E�!NS

m �" > c > E�!FSm �−E�!PSi

m �"�

Thus, if there are diminishing returns to revealinginformation to the second retailer, given that oneretailer has already been informed, the manufacturermay choose to share its information with only oneretailer rather than with both retailers.18

Proposition 2 states that when the retailers aresufficiently differentiated and the quality of theirsignals is markedly different, there are diminishingreturns to revealing information for the manufacturer.Higher differentiation, and therefore relaxed competi-tion between the retailers makes the double-marginal-ization problem severe, and the manufacturer is

18 If E�!PSim �−E�!NS

m �" < c, the manufacturer does not share its infor-mation with any of the retailers, and if E�!PSi

m �−E�!NSm �", E�!FS

m �−E�!PSi

m �" > c, it shares with both. If there are no diminishing returnsto sharing information, the asymmetry (i.e., sharing with only oneretailer) cannot arise.


tempted to reduce its wholesale price. However, whenthe well-informed retailer’s signal is of sufficientlyhigher quality, there is little gain for the manufac-turer from sharing information with this retailer. Thewell-informed retailer relies only a little on its infer-ences from the manufacturer’s wholesale price whenforming its expectations about the demand, and themanufacturer is not tempted to make significant pricereductions. Therefore the manufacturer does not ben-efit much from sharing information with the well-informed retailer given that it already has sharedwith the less-informed one. This result, together withProposition 1, implies that if the cost associated withinformation sharing is sufficiently high, the manufac-turer may choose to share information with the less-informed retailer rather than both retailers.19

4. Two-Sided Information SharingThe model of §3 involved one-sided informationtransmission. In this section, we extend this model toinclude bilateral IE. When the manufacturer decidesto share information with a retailer, information istransmitted not only from the manufacturer to theretailer, but also from the retailer to the manufacturer.In this section, we show that the inference effect maystill sway the manufacturer in the direction of sharinginformation with the less-informed retailer in spiteof the fact that it receives less precise information inreturn.To simplify the derivation, we restrict attention to

the case that one of the retailers is perfectly informed,and the other does not have access to any valu-able information about the state of the demand.Let retailer 1 be the perfectly informed retailer andretailer 2 be the perfectly uninformed retailer, thenusing our earlier notation, s1 = 0 and s2→�. We nowinvestigate the relative benefit to the manufacturer ofsharing information with retailer 1 versus retailer 2.To evaluate this relative benefit, in Lemma 3, wederive the expected profits of the manufacturer frompartial information sharing with only one retailer(retailer 1 or retailer 2).

Lemma 3. When s1 = 0 and s2→�, the expected profitof the manufacturer from partial information sharing withonly one retailer is given as follows:

E�!PS1m � = a2+ �b+ d�2 " 6b2− bd− d2" 2b2+ bd+ d2"

�2b− d��b+ d�32b3�

19 Another benefit for exclusive sharing with a less informed retailermay be the following. Suppose the less informed retailer has alsoless channel power than the more informed one. If sharing demandinformation improves supply chain efficiency and, thereby, lowersthe weaker retailer’s cost, then this retailer can, in principle, com-pete more aggressively with the stronger retailer. The manufacturermay benefit from more channel power with the stronger retailer, asa result.

E�!PS2m � = 1

�2b− d��b+ d�128b5

[a2+ �b+ d�2 2

+ s0

]

· 8b3+d�2b+d��b−d�" 8b3−d�2b+d��b−d�"�

From Lemma 3, we can calculate the net benefit,denoted by DD, to the manufacturer from sharinginformation with the uninformed instead of theinformed retailer, as follows:

DD = E�!PS2m �−E�!PS1

m �

= a2+�b+d�2 "�b−d�2 16b3�b+d�+2b2d�b+d�−d3�2b+d�"

�2b−d��b+d�128b5

− 6b2− bd− d2" 2b2+ bd+ d2"�b+ d� s0�2b− d�32b3� + s0�

� (12)

Communicating with the uninformed retailer,retailer 2, instead of the informed retailer, introducesthe following trade-off for the manufacturer. On theone hand, the benefits of alleviating the inferenceeffect is higher with the uninformed retailer. On theother hand, the manufacturer gets worse informationin return with this retailer. The expression for DD in(12) captures these counteracting incentives. The firstterm, which is positive, precisely measures the benefitaccruing to the manufacturer when retailer 2 does notuse wholesale price pw to make inferences about thesignal x0. The second term, which is negative, reflectsthe opportunity cost of the manufacturer from notcommunicating with retailer 1 and learning the pre-cise signal, x1.It is directly seen that the first term of DD dom-

inates the second for relatively small values of theparameters of d and s0. Hence, as the degree of dif-ferentiation between the retailers increases, and as theprecision of the private signal of the manufacturerimproves, the manufacturer is more likely to commu-nicate with the uninformed retailer, if it chooses tocommunicate with only one retailer. As was pointedout earlier, the adverse consequences of the inferenceeffect are especially pronounced when the retailers arehighly differentiated because the problem of doublemarginalization is severe in this case. As well, whenthe signal of the manufacturer is relatively precise, theadded benefit of obtaining more precise informationfrom the perfectly informed retailer is relatively small.When the values of the parameters d and s0 are not

sufficiently small, the manufacturer prefers communi-cation with the informed retailer, retailer 1. In Propo-sition 3, we summarize the relative incentives of themanufacturer to communicate with the uninformedversus informed retailer.

Proposition 3. When there is two-way communica-tion between the manufacturer and a single retailer ands1 = 0 and s2 → �, the manufacturer will communicatewith the uninformed retailer (retailer 2) if the parameters


d and s0 are sufficiently small. Otherwise, it will commu-nicate with the perfectly informed retailer (retailer 1).

Recall from §3 that the inference effect for a givenchannel is intimately related to the level of doublemarginalization. Our modeling framework provides amechanism for controlling the extent of this doublemarginalization through the differentiation parame-ter d. By considering d at 0 and at b, we see inCorollary 2 how double marginalization affects therelative trade-off of partial communication describedin (12) by DD.

Corollary 2. With partial communication,(i) when d = 0, the manufacturer will share infor-

mation with the uninformed retailer if s0/� + s0� <�a2+ b2 �/3b2. The latter inequality holds, in particular,when s0 ≤ /2.(ii) when d = b, the manufacturer will always share

information with the perfectly informed retailer.

Corollary 2, part (i) states a formal conditionfor when two-sided information exchange with theuninformed retailer is optimal for the manufacturer,as mentioned in the above discussion. Part (ii) ofthe corollary confirms the following intuition. Whenretailers are perfectly competitive (d = b), the double-marginalization problem does not exist. Therefore themanufacturer has nothing to gain from sharing infor-mation with the uninformed retailer because there isno inference effect. In terms of (12), the first term iszero, which implies that DD is negative.

5. Detecting the Incentives forInformation Sharing

As mentioned in the introduction, smoothing pro-duction and delivery schedules is a common benefitattributed to information sharing. Our model isolatesa second benefit: the reduction of the inference effect.The comparative statics we conduct in our analysisallows us to derive two hypotheses to help us identifythe possible existence of this second incentive.The first hypothesis relates to the degree of retail

competition in a given setting. Recall that on theone hand, the inference effect is less pronounced inhighly competitive retail environments as competi-tion reduces double marginalization. On the otherhand, highly competitive retailers have incentives tocut operating costs to price more aggressively. Oneway to cut costs is to improve supply chain efficiencythrough information sharing. Thus we arrive at thefollowing:

Hypothesis 1. In more competitive retail environ-ments,20 there are fewer information-sharing alliances

20 Various measures of the extent of the competition in a given mar-ket have been developed in economics, including the Herfindahl-Hirschman Index and n-firm concentration ratios.

(two-sided information-sharing arrangements) betweenmanufacturers and retailers.

If empirical research reveals an inverse relation-ship between the extent of retail competition and theincidence of information-sharing alliances, then it islikely that the inference effect is indeed present inaddition to efficiency considerations. If, on the otherhand, a direct relationship between those two vari-ables is empirically observed, then improving supplychain efficiencies may be the dominating force behindthe incentives to share information between manu-facturers and retailers.21 (According to Proposition 3,although the inference effect may still be a factor, it isimpossible, in this case, to distinguish it from supplychain efficiency considerations.)A second hypothesis that is implied by our model

offers another test to identify the possible existenceof the inference effect. This hypothesis relates to theprecision of the information that is available to theretailers. According to our analysis, the inferenceeffect is more pronounced in channels with poorlyinformed retailers. Hence, when retailers make rela-tively small investments in IT, manufacturers may bemore inclined to form information-sharing allianceswith them to eliminate the distortions that arisebecause of the inference effect. However, when man-ufacturers are motivated by supply chain efficiencies,they gain more by forming alliances with well-informed retailers that make significant investmentsin information infrastructure. Hence we obtain thefollowing hypothesis:

Hypothesis 2. In channels where retailers make largeinvestments in ITs, there are fewer information-sharingalliances between manufacturers and retailers.22

If empirical research shows an inverse relation-ship between the extent of investments undertaken bythe retailers and the incidence of information-sharingalliances, then it is likely that the inference effect playsa role in such initiatives.23 If, on the other hand, the

21 The example of Delta Faucet that was mentioned in the intro-duction is consistent with Hypothesis 1. The fact that Delta Faucetchose to establish an information-sharing alliance with a nicheretailer like True Value Hardware, and not with a large-scale big-box retailer like Home Depot, implies that Delta Faucet might havebeen motivated by the elimination of the price distortions causedby the inference effect. Niche retailers face moderate pressures tocut prices in comparison to the big-box retailers, thus giving rise tosignificant distortions because of the inference effect.22 Note that both Hypotheses 1 and 2 assume that manufactur-ers use linear pricing. These hypotheses cannot be used in envi-ronments where nonlinear wholesale pricing is employed (see therelated discussion in §6.2).23 Note that retailers that can afford to make large-scale investmentsin IT may also carry greater channel power. The greater extent towhich this additional channel power permits the retailer greatersay in decisions made with the manufacturer, the further we departfrom our assumption of the manufacturer as the Stackelberg leader.


relationship between those two variables is shown tobe direct, then it is more likely that improving sup-ply chain efficiencies is the dominating force in deter-mining the incentives to form information-sharingalliances in retail channels.24 (Once again, Proposi-tion 3 supports the possible existence of the inferenceeffect in this case as well. With a direct relation-ship, it is impossible to distinguish, however, betweenthis effect and the benefit of improving supply chainefficiencies.)

6. Concluding Remarks andExtensions

6.1. Summary of the ResultsThis paper investigates the nature of information-sharing arrangements in a distribution channel whenretailers are asymmetrically informed. Specifically, weasked: Should a manufacturer, possessing key infor-mation about the state of demand for its product,share this information with the retailer better orworse informed than a rival? Indeed, casual intu-ition might suggest a retailer already poised withsuperior information will offer a better return on themanufacturer’s investment on an information-sharingarrangement. We showed, however, that this reason-ing misses the role of retailers’ inferences on thestate of demand communicated through the whole-sale price set by the manufacturer. Accounting forwhat we called the inference effect, this research sug-gests that there may be larger benefits from sharingwith the more poorly informed retailer. When themanufacturer does not share its private informationabout the state of demand, the inference effect forcesthe manufacturer to distort wholesale price down-ward to alleviate double-marginalization problems.This effect is present for either retailer. However, itis more pronounced the less precise a retailer’s owninformation is about demand conditions. Of course,there can be benefits from sharing information uni-formly across all retail channels. But, if setting up andinstalling such systems is costly, then trade-offs arise.

24 Hypothesis 2 is consistent with another example we have dis-cussed in the introduction. The snack producer, Nabisco, initi-ated an information-sharing arrangement with the relatively small(67 stores in 2004) grocery chain, Wegmans (Boyle 2005, VICS 1999).Such a choice would seem to be inconsistent with a recent obser-vation made by the Grocery Manufacturers of America (GMA).Based on surveys conducted by GMA, mass merchandisers werethe retailers most likely to adopt CPFR, and the main reason citedfor such information-sharing arrangements was to “reduce out-of-stocks” (GMA: 2002 CPFR Baseline Study). It seems, therefore,that reducing the adverse consequences of the inference effect mayhave guided Nabisco in choosing a smaller chain that is likelyto be far less informed about demand conditions than the massmerchandisers.

We also investigated the benefits accruing to a man-ufacturer when it can acquire retailer-specific infor-mation from a sharing arrangement. This complicatesthe above trade-off because exclusive informationexchange with the less-informed retailer, offers themanufacturer, in return, a less precise signal of thedemand than if it had shared with the other, better-informed retailer.

6.2. ExtensionsTo investigate the issues mentioned here, we con-structed an analytical model that employed a numberof simplifying assumptions. It is instructive, however,to anticipate the implication of relaxing some of them.We assumed, for instance, that the manufacturer

makes its wholesale pricing decision based solely onthe demand signal observed. This implies that theretailers can perfectly infer the manufacturer’s privatesignal when observing its wholesale price. We madethis simplifying assumption to highlight the inferenceeffect. However, in reality, there may be additionalsupply-side uncertainties that face the manufacturerand affect its pricing decision, and therefore intro-duce noise in the wholesale price. When there isnoise in the wholesale price, the degree of infer-ence is lessened, thus reducing the manufacturer’slosses through the inference effect distortions. Notethat information sharing, in this case, introduces addi-tional benefits to the retailers as well, because theycan directly observe the private demand informationof the manufacturer. In the absence of sharing, theretailers can only infer a noisy signal of the manufac-turer’s private information.We also assumed that the manufacturer is restricted

to uniform wholesale pricing. If the manufacturer isable to price discriminate, retailers may still infer themanufacturer’s signal through the channel-specificwholesale price. Recall that a retailer’s inferenceis possible because it can solve the manufacturer’soptimal decision rule to learn the signal. Thus themanufacturer benefits through the reduction of theinference effect when sharing information with aretailer. However, with the ability to set retailer-specific prices, the economics of price discriminationsuggests that the manufacturer appropriates more ofthe channel profit, which makes information sharingmore likely.The inference effect in our model is driven by

the double-marginalization problem in the channel.As is well known, nonlinear wholesale pricing canperfectly alleviate this problem. To the extent thatthe manufacturer can use nonlinear pricing, the ben-efits of information sharing revealed here may bereduced. However, given that linear (or unit) pricingis commonly observed in practice (Iyer and Villas-Boas 2003), we expect the inference effect to be presentin many actual retail settings.


Our model also assumed that the manufacturerposts a nonnegotiable wholesale price. It is reason-able, however, to imagine that a retail buyer can hag-gle or negotiate wholesale terms. To consider thispossibility in the context of our model, suppose aretailer and the manufacturer enter a bargaining pro-cess in stage 3 in which both parties make alternat-ing offers of price (Rubinstein 1982).25 In principle,offers made by each party reflect its own private infor-mation. Specifically, the manufacturer’s offers can beused by the retailer to infer x0, leading to the familiardistortions of the inference effect.26

Finally, in contrast to our model, a retailer mayhave supply alternatives rather than a single man-ufacturer. It is therefore interesting to consider theconsequence of upstream competition. The presenceof a competing supplier puts downward pressure onwholesale prices. Nevertheless, the retailer’s ability toinfer the manufacturer’s private signal is, in principle,undeterred. Therefore we expect the inference effect toremain present even in the case of multiple suppliers.

AcknowledgmentsThe authors thank the editor, the area editor, and threeanonymous reviewers for helpful comments.

AppendixIn the Technical Appendix at http://mktsci.pubs.informs.org. we establish that it is sufficient to restrict attention tolinear decision rules when random variables are normallydistributed and demand is linear. Based on this result, weassume that the manufacturer follows a linear pricing ruleand deduce, in Lemma A.1, the retailers’ decision rules inall information regimes of the one-way sharing game.

Lemma A.1. Assuming that the manufacturer follows a lin-ear decision rule in choosing wholesale price (i.e., pw = �0+�x0),then retailer i also follows a linear decision rule of the formpi = Bi

0+Bi1xi +Bi

2pw +Bi

3x0, when it has access to x0, and of theform pi =Di

0+Di1xi +Di

2pw when it does not.

Proof of Lemma A.1. When retailer i has access to infor-mation about the signals xi and x0, it can update beliefs con-cerning the state of the demand, u, and the private signalobserved by retailer j , xj . Using DeGroot (1970, pp. 51–56),we obtain the posterior expectations as given in (7). If thereis direct communication with retailer i, it can observe thevalue of x0. Otherwise, this retailer uses the observed value

25 As is done in the marketing channels literature, we could alsoinvestigate alternative distributions of channel power by verticalNash and retailer leadership.26 It is also interesting to consider further the possibility that bar-gaining abilities of each retailer are different. For example, the bar-gaining power could be better for the better informed retailer (asin Geylani et al. 2007). Suppose this retailer has full ability to dic-tate wholesale price upstream but the manufacturer has the powerto set a take-it-or-leave-it price to the other retailer. Our analysisimplies that the inference effect remains vis-à-vis the less-informedretailer but disappears for the well-informed retailer.

of pw to draw inferences about the value of x0 by invertingf0 in (6). We now consider, in sequence, the three informa-tional regimes that can arise.No-Information Sharing �NS�: Note that the NS game was

partially analyzed in §3. The system of FOC’s leads to thefollowing system of six equations in six unknowns:

a�b− d�− 2bDi0+ dD

j0−

dDj1�0 si

�(i

− �b2− d2��0 si

�(i

= 0

−2bDi1+

dDj1 s0(i

+ s0�b2− d2�

(i

= 0

−2bDi2+

dDj1 si

�(i

+ dDj2+

si�b2− d2�

�(i

+ b = 0�

(13)

where (i ≡ � + s0�si + s0, i = 1�2, and i �= j .Solving system (13) for the coefficients Di

k in terms of �0and � yields

Di0 =

a�b− d�

2b− d

−2b �b2−d2��0�2b�2bsi(j +dsj(i�+d s0�2bsi+dsj ��

��4b2(i(j −d2 2s20��4b2−d2��

Di1 =

�b2− d2� s0�2b(j + d s0�

�4b2(i(j − d2 2s20��

Di2 =

b

2b− d

+ 2b �b2−d2��2b�2bsi(j +dsj(i�+d s0�2bsi+dsj ��

��4b2(i(j −d2 2s20��4b2−d2��

(14)

where (i ≡ � + s0�si + s0, (j ≡ � + s0�sj + s0, i = 1�2, andi �= j .Partial Information Sharing �PSi�: Let retailer i be the one

with whom the manufacturer shares information, and letretailer j be the competitor, then the retailers choose theirprices to maximize the following objectives:

maxpi

E

[(a

b+d− bpi

b2−d2+ dpj

b2−d2+u

)�pi−pw� �xi�x0

]

maxpj

E

[(a

b+ d− bpj

b2− d2+ dpi

b2− d2+u

)�pj − pw� � xj� pw

]�

(15)where the asserted linear decision rules followed by theretailers are given as

pi = Bi0+Bi

1xi +Bi2p

w +Bi3x0

pj =Dj0+D

j1xj +D

j2p

w�(16)

In (15) therefore for i’s objective: E�pj � xi� x0� = Dj0 +

Dj1�1/(i� s0xi + six0" + D

j2p

w , and for j’s objective:E�pi � xj� pw�= Bi

0+Bi1�1/(j� s0xj + sj �p

w −�0/��"+Bi2p

w +Bi3�p

w −�0/��.Optimizing (15) with respect to retail prices yields the

FOC of the retailers as follows:

a

b+ d− 2bpi

b2− d2+ dE�pj � xi� x0�

b2− d2+E�u � xi� x0�+

bpw

b2− d2= 0

a

b+ d− 2bpj

b2− d2+ dE�pi � xj� pw�

b2− d2+E�u � xj� pw�+ bpw

b2− d2= 0�

(17)


Requiring that the FOC (17) is valid for every possible real-ization of the arguments of the pricing rules (xi, pw , and x0for retailer i, and xj and pw for retailer j) yields a system ofseven equations in seven unknowns (Bi

k k = 0�1�2�3, andD

jl l = 0�1�2). Solving for the unknowns yields the solution

Bi0=

a�b−d�

2b−d− d�b2−d2� �0 2b� +s0�sisj + s0�2bsj +dsi�"

�2b−d��4b2(i(j −d2 2s20��

Bi1 =

�b2− d2� s0�2b(j + d s0�

�4b2(i(j − d2 2s20��

Bi2 =

b

2b− d+ d�b2− d2� 2b� + s0�sisj + s0�2bsj + dsi�"

�2b− d��4b2(i(j − d2 2s20��

Bi3 =

�b2− d2� si�2b(j + d s0�

�4b2(i(j − d2 2s20��

Dj0 =

a�b−d�

2b−d− 2b�b

2−d2� �0 2b� +s0�sisj + s0�2bsj +dsi�"

�2b−d��4b2(i(j −d2 2s20��

Dj1 =

�b2− d2� s0�2b(i + d s0�

�4b2(i(j − d2 2s20��

Dj2 =

b

2b− d

+ 2b�b2− d2� 2bsj �2b(i + d s0�+ dsi�2b(j + d s0�"

�4b2− d2��4b2(i(j − d2 2s20��

(18)Full Information Sharing �FS�: With full information shar-

ing, the objective functions of the retailers become

maxpi

[a

b+ d− bpi

b2− d2+ dE�pj �xi� x0�

b2− d2+E�u � xi� x0�

] pi − pw"�

(19)where i = 1�2, and i �= j , and the asserted linear pricing ruletakes the form

pi = Bi0+Bi

1xi +Bi2p

w +Bi3x0 i = 1�2�

Using derivations similar to those used earlier, yields asystem of eight equations in the above coefficients asunknowns. The solution of the system is given as follows:

Bi0 =

a�b− d�

2b− d�

Bi1 =

�b2− d2� s0�2b(j + d s0�

�4b2(i(j − d2 2s20��

Bi2 =

b

2b− d�

Bi3 =

2b �b2− d2� 2b� + s0�sisj + s0�2bsi + dsj �"

�2b− d��4b2(i(j − d2 2s20��

(20)

Proof of Lemma 1. The manufacturer chooses pw in thesecond stage to maximize expected profits expressed asfollows:

maxpw

E �qi + qj �pw � x0"� (21)

where qi = a/�b+ d�−bpi/�b2− d2�+dpj/�b2− d2�+u, pi, andpj are linear decision rules with coefficients expressed by(14), (18), (20) for the NS, PSi, and FS environments, andE�xi � x0�= E�xj � x0�= E�u � x0�= /� + s0�x0.

No-Information Sharing �NS�: From (14),

E�qi + qj � x0�

= 2ab−2bpw

�b+d��2b−d�+ 2b x0 4b(i(j −�b−d� s0�(i+(j�−d 2s20"

� +s0��4b2(i(j −d2 2s20�

− 2b �b− d��pw −�0� 4b� + s0�sisj + �2b+ d� s0�si + sj �"

��2b− d��4b2(i(j − d2 2s20��

(22)

and

Di2+D

j2 =

2b2b− d

+2b �b2−d2� 4b� +s0�sisj +�2b+d� s0�si+sj �"

��2b−d��4b2(i(j −d2 2s20��

(23)

Optimizing (21) with respect to pw yields

− �Di2+D

j2�p

w

b+ d+E�qi + qj � x0�= 0� (24)

Substituting into (24), the expressions obtained in (22) and(23) yields the FOC for the manufacturer. This conditionshould hold for every possible realization of the signal x0.Recall that the coefficients Di

k were derived under theassumption that pw is a linear decision rule of the formpw = �0+�x0. We substitute this assumption back into (24),and require this condition to hold irrespective of the valueof x0. This requirement yields a system of two equations inthe coefficients �0 and � as unknowns. Solving the systemyields that

pw = yNS

(a+ �b+ d�

+ s0x0

)�

as claimed in the lemma.Since there exist coefficients �0 and � that satisfy the

equilibrium condition (24), the derivation implies that alinear decision rule for pw is indeed a Bayesian Nashequilibrium.Partial Information Sharing �PSi�: From (18),

E�qi + qj � x0�

= 2ab− 2bpw

�b+ d��2b− d�

+ x0 2b(i(j�3b+d�−�b−d� s0(i�2b+d�−d 2s20�b+d�"

� +s0��4b2(i(j −d2 2s20�

− �b−d� �2b+d��pw−�0� 2b� +s0�sisj +�2bsj +dsi� s0"

��2b−d��4b2(i(j −d2 2s20��

(25)

and

Bi2+D

j2 =

2b2b− d

+ �2b+d��b2−d2� 2b� +s0�sisj + s0�2bsj +dsi�"

��2b−d��4b2(i(j −d2 2s20��

(26)



− �Bi2+D

j2�p

w

b+ d+E�qi + qj � x0�= 0� (27)

Substituting into (27), the expressions obtained in (25)and (26) and requiring that the FOC (27) holds for all pos-sible realizations of x0 yields a system of two equations in�0 and � as unknowns. The solution of the system yields

pw = yPSi

[a+ �b+ d�

+ s0x0

]�

as claimed in the lemma.Full Information Sharing �FS�: From (20),

E�qi + qj �x0�=2ab− 2bpw

�b+ d��2b− d�+ 2b x0

� + s0��2b− d��

and

Bi2+B

j2 =

2b2b− d

�

(28)


− �Bi2+B

j2�p

w

b+ d+E�qi + qj � x0�= 0� (29)

Substituting (28) into (29) and requiring that (29) holds forall values of x0 yields that,

pw = yFS

[a+ �b+ d�

+ s0x0

]� where yFS = 1/2� �

Proof of Corollary 1. From Lemma 1,(i)

yPSi − yNS = 12�4b2(i(j − d2 2s20�

�2b− d�� + s0��b− d�

· � + s0��sisj �+ s0si�2b+ d��2b�−1" > 0

yFS − yPSi = 12�4b2(i(j − d2 2s20�

�2b+ d�� + s0��b− d�

· � +s0��sisj �+ s0�2bsj +dsi��2b�−1">0� (30)

Hence pFS > pPSi > pNS .(ii) The gaps expressed in (30) are increasing with the

difference (b − d). Hence, greater differentiation increasesthe gaps. �

Proof of Lemma 2. From (24), (27), and (29) in theproof of Lemma 1, it follows that the equilibrium first-stageexpected profits of the manufacturer are given as follows:

E�!NS�= �Di2+D

j2�

NSE�pwNS�

2

b+ d�

where �Di2+D

j2�

NS is given by (23),

E�!PSi�= �Bi2+D

j2�

PSiE�pwPSi�

2

b+ d� (31)

where �Bi2+D

j2�

PSi is given by (26),

E�!FS�= �Bi2+B

j2�

F SE�pwFS�

2

b+ d�

where �Bi2+B

j2�

F S is given by (28).From Lemma 1, E�pw

k �2 = �yk�2 a2 + ��b+ d�2 2/ + s0�"since E�x0�

2 = + s0.Substituting E�pw

k �2 into (31) yields the given profitexpressions. �

Proof of Proposition 1.(i) From the expressions obtained in Lemma 2, it fol-

lows that

E�!PSim �−E�!NS

m �= V{2b�yPSi − yNS�2

+ [�2b+ d��b− d�� + s0��y

PS − yNS�

2b� + s0�sisj + �2bsj + dsi� s0"]

· � 4b2(i(j − d2 2s20"�−1}� (32)

and

E�!FSm �−E�!PSi

m �= V 2b�yF S − yPSi�2�

Since yFS > yPSi > yNS , it follows that E�!FSm � > E�!PSi

m � >E�!NS

m �.(ii) From the expressions obtained for E�!PSi

m � inLemma 2, it follows that

E�!PS1m �−E�!PS2

m � = V{2b�yPS1− yPS2�2

+ [�2b+ d��b− d�� + s0��y

PS1− yPS2�

2b� + s0�s1s2+ �2bs2+ ds1� s0"]

· � 4b2(1(2− d2 2s20"�−1}�

where

yPS1− yPS2 = � + s0�� s0��b− d��s1− s2��4b2− d2�

4b�4b2(1(2− d2 2s20��

Hence, if s1 > s2, yPS1 > yPS2 and E�!PS1m � > E�!PS2

m �. �

Proof of Proposition 2. From (32), a sufficient con-dition that E�!PSi

m � − E�!NSm � > E�!FS

m � − E�!PSim � is that

yPSi − yNS > yFS − yPSi. From (30), the latter inequality holdsif the condition stated in the proposition is valid. �

Proof of Lemma 3. When si → � and sj = 0 (sharingwith retailer 2), retailer 2 is perfectly uninformed. Hence,this case is equivalent to one-way communication given thatthe information from retailer i (2 in this case) is worthless.Substituting, therefore si →� and sj = 0 into the expressionobtained for E�!PSi

m � in Lemma 2 yields E�!PS2m �.

When si = 0 and sj → � (sharing with retailer 1),retailer 1 is perfectly informed, and the manufacturer usesthis retailer’s private signal in updating its belief aboutthe uncertainty. Therefore we need to explicitly solve for theequilibrium of the partial information-sharing game for thetwo-sided communication case. Using similar techniques asin the proof of Lemma A.1, we can get the coefficients ofthe retailers’ decision rules, pi = Bi

0+Bi1xi +Bi

2pw +Bi

3x0 and


pj = Dj0 + D

j1xj + D

j2p

w , given the manufacturer’s decisionrule, pw = �0+�x0+�ixi as follows:

Bi0 =

a�b− d�

2b− d− d�b2− d2� �0��+�i� 2b(isj + d s0si"

�2b− d� 4b2D(i − d2 2��s0−�isi�2"

�

Bi1 =

�b2− d2� s0 2bD+ d ��2s0+�2i si�"

4b2D(i − d2 2��s0−�isi�2"

�

Bi2 =

b

2b− d+ d�b2− d2� ��+�i� 2b(isj + d s0si"

�2b− d� 4b2D(i − d2 2��s0−�isi�2"

�

Bi3 =

�b2− d2� si 2bD+ d ��2s0+�2i si�"

4b2D(i − d2 2��s0−�isi�2"

�

Dj0=

a�b−d�

2b−d− 2b�b

2−d2� �0��+�i� 2b(isj +d s0si"

�2b−d� 4b2D(i−d2 2��s0−�isi�2"

�

Dj1 =

�b2− d2� 2b(i��2s0+�2i si�+ d ��s0�isi�

2"

4b2D(i − d2 2��s0−�isi�2"

�

Dj2 =

b

2b− d+ 2b�b2− d2� ��+�i� 2b(isj + d s0si"

�2b− d� 4b2D(i − d2 2��s0−�isi�2"

�

(33)

where

(i ≡ � + s0�si + s0� (j ≡ � + s0�sj + s0� and

D ≡ �2�s0 + sj + s0sj �+�2i �si + sj + sisj �+ 2��i sj �

Substituting si = 0 and sj →� into (33), we get

Bi0 =

a�b− d�

2b− d− d�b2− d2��0

�2b− d�2b�i

� Bi1 =

b2− d2

2b�

Bi2 =

b

2b− d+ d�b2− d2�

�2b− d�2b�i

� Bi3 = 0�

Dj0 =

a�b− d�

2b− d− �b2− d2��0

�2b− d��i

� Dj1 = 0�

Dj2 =

b

2b− d+ b2− d2

�2b− d��i

�

(34)

Using (34) and similar techniques as in the proof ofLemma 1, we get the manufacturer’s pricing rule

pw = 2b2+ bd+ d2

8b2 a+ �b+ d�xi"� (35)

Upon substitution of pw into the objective of the manufac-turer (similar to the derivation of (27) in Lemma 1), it fol-lows that the equilibrium first-stage expected profits of themanufacturer can be expressed as follows:

E�!PSi�= �Bi2+D

j2�E�pw�2

b+ d� (36)

Substituting (35) and the expressions for Bi2 and D

j2 from

(34) into (36), yields E�!PS1m �. �

Proof of Proposition 3. It follows since the first term ofDD is relatively big when d is small (the gap (b−d) is big),and the second term is relatively small when s0 is relativelysmall, (the expression s0/� + s0� is an increasing functionof s0). �

Proof of Corollary 2.(i) Follows by substituting d = 0 into the expression

obtained for DD.

(ii) Follows since the first term of DD vanishes whend = b, implying that E�!PS2

m �−E�!PS1m � < 0 when d = b. �

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