information acquisition and sharing in a vertical...

Vol. 29, No. 3, May–June 2010, pp. 483–506issn 0732-2399 �eissn 1526-548X �10 �2903 �0483

informs ®

doi 10.1287/mksc.1090.0534©2010 INFORMS

Information Acquisition and Sharing ina Vertical Relationship

Liang GuoDepartment of Marketing, Hong Kong University of Science and Technology, Hong Kong, China,

[email protected]

Ganesh IyerHaas School of Business, University of California, Berkeley, Berkeley, California 94720,

[email protected]

Manufacturers can acquire consumer information in a sequential manner and influence downstream retailbehavior through sharing the acquired information. This paper examines the interaction between a manu-

facturer’s optimal information acquisition and sharing strategies in a vertical relationship, capturing the impactsof both the flexibility to sequentially control information collection and the flexibility in ex post voluntarysharing. We show that when information acquisition is sequential, the manufacturer may not acquire perfectinformation even if it is costless to do so. This self-restriction in information acquisition follows from the man-ufacturer’s motivation to strategically influence retail behavior. When information acquisition is inflexible andconstrained to be either zero or perfect information, the manufacturer acquires less (more) information undermandatory (voluntary) sharing. Moreover, voluntary sharing unambiguously leads to more information beinggenerated, because the manufacturer has the option to strategically withhold the acquired information that turnsout to be unfavorable. Finally, the conditions under which the manufacturer ex ante prefers a particular sharingformat are examined.

Key words : information acquisition; information sharing; channel; disclosure; vertical relationshipHistory : Received: June 25, 2008; accepted: July 28, 2009; processed by Chakravarthi Narasimhan. Published

online in Articles in Advance December 2, 2009.

1. IntroductionIt is ubiquitous that firms are uncertain about con-sumer preferences and demand, and such uncertaintymay arise for a number of reasons. In markets forfashion or seasonal goods (e.g., apparel, cosmetics,motion pictures, sporting goods), consumer tastesare inherently uncertain. The proliferation of newproducts—in industries ranging from automobile,electronics, to consumer goods—can result in shorterproduct lifetime and increasingly volatile demand.A challenge for firms selling through a distributionchannel is then about how to match supply withuncertain consumer preferences. This has led to agrowing need for uncertainty-resolving information.Manufacturers in fashion and seasonal goods indus-tries (e.g., L.L.Bean and Timberland) have investedin sophisticated information gathering and demandforecasting systems (Fisher et al. 1994). Another exam-ple is Sport Obermayer in the sporting goods indus-try which instituted information systems based onearly demand signals to more accurately forecastdemand. Moreover, the acquisition and the shar-ing of consumer or market information with chan-nel partners to influence their behavior has been

recognized in the descriptive and the trade literatureas a strategic tool in channel relationship manage-ment, i.e., “information power” (Eyuboglu and Atac1991, Williams and Moore 2007).

Manufacturers of national brands can become bet-ter informed of consumer preferences and demandthrough market research, product testing, or access-ing ongoing syndicated research (Blattberg and Fox1995). However, downstream firms may lack the nec-essary expertise and resources and thus have torely on upstream firms for information (Agency Sales1992, 2003). For instance, members in the Associa-tion of Better Computer Dealers indicated that theyfrequently obtain information from their focal man-ufacturer (Mohr and Sohi 1995).1 In addition, withthe proliferation of new products launched, manyretailers increasingly realize that, as the scale andscope of the carried items increase, they are less

1 Brown et al. (1983) demonstrate that a retailer’s dependence onits supplier is positively related to the extent to which superiorupstream information is provided. Eyuboglu and Atac (1991) findthat upstream channel members who are perceived to communi-cate more informative messages exert more control over others’decisions.

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Guo and Iyer: Information Acquisition and Sharing in a Vertical Relationship484 Marketing Science 29(3), pp. 483–506, © 2010 INFORMS

informed about consumer preferences and demandthan their upstream manufacturers. Consequently, agrowing practice for manufacturers like Kraft, Procter& Gamble, and Warner-Lambert is to get involved inthe decision-making process of downstream retailersthrough information sharing (Niraj and Narasimhan2004, Kurtulus and Toktay 2007).

This paper analyzes a manufacturer’s incentiveto acquire and share consumer preference informa-tion in order to manage its retailer’s behavior. Weaddress several questions that have not been inves-tigated in the literature. In particular, how muchinformation should be acquired? When should theacquired information be shared with the retailer?How do the information acquisition and sharing deci-sions interact with each other? Moreover, what typeof sharing format should be implemented by themanufacturer? We consider a model in which thechannel members have uncertainty about how wellthe product fits consumer preference, which can bepotentially resolved by the manufacturer throughacquiring (imperfect) signals. In addition, it is uncer-tain to the retailer about whether useful informa-tion is available to the manufacturer. We highlightthe manufacturer’s strategic incentive for informationacquisition, i.e., manipulating the retailer’s belief andthus its behavior through information sharing.

Advances in information collection technologiesand Internet-based information gathering have ledto increasing sophistication in the manner in whichfirms track consumer preferences, test new prod-ucts, and monitor reactions to product modifications.Central to these advances is the increasing flexibilityto sequentially control the generation of information.For example, with syndicated databases or online sur-veys, signals that are useful for decision making (i.e.,data) may flow in continuously and sequentially, anda manufacturer can decide, at each point after observ-ing the collected signals, whether to acquire addi-tional signals. We examine the effect of sequentiallyacquiring information and compare it with the casewhen information acquisition is “inflexible,” wherebythe manufacturer can choose to acquire only eithernone or infinite signals.

Furthermore, we investigate and compare two dis-tinct formats of (truthful) information sharing. In the“ex ante mandatory sharing” case, the manufacturercontractually commits to share all the acquired infor-mation with the retailer before the information isactually acquired. For example, manufacturers suchas Procter & Gamble and Warner-Lambert stream-line the sharing process by setting up formal arrange-ments, such as collaborative planning, forecasting, andreplenishment (CPFR), that automatically transmit theacquired data to the collaborating retailer (Gal-Or et al.

2008). In contrast, under the “ex post voluntary shar-ing” format, the manufacturer can decide after infor-mation collection whether to share the acquired infor-mation. This can represent informal communicationsbetween managers or sales personnel of upstreamfirms and their retail partners. Many firms shareinsights with their retailers from time to time, butdo not contractually commit to share information ona long-term basis. Indeed, according to the exten-sive surveys conducted by BearingPoint, firms in theUnited States rely primarily on traditional devices(e.g., e-mail, phone, fax, meeting) to communicatewith their channel partners (Chain Store Age 2003).

1.1. Summary of ResultsThe first result of our analysis is that when informa-tion acquisition is sequential, the manufacturer maynot acquire an infinite number of signals that perfectlyreveal consumer preference, even though informationacquisition is costless. The manufacturer in equilib-rium exercises self-restriction in information acquisi-tion and continues to generate signals if and only ifthe posterior belief is between some upper and lowerbound. This stems from the manufacturer’s motiva-tion to strategically influence retailer behavior. If theinformation acquisition process reaches a stage wherethe posterior belief is at a high enough level, the man-ufacturer may stop the acquisition simply because nobetter outcome can be achieved in terms of inducingmore retail ordering. Conversely, the manufacturermay also terminate information acquisition when asufficiently low posterior belief is reached because ofthe risk that further collection of signals may lead tooverly adverse results. In summary, this result iden-tifies “strategic ignorance” in information acquisitionas a new mechanism that manufacturers may use togovern the behavior of their retailers.

The equilibrium amount of information generatedis influenced by the interaction between the flexi-bility in information acquisition (sequential versusinflexible) and the flexibility in information shar-ing (voluntary versus mandatory). First, whether theflexibility to sequentially control information acqui-sition leads to an increasing incentive to acquiremore information depends on the sharing format.When the manufacturer has committed to manda-torily share information, it will choose not to col-lect any information if information acquisition isinflexible, whereas sequential information acquisitionwill lead to a positive amount of information beingacquired. In contrast, under voluntary sharing, themanufacturer in equilibrium always acquires infor-mation if acquisition is inflexible, and as a resultthe flexibility in information acquisition may actuallylead to reduced information generation. Overall, theimpact of the flexibility in information acquisition on

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Guo and Iyer: Information Acquisition and Sharing in a Vertical RelationshipMarketing Science 29(3), pp. 483–506, © 2010 INFORMS 485

the equilibrium amount of information acquired ismoderated by the flexibility in information sharing.

Interestingly, the flexibility in information sharingcan unambiguously induce the manufacturer to gen-erate more information. This obtains from the man-ufacturer’s ability to select whether to disclose theacquired information. Suppose that the manufacturercontinues to acquire additional information, and whenthe acquired information turns out to be unfavorable,the manufacturer has the option to withhold the badnews and hence may not necessarily induce unfavor-able responses from the retailer. Such information con-cealment is feasible: the retailer cannot distinguishbetween the cases when useful information is indeedunavailable and when the manufacturer’s acquiredinformation is unfavorable, because no informationwill be received by the retailer in both cases.

We then examine the manufacturer’s preference forthe information-sharing formats. Counterintuitively,when the prior belief about consumer preference issufficiently low, the manufacturer prefers to committo mandatorily share any information that will beacquired and thereby gives up the ex post flexibilityto voluntarily disclose information. This is becausemore information may induce on average lower retailordering, which can be alleviated by a mandatorysharing commitment that serves as the manufac-turer’s self-discipline in information generation.

1.2. Related ResearchThere is a substantial literature starting from Novshekand Sonnenschein (1982) and Vives (1984) on (ex antemandatory) information sharing between oligopolis-tic firms. The general theme in this literature isthat the equilibrium impact of information sharingdepends on the interplay of two effects: First, thereis an efficiency effect whereby each firm has betterinformation about supply or demand uncertainty. Sec-ond, the sharing of information leads to greater cor-relation in the strategies of the competing firms. Thenet impact of these effects differs across the variouscontexts considered. For example, Gal-Or (1985) andLi (1985) investigate a Cournot oligopoly with uncer-tainty about a common demand parameter and showthat firms will not share information; however, Gal-Or(1986) and Shapiro (1986) derive the opposite resultwith uncertainty about costs. Vives (1984) shows thatthe incentives to share information change depend-ing on whether the products are substitutes or com-plements and whether the competition is Cournotor Bertrand.2 Villas-Boas (1994) studies the effects of

2 Raith (1996) presents a general model of information sharing thataccommodates and clarifies the effects of information sharing inmany of the major models in the literature.

information transmission that might result from com-petitors sharing the same advertising agency. In con-trast to the above literature, this paper investigatesthe acquisition and the transmission of informationin a vertical relationship. The economic incentive atplay in our paper involves the effect of informationacquisition and sharing on retailer behavior.

Another stream of research examines the acquisitionof information by oligopolistic firms. For example, Liet al. (1987) and Vives (1988) analyze optimal infor-mation acquisition about demand uncertainty andshow that the equilibrium level of information acqui-sition decreases with the cost of information acqui-sition and the slope of the demand function. Hwang(1993) extends these models to the case of noniden-tical and increasing marginal costs to show that thefirm with smaller marginal costs acquires more infor-mation in equilibrium. In these studies, firms make aone-time (static) decision on how much informationto acquire, and perfect information acquisition wouldarise in equilibrium when the acquisition cost is zero.In contrast, we examine sequential information acqui-sition, which implies that after each signal there is adecision on whether to acquire additional signals. Asa result, in our analysis the manufacturer may prefernot to acquire full information, even if it is costless,because of the motivation to control retail behavior.Moreover, we examine how information acquisitioninteracts with the subsequent sharing decision in avertical channel.

There are also some papers that focus on infor-mation sharing in vertical relationships (e.g., Nirajand Narasimhan 2004, He et al. 2008).3 Li (2002) isperhaps the first analysis of the incentives of com-peting retailers to share private information with anupstream manufacturer.4 It identifies a direct effectdue to changes in the actions of the parties involvedin the sharing, and an indirect effect as a result ofthe changes in the actions of the competing retailer.Gal-Or et al. (2008) examine information sharingbetween a manufacturer and two competing retail-ers, which can alleviate demand uncertainty and thusmitigate distortions in wholesale price. Our focusdiverges significantly from these papers in that we

3 There is a substantial literature in supply chain management,originating from Lee et al. (1997), that examines the efficiency-improving role of information sharing in reducing production,logistical, or inventory-related costs (e.g., Cachon and Fisher 2000,Kulp et al. 2004). In this vein, Iyer et al. (2007) investigates the sub-stitutability between information sharing and inventory holding ina distribution channel.4 Gal-Or et al. (2007) study whether buyers should share supplier-specific fit information with prospective suppliers to extract moresurplus in input procurement. Creane (2007) looks at an analogousproblem of downstream firms sharing their productivity informa-tion with an input supplier.

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analyze sequential information acquisition by a man-ufacturer and its subsequent sharing with the retailer.Moreover, only mandatory sharing is considered inthese studies,5 whereas we examine how the formatof sharing (voluntary versus mandatory) affects theamount of information that the manufacturer willacquire.

The rest of this paper is organized as follows. Thenext section describes the model. Section 3 presentssome preliminary results. This is followed by the anal-ysis of mandatory sharing in §4. Next, §5 addressesthe case of voluntary sharing, where the manufac-turer’s equilibrium ex ante payoffs across the alterna-tive sharing formats are also compared. Some modelextensions are analyzed in §6, and §7 concludes thepaper.

2. The ModelAn upstream manufacturer produces a good and sellsto end consumers through a retailer. The manufac-turer has a constant and zero marginal cost of pro-duction. There is a competitive supply of the productin the upstream market, over which the manufacturerenjoys a margin d > 0. The retailer would order theproduct from the manufacturer only if the per-unitwholesale price � is not higher than d� which repre-sents a measure of competitiveness in the upstreammarket. The firms are risk neutral and maximizeexpected payoffs.

Consumers belong to one of two segments whoseproduct valuation are denoted by

Vi = �iQ� (1)

where i ∈ h� l� denotes consumer segments; Q rep-resents the consumers’ perception of the fit of theproduct with their preference; and �i captures con-sumer segment i’s valuation conditional on productfit, where 0 < �l < �h. The relative size of the high andthe low consumer segments are � and 1− �, respec-tively, where � ∈ �0�1�. Consumers know their per-ceived product fit, which is initially unknown to thefirms.6 Suppose without loss of generality that thereare two possible states of nature, S ∈ G�B�, such thatQ = 1 if the product is “good” (i.e., S =G) and Q = 0if it is “bad” instead (i.e., S = B). The firms have com-mon prior belief about the true state on consumerpreference; i.e., Pr�S = G� = � and Pr�S = B� = 1− �,where � ∈ �0�1��

5 One exception is Guo (2009), which examines the payoff impli-cations of a downstream retailer sharing privately acquired infor-mation with an upstream manufacturer on an ex post voluntarybasis.6 Alternatively, one can interpret the consumers’ perceived productfit Q as “perceived quality” in that products with higher quality fitconsumer preference better. To simplify exposition, we will use theterms consumer preference and perceived product fit interchange-ably whenever no confusion arises.

This paper deals with information on consumers’perceived product fit, which the manufacturer canacquire (e.g., through market research, focus groups,online surveys, syndicated consumer databases) andtransmit to the retailer. This may be particularly rel-evant for new products, modifications to products,or consumer taste changes (e.g., in fashion markets),where significant firm uncertainty may exist aboutproduct fit with consumer preferences. In the basemodel we assume that the retailer has no indepen-dent means to improve its knowledge about the per-ceived product fit. This represents situations wherethe manufacturer has superior access to product fitinformation, and the firms’ ability for informationcollection are asymmetric (Agency Sales, 1992, 2003).Nonetheless, we shall extend the model to incorpo-rate downstream information acquisition in §6�2 anddiscuss the implications of retailers exerting influenceon upstream suppliers through strategic informationacquisition and sharing in §7.2.

The timing of the game is shown in Figure 1.In the first stage, the firms sign and commit to acontract that includes the specification of a per-unitwholesale price � for the transfer of the product,and the format of information sharing. Two alterna-tive sharing arrangements therefore arise. The firstone is ex ante information sharing in which themanufacturer commits to mandatorily share informa-tion with the retailer. For example, manufacturerslike Procter & Gamble collaborate with retailers todevelop shared databases. In contrast, the manufac-turer can choose not to commit to transfer the to-be-acquired information to the retailer. Rather, afteracquiring the information in stage 2� the manufac-turer will voluntarily decide whether to disclose theacquired information. This case can represent infor-mal communications between sales managers of firmsand their downstream partners. The essential differ-ence between these two sharing formats hinges onwhether the manufacturer, prior to knowing the con-tent of the acquired information, commits ex ante toshare the information. Note that if information shar-ing cannot be credibly committed in a contract, themanufacturer can always share its private informationvoluntarily on an ex post basis. We will investigateand compare these two alternative sharing formats,which allows us to capture the impact of the flexibil-ity in information sharing.

Nevertheless, useful information may not alwaysbe available. For example, the design of survey instru-ments may involve bias, the data collection technol-ogy may only yield signals that are too complex orirrelevant for decision making, or the capability toprocess the collected raw data may be absent. Specifi-cally, the availability of useful information is denoted

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Figure 1 Timing of the Model

Wholesale price andsharing format

Stage 1

Informationacquisition

Stage 2

Informationsharing

Stage 3

Retail orderingand pricing

Stage 4

as I ∈ y� �y�, where y or �y is realized in the sec-ond stage of the game each with a probability ofone half and represents the state in which usefulinformation is available or unavailable, respectively.7

The retailer is uncertain about whether useful infor-mation is available to the manufacturer, unless theacquired information is disclosed (either mandato-rily or voluntarily). As we will see in the analysis,this uncertainty has implications for the informa-tion sharing strategy of the manufacturer. To facili-tate notation, we define the manufacturer’s and theretailer’s expected payoffs in stage 2 as �′ and � ′

(or �′′ and � ′′), respectively, conditional on the whole-sale price � and the realized information state beingI = y (or I = �y), and taking into account the manufac-turer’s optimal information acquisition and sharingstrategies. Moreover, the firms’ equilibrium subgameprofits in stage 2, prior to the realization of the infor-mation state, are defined as ��w� = ��′ + �′′�/2 and��w�= �� ′ +� ′′�/2, respectively.

If I = y� the manufacturer can acquire (imper-fect) signals about the perceived product fit at zeromarginal cost per signal.8 Each signal s ∈ g� b�is independently generated from the true state Swith probability � ∈ 1/2�1!: Pr�g �G�= Pr�b � B�= �.Conditional on a signal s, the updated probabili-ties of the states of the perceived product fit arePr�G � g� = ��/�� + �1−��1−�� and Pr�B � b� =�1−��/��1−��+ �1−��. The parameter � cap-tures the informativeness of the signals. When� → 1/2, a signal provides no additional informationbeyond the prior: Pr�G � g� = � and Pr�B � b� = 1− �.When � → 1, the signals reveal the truth with full cer-tainty: Pr�G � g�= Pr�B � b�= 1.

We consider two alternative scenarios on infor-mation acquisition. In the first scenario, information

7 Equivalently, the state y (�y) can represent the scenario when themanufacturer’s cost of information acquisition is negligible (pro-hibitively high). We thank an anonymous reviewer for suggestingthis alternative interpretation.8 This may represent the (negligible) cost of converting the dataobtained from a vendor or an online survey, if informative (i.e.,I = y), into useful insights for decision making. For example, manyinformation vendors typically charge a fixed fee for unlimitedaccess to their database. In online surveys, once the fixed cost ofsetting up the survey is incurred, the cost of eliciting an additionalresponse is negligible. Generally, the setup can be interpreted asone in which masses of data can be generated by investing a fixedcost on a data collection technology, and the subsequent cost of con-verting each unit of the collected data into managerially relevantinformation is minimal.

acquisition is inflexible in the sense that the manu-facturer can choose to acquire only either none oran infinite number of signals. In contrast, if informa-tion acquisition is sequential, at each point when atotal of n≥ 0 signals have been accumulated and pro-cessed, the manufacturer decides whether to generatean additional signal.9 The comparison between thesetwo scenarios allows us to capture the impact of theflexibility in information acquisition.

In stage 3 the manufacturer can share the acquiredinformation with the retailer who may then update itsbelief about the perceived product fit. Under manda-tory sharing, all acquired signals are truthfully andcompletely transmitted to the retailer. Therefore themanufacturer’s sharing decision is immaterial, andthe firms have a common posterior belief. When infor-mation sharing is ex post and voluntary, the manufac-turer decides whether to transfer the acquired signalsto the retailer. The manufacturer truthfully disclosesall the acquired signals if it decides to share, with thealternative option to remain silent and disclose noneof the signals.10 The firms’ posterior beliefs are thenthe same if sharing occurs but may diverge from eachother if otherwise.

In the final stage the retailer decides on the orderingunits, x ∈ 0�1!.11 The retailer has to carry the orderedstock to be able to sell to the end consumers. Whenmaking the ordering decision, the retailer remainsuncertain about the fit of the product with consumerpreference unless an infinite number of signals (i.e.,almost perfect information) are acquired and dis-closed by the manufacturer. Finally, the perceivedproduct fit is revealed, and the retail price p is set.12

9 An equivalent interpretation of the information acquisition prob-lem is that the signals flow in sequentially (e.g., online surveys) andthe manufacturer chooses when to stop the information acquisitionprocess.10 The truth-telling assumption is standard in the existing literatureon information sharing and implies either that verification costs arenegligible or that the firms have long-term reputation concerns.11 The implicit assumption is that retail ordering does not occurbefore information acquisition and sharing. Therefore, this timingrepresents all the information collected by the manufacturer that isrelevant for the retail ordering decision. For example, in the fashionindustry or for new product introductions, there is often a signif-icant interval from the time when wholesale transfer contracts aresigned to the time when actual retail orders are placed. This interimtime is relevant for information acquisition and sharing. We thankthe area editor for comments on this issue.12 The results are unchanged when the retail price is determinedbefore the perceived product fit is revealed.

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Some elaboration on model assumptions are war-ranted. We intentionally assume that the deter-mination of the wholesale price precedes themanufacturer’s information acquisition, because thisenables us to isolate the strategic effect of upstreaminformation acquisition/disclosure on the retailer’sbehavior from the efficiency effect of improving themanufacturer’s own decision making. Nevertheless,we show in §6�1 that the main results are robustto making the alternative timing assumption thatthe wholesale price is determined conditional on theacquired information (i.e., in stage 3). Next, underthe assumption of zero marginal cost of informationacquisition, the manufacturer can choose to acquirean infinite amount of signals and become (almost)fully informed of consumers’ true preference withoutincurring any additional cost. However, the interest-ing point we want to investigate is the possibility thatthe manufacturer may choose not to know the truthfor certain even when it is completely costless to doso because of the incentive to strategically manipu-late the downstream retailer’s belief. It is this role ofinformation sharing in influencing the manufacturer’sinformation acquisition strategy that we highlight inthe analysis.

We focus on market conditions under which the rel-ative size of consumer segments satisfies ��h < �l <��2−��h� The first inequality rules out the trivial sce-nario when the low-type consumers are never servedand ensures that a vertically integrated manufacturerwould serve the whole market. The second inequalityrepresents the case in which the low-type consumerswill not buy in equilibrium in a decentralized channelwithout further information. This captures the rele-vant range of market conditions that help us exam-ine the relationship between information acquisitionand sharing and the trade-off between greater mar-ket coverage and surplus extraction through higherwholesale prices. To solve the game, we use backwardinduction to insure subgame perfection.

3. Preliminaries3.1. Retailer DecisionsLet the retailer’s updated belief about consumer pref-erence be � when making the ordering decision.With probability �� the consumers’ product valua-tions are Vh = �h and Vl = �l, respectively; with prob-ability 1 − �, we have Vh = Vl = 0� As a result, theretailer would consider only three possible levels ofordering quantity, i.e., x ∈ 0��1�, serving none, thehigh type, or both consumer types, respectively. Inparticular, the retailer’s expected payoff of order-ing x = � is � = max� ��h − ��0�� and orderingx = 1 is � = max ��l − ��0�. Define �l ≡ �/�h and

�h ≡ �1−��/��l −��h�. We can then characterize theretailer’s optimal ordering strategy:

x =

0� if � < �l%

�� if �l ≤ � < �h%

1� if otherwise�

The optimal ordering quantity increases with theupdated belief �; the retailer makes a trade-offbetween serving more consumers when the productturns out to be good and saving on overordering whenthe product is bad. If the product is unlikely to bea good ( � < �l), the saving incentive dominates andthe retailer would order nothing from the manufac-turer. When the perceived likelihood that the productis good is sufficiently high ( �≥ �h), the retailer wouldmake an order of size one. In addition, an intermedi-ate belief (�l ≤ � < �h) would lead the retailer to stockonly an intermediate amount such that only the high-type consumers are served.

3.2. Sequential Signal Acquisition andPosterior Beliefs

We now investigate how sequential informationacquisition influences the updating of posteriorbeliefs, starting from an arbitrary initial belief �̇. Con-ditional on a series of ng good signals and nb badsignals having been acquired, the posterior belief isupdated as follows:

Pr�G �ng�nb� =Pr�G�Pr�ng�nb �G�

Pr�G�Pr�ng�nb �G�+Pr�B�Pr�ng�nb �B�

= �̇

�̇+�1−�̇��1−��/��ng−nb��

Note that the updated posterior belief is dependentonly on the difference between the number of goodand bad signals. We can then define the posteriorbelief, updated from an initial belief �̇, as a functionof the number of accumulated “net good” signals N ≡ng −nb:

��N�≡ �̇

�̇+ �1− �̇��1−��/��N� (2)

To facilitate the analysis, suppose that N is a realnumber, which is without loss of generality when thenumber of signals becomes sufficiently large. Given� ∈ 1

2�1!, it is obvious that �' ��N�/'N� > 0. Intu-itively, this suggests that the larger the number of goodsignals relative to bad ones, it is believed that the truestate is more likely to be the former. Moreover, wehave limN→−� ��N�= 0 and limN→+� ��N�= 1, whichimplies that the true state can become almost certainlyknown if an infinite number of signals are acquired.

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Suppose that, starting from an initial belief �̇, infor-mation acquisition will not stop until either NH > 0or NL < 0 signals are generated. Then conditional onthe true state being S ∈ G�B�, what is the probability,formally defined as *S��̇ � �L� �H�, of reaching theposterior belief �H ≡ ��NH� > �̇ before reaching�L ≡ ��NL� < �̇? Similarly, what is the unconditionalprobability *��̇ � �L� �H� ≡ �̇*G��̇ � �L� �H� +�1 − �̇�*B��̇ � �L� �H�? To derive these probabilities,let us define + S�N� ≡ *S� ��N� � �L� �H� as the condi-tional transition probability that the upper bound NH

is hit before the lower bound NL, as a function of thecurrent net good signals N ∈ NL�NH!. Suppose thatan additional signal is to be generated. Then condi-tional on S =G, the posterior belief would be updatedupward to ��N + 1� or downward to ��N − 1�, witha probability � or 1 − �, respectively. This impliesthat the conditional transition function + G�N� is alsoupdated to + G�N + 1� or + G�N − 1� with probability� or 1 − �, respectively. If the true state is S = Binstead, then an additional signal would move theupdated posterior belief toward ��N + 1� or ��N − 1�,leading to the updated conditional transition function+ B�N + 1� or + B�N − 1�, with probability 1−� or�, respectively. The above discussion suggests thatwe can derive second-order difference equations for+ G�N� and + B�N�, respectively. These differenceequations can be solved using the boundary condi-tions + S�NL� = 0 and + S�NH� = 1, where S ∈ G�B�.Noticing that by definition *S��̇ � �L� �H�=+ S�0�, wecan obtain the following:

Lemma 1.

*G��̇ � �L� �H�=�H��̇− �L�

�̇� �H − �L��

*B��̇ � �L� �H�= �1− �H��̇− �L�

�1− �̇�� H − �L�� and

*��̇ � �L� �H�= �̇− �L

�H − �L

�

This lemma captures several interesting featuresof the probabilities of arriving at a posterior upperbound �H before a lower bound �L, starting froman initial belief �̇. First, it can be seen that*G��̇ � �L� �H� > *��̇ � �L� �H� > *B��̇ � �L� �H� forall �L, �H , and �̇ ∈ �L� �H!. Thus the accumu-lated signals are more likely to update the poste-rior belief toward the upper bound before the lowerbound, when the true state is G than when it is B.Intuitively, the g signals move the posterior beliefupward while the b ones move it downward. Notealso that these probabilities are proportional to thedistance between the initial belief and the lower

bound (i.e., �̇− �L) relative to the difference betweenthe upper and the lower bound (i.e., �H − �L). Allelse being equal, the closer the initial belief is tothe upper bound (or the farther from the lowerbound), the more likely the upper bound is reachedbefore the lower bound. Moreover, one can read-ily verify that *S� �L � �L� �H�=*� �L � �L� �H�= 0, and*S� �H � �L� �H� = *� �H � �L� �H� = 1, S ∈ G�B�. Thissuggests that, irrespective of the true state, a posteriorbound would be almost surely approached if it is suf-ficiently close to the initial belief before reaching theopposite posterior bound.

3.3. Benchmark ModelsBefore we begin the main analysis, let us considertwo benchmark cases. The first one is a verticallyintegrated channel in which the manufacturer sellsdirectly to end consumers. The optimal informationacquisition strategy is to collect an infinite numberof signals that (almost) perfectly reveal the product’sfit. When the revealed product fit is good (or whenno useful information is available), all consumers areserved; if the product fit turns out to be bad, the man-ufacturer will not sell the product. Thus the ex anteexpected profit is ��l. Consider now how contracts ina decentralized channel can be used to achieve thisfirst-best outcome, which involves (i) maximizing thetotal channel profits and (ii) transfering the profits atthe retail level back to the manufacturer. Two typesof externalities need to be corrected to maximize thetotal system’s profits: the contract must induce themanufacturer to collect full information and removethe vertical (double marginalization) externality aswell. In particular, the first-best outcome can beobtained in a decentralized channel through two-part tariff contracts with a fixed up-front payment(i.e., ��l) and variable transfer terms that are con-tingent on verifiable posterior beliefs: x� �� = 1 if� > 0 and x� �� = 0 if � = 0, and �� = , if �= 1and �� = 0 if � < 1, where , > 0 is sufficientlysmall.

The second benchmark case arises when informa-tion sharing in a decentralized channel is either infea-sible or not credible. For example, if the message sentby the manufacturer is unverifiable or if the manufac-turer can select only the good signals for disclosurewhile withholding all the bad ones, then the retailerwill completely discard any information disclosed bythe manufacturer. As a result, no information wouldbe acquired by the manufacturer; information acqui-sition has no role if it is impossible for the manu-facturer to influence the retailer’s behavior throughinformation sharing. The retailer will hence maintainthe prior belief �. We can then readily obtain that

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Figure 2 The Manufacturer’s Expected Payoffs Without InformationSharing

d, w

Πns

Π(w)

��h

��h

�(�l – ��h)

�(1 – �)

�(�l – ��h)

1 – �

�(�l – ��h)

1 – �

in equilibrium, the manufacturer’s and the retailer’sex ante profits are, respectively,

�ns =

min

{d�

��l −��h�

1−�

}� if d ≤ ��l −��h�

��1−��%

�mind��h�� if otherwise%

�ns=

��l−min{d�

��l−��h�

1−�

}� if d≤ ��l−��h�

��1−��%

��h−�mind��h�� if otherwise�

The manufacturer’s equilibrium ex ante pay-off without information sharing, �ns, is shown inFigure 2. When the competitive margin is sufficientlysmall, i.e., d ≤ ��l − ��h�/��1 − ��, the manufac-turer is induced to charge low wholesale prices suchthat the whole market is served in equilibrium. How-ever, when the manufacturer’s competitive margin issufficiently large, i.e., d > ��l − ��h�/��1− ��, thelow-type consumers are not served in equilibrium,resulting in a loss of market coverage.

4. Ex Ante Mandatory InformationSharing

In this section we analyze mandatory informationsharing in which the manufacturer commits ex anteto share all the acquired information. The manufac-turer’s third-stage decision hence becomes immate-rial, and we can focus on the its second-stage decisionabout how much information should be acquired.Note that the firms necessarily share the same pos-terior belief, which can be denoted as �. In char-acterizing the manufacturer’s optimal informationacquisition strategy, we highlight the strategic influ-ence exerted on the retailer’s posterior belief andordering decision.

4.1. Inflexible Information AcquisitionWe start with the scenario when information acquisi-tion is inflexible such that only either none or an infi-nite number of signals can be generated when I = y.

The manufacturer’s information acquisition decisionthus amounts to either maintaining the prior belief� or becoming (almost) fully informed of the truestate on consumer preference. Should no informationbe acquired at all, the retailer’s belief will not beupdated from the prior. If the manufacturer decidesto acquire information, then the retailer’s posteriorbelief is updated to either � = 1 or � = 0, with theex ante probability � or 1−�, respectively. Given thatthe belief updating can subsequently influence theretailer’s optimal ordering decision, which of thesetwo options is more beneficial for the manufacturer?

Proposition 1. Under ex ante mandatory informationsharing and when information acquisition is inflexible, inequilibrium the manufacturer decides not to acquire infor-mation even when the information state is I = y. The equi-librium wholesale price and the firms’ ex ante payoffs arethe same as those in the benchmark without informationsharing (i.e., �ns and �ns).

Interestingly, when the acquired information ismandatorily shared with the retailer and the acquisi-tion process is inflexible, the manufacturer in equilib-rium would not charge wholesale prices under whichinformation acquisition is desirable. Under the equi-librium wholesale price, the manufacturer is strictlybetter off acquiring no information at all than mak-ing the retailer (almost) perfectly informed of con-sumer preference. Intuitively, providing informationto the retailer only leads to more stochastic retailordering, intensifying the double marginalization andmarket recession problem when the acquired informa-tion indicates bad product fit (i.e., � = 0). Thus, eventhough the cost of information acquisition is negli-gible, the manufacturer may not necessarily acquireinformation if it is constrained to choose between zeroand perfect information.

4.2. Sequential (Flexible) Information AcquisitionLet us now investigate the scenario when the man-ufacturer can decide on the number of signals toacquire in a sequential manner. We start by investi-gating the manufacturer’s optimal stopping rule forinformation acquisition when I = y and then examinethe payoff implications of strategically manipulatingthe information acquisition process.

4.2.1. Optimal Information Acquisition Strategy.The manufacturer’s optimal information acquisitionstrategy pertains to whether to stop at each updatedposterior belief � ∈ �0�1� that is commonly shared byboth firms.13 Recall that the retailer’s optimal order-ing quantity x increases with �. It is obvious that

13 It is assumed that when � is arbitrarily close to either zero or one,perfect information is (almost) surely obtained, and the informationacquisition process is hence terminated naturally.

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the manufacturer would not continue informationacquisition whenever � ≥ �h, or � ≥ �l and �h > 1.Conversely, the manufacturer would continue to col-lect more information whenever � < �l: the manu-facturer’s payoff would be zero if the retailer’s beliefremains below �l, whereas sampling additional sig-nals may induce the retailer to order x = � if �l isreached. Similarly, when �l < � < �h ≤ 1, informationacquisition will not be terminated, because samplingadditional signals would not decrease the amountordered but may induce more ordering if the poste-rior belief is updated upward to �h.

What remains to be determined is the informa-tion acquisition decision when � = �l (and �h ≤ 1).If no additional information is collected, a payoffequal to � = �� can be guaranteed. However, col-lecting additional information would lead to either� > �l or � < �l, and from the discussion above weknow that information acquisition will continue fromthen on until the posterior belief reaches either �h

or zero, moving the manufacturer’s ultimate payoffto either � or zero, with probability *��l � 0��h� or1−*��l � 0��h�, respectively. Using Lemma 1, we have*��l � 0��h�� = ��l/�h�� = ��l − ��h��/��1 − ��h� <��.14 Thus, the manufacturer will stop informationcollection when �= �l.

Proposition 2. Under ex ante mandatory informationsharing and when information acquisition is sequential,the optimal stopping rule of information acquisition whenI = y is characterized by two boundary points, � ∈ 0��!

and �̄ ∈ ��1!, such that the manufacturer continues tocollect information unless the updated posterior belief �reaches either � or �̄. In particular,

(i) If �≤ ��l −��h�/�1−��, then �= �̄= �, �′ =�,and � ′ = ��l −�;

(ii) If

��l −��h�

1−�< �≤min

{��h�

�l −��h

1−�

}�

then �= �l, �̄= �h,

�′ = �1−��h��l −��h�

�h − �l

+ ��2−��h − �l!�

�h − �l

�

and � ′ = ��h −��;(iii) If ��l − ��h�/�1− �� < � ≤ ��h, then � = �̄ = �,

�′ = ��, and � ′ = ��h −��; and(iv) If � > ��h, then � = 0, �̄ = �l, �′ = ��h, and

� ′ = 0.

14 This is because, under the market condition our analysis concen-trates on (i.e., �l < ��2−��h), a decentralized channel will not findit sufficiently profitable to serve the low-type consumers withoutany information. If instead �l ≥ ��2−��h, the manufacturer wouldcontinue information acquisition when �= �l.

This proposition establishes an important result ofthe paper: the manufacturer will not collect an infi-nite number of signals to fully resolve the uncer-tainty on consumer preference, even if the costs ofinformation acquisition (both fixed and marginal) arezero. In other words, the manufacturer in equilib-rium exercises self-restriction in information acquisi-tion, which is bounded by two posterior beliefs �

and �̄, where ��̄ − �� < 1. The incentive underlyingthis self-restriction is the strategic influence exertedon the retailer’s behavior. Under mandatory sharing,the only way the manufacturer can manipulate theretailer’s belief is through controlling the acquisitionof information. Nevertheless, collecting more infor-mation is a double-edged sword, moving the poste-rior belief either upward or downward. As a result,to control the generation of information to its ownadvantage, the manufacturer would stop the informa-tion acquisition process if the updated posterior beliefis already sufficiently high or if the expected pay-off improvement from obtaining good signals cannotcompensate for the potential loss when adverse sig-nals are generated.15

Two points are warranted in interpreting the man-ufacturer’s equilibrium self-restriction in informationgeneration. First, under mandatory sharing, the man-ufacturer does not enjoy any informational advan-tage over the retailer; i.e., any incompleteness ininformation is symmetric across the firms. As a result,the discontinuation of information acquisition andtransmission cannot play any signaling role. Second,because information disclosure is truthful, the retailerwould always believe in the received information,even though it is known that the acquisition of infor-mation has been strategically manipulated by themanufacturer. Therefore, the retailer would not, evenif it could, commit ex ante not to accept and act onthe ex post shared information.

Nevertheless, in comparison to inflexible infor-mation acquisition under which no information isacquired in equilibrium at all, the manufactureracquires more information when information acqui-sition can be sequentially controlled. Thus, para-doxically, it is only when the manufacturer cansequentially control the amount of information acqui-sition that there will be a positive amount ofinformation acquired. In other words, the flexibil-ity in the manufacturer’s information acquisition

15 This does not necessarily mean that the signals ultimately gener-ated include on average more good ones than bad ones or, moregenerally, that the empirical sample is biased upward. For exam-ple, when � is sufficiently close to �l from above, it is almost thecase that only bad signals would be observed towards the end ofinformation collection. In this case, it is optimal to stop when theupdated posterior belief hits �l.

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leads to a larger amount of information collection inequilibrium.

One may expect that the manufacturer canderive economic rents from sequentially controllinginformation acquisition. From Proposition 2(ii), forinstance, it is obvious that when ��l −��h�/�1−�� <� ≤ min��h� ��l −��h�/�1−��, the manufacturer’sexpected payoff under sequential information acqui-sition when I = y (i.e., �′) is indeed higher than thatwhen I = �y (i.e., �′′ = ��). Note that when the whole-sale price is within this range, the retailer would orderonly x = � if it maintains its prior belief �. How-ever, with the strategic control of information flow,the manufacturer can induce the retailer to order x = 1when the updated posterior belief reaches the upperbound �h but never order below x = � even whenthe lower bound �l is hit. This is demonstrated inFigure 3.

Interestingly, this strategic effect of sequential infor-mation acquisition works to the advantage of themanufacturer without necessarily hurting the retailer.Indeed, conditional on any wholesale price, theretailer’s expected payoff remains the same as inthe benchmark without information sharing. Again,this is because the information transmitted to theretailer, although strategically manipulated by themanufacturer, is truthful. This suggests that, withthe manufacturer’s sequential control of informationacquisition, there can be a Pareto improvement in thechannel members’ expected payoffs. Essentially, thedemand recession problem of being unable to fullycover the whole market can be mitigated and theretailer’s expected ordering quantity can be higher,when the retailer’s updated posterior belief is strate-gically boosted.

4.2.2. Equilibrium Ex Ante Profits. We now char-acterize the optimal wholesale price and derive thefirms’ equilibrium ex ante profits.

Proposition 3. Under ex ante mandatory informationsharing and when information acquisition is sequential,

Figure 3 The Manufacturer’s Expected Payoffs Under MandatorySharing �< ��l − ��h�/��1− ��h�

d, w

Πm

Π(w)Π′′Π′

��h

��h

�(�l – ��h)

1 – �

�(�l – ��h)

1 – �

(i) if � is sufficiently large (i.e., � > �̃), in equilibrium themanufacturer does not acquire any information even whenI = y, where �̃ ∈ ��l −��h�/��1−��h��1� is given in theappendix. The manufacturer’s equilibrium ex ante payoff isstrictly higher than that without information sharing (i.e.,�ns), if and only if � is sufficiently small and d is interme-diate. (ii) The retailer’s equilibrium ex ante payoff can bestrictly higher than that without information sharing (i.e.,�ns), if both � and d are intermediate.

The first point of this proposition is that sequen-tial information acquisition may not strictly improvethe manufacturer’s ex ante payoff when the priorbelief is sufficiently high. This has to do with theuncertainty about the availability of useful informa-tion at the time when the wholesale price is deter-mined. Recall that the manufacturer can benefit fromsequential information acquisition (i.e., �′ > �′′) whenthe charged wholesale price is such that the retailerwould order x = � in the absence of information shar-ing (i.e., ��l −��h�/�1 − �� < � < ��h). When theprior belief is already high, the extent to which theretailer’s belief can be manipulated upward is limited,and this constrains the potential benefit of sequentialinformation acquisition. However, with one half prob-ability, no information can be acquired (i.e., I = �y), inwhich case the manufacturer would have been betteroff had it charged a lower wholesale price (i.e., � =��l −��h�/�1−��) under which the whole market isserved. As a result, when � is sufficiently large, theequilibrium wholesale price is such that it is optimalfor the manufacturer to acquire no information evenwhen I = y.

It is only when the prior belief � is sufficiently lowthat the manufacturer would in equilibrium acquireinformation and thus benefit from sequentially con-trolling information acquisition. In this case, the dif-ference in the manufacturer’s equilibrium ex anteprofits between sequential and inflexible informa-tion acquisition, has an inverted U-shaped relation-ship with the manufacturer’s competitive margin d.In other words, the equilibrium ex ante benefit frommanipulating the retailer’s belief through sequentialinformation acquisition reaches its peak when d isintermediate. On the one hand, the manufacturer cancharge a higher wholesale price as d increases, mag-nifying the benefit of sequential information acquisi-tion in that on expectation there is greater coverage ofconsumer segments. On the other hand, both �l and�h increase with a higher wholesale price, leading toa lower probability that the retailer’s posterior beliefreaches �h before �l (i.e., a lower likelihood that bothconsumer segments are covered in equilibrium). Con-sequently, the effect of d on the difference betweenthe manufacturer’s equilibrium ex ante profits is non-monotonic.

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Interestingly, the retailer can ex ante benefit fromthe manufacturer’s sequential information acquisi-tion. This occurs when the prior belief � is neithertoo large such that information acquisition can arisein equilibrium nor too small such that there existsa set of wholesale prices (i.e., ��l −��h�/�1−�� <� ≤ ��h) under which the retailer orders x = �but never x = 1. If instead � = ��l −��h�/�1−�� ischarged, the manufacturer would acquire informa-tion to potentially induce the retailer to order morequantity, leading to a discontinuous increase in themanufacturer’s expected payoff from that when � =��l −��h�/�1−��+ , (i.e., a sufficiently small increasein the wholesale price). Therefore, if the competi-tive margin d is sufficiently close to the cutoff point��l −��h�/�1−�� from above, the equilibrium whole-sale price will be � = ��l −��h�/�1−�� < d. In con-trast, under inflexible information acquisition, theoptimal wholesale price would be � = d. This meansthat the prospect of sequentially manipulating infor-mation collection may induce the manufacturer tocharge a lower equilibrium wholesale price. As aresult, both firms can be strictly better off when infor-mation flow is strategically controlled by the manu-facturer, i.e., a Pareto-improving win-win situation.

5. Ex Post Voluntary InformationSharing

In this section we look at voluntary information shar-ing where the manufacturer can decide whether toshare information on an ex post basis after the infor-mation has been acquired. Thus, in contrast to manda-tory sharing, the retailer’s updated posterior belief,�r , may not coincide with that of the manufacturer,�m, because the manufacturer can choose not to dis-close the acquired signals. Formally, define the man-ufacturer’s information disclosure strategy at stage 3as m� �m�/ �m → M ≡ �m�⊗�, where M is the manu-facturer’s feasible set of messages conditional on �m,and ⊗ represents “no disclosure.” Note that the man-ufacturer’s updated posterior belief �m at the time ofmaking the disclosure decision is determined by itsinformation acquisition strategy at stage 2.

Moreover, we need to characterize the updating ofthe retailer’s posterior belief, �r�m�, in response to thereceived message m ∈ M . Note first that �r� �m�= �m.In addition, the message m=⊗ can be received eitherwhen no useful information is available (i.e., I = �y)or when I = y but the manufacturer withholds itsacquired information. This implies that the updatingof the retailer’s posterior belief �r�⊗� and the man-ufacturer’s optimal information acquisition and dis-closure strategies may influence each other, whichtherefore need to be derived together.

5.1. Inflexible Information AcquisitionWe start with deriving the manufacturer’s optimalinformation sharing strategy. Suppose that the man-ufacturer chooses to acquire information when I = yand is (almost) fully informed. When it is revealedto the manufacturer that S = G, it is in its best inter-est to disclose the information and move the retailer’supdated posterior belief toward �r = �m = 1. Con-versely, when the manufacturer learns that S = B, itwould choose not to disclose the information. Thisimplies that the manufacturer’s optimal informationsharing strategy is m�1�= 1, and m�0�=⊗. Therefore,the message m = ⊗ would be sent by the manufac-turer either when I = �y, or when I = y and the man-ufacturer conceals its updated posterior belief �m = 0.The ex ante probabilities for these two scenarios are1/2 and �1−��/2, respectively. We can use the Bayestheorem to obtain the retailer’s updated belief as�r�⊗�= �/�2−��We can then determine whether the manufacturer

should acquire information when useful informationis available (i.e., I = y) and derive the manufacturer’sequilibrium ex ante payoff.

Proposition 4. Under ex post voluntary informationsharing and when information acquisition is inflexible, inequilibrium the manufacturer decides to acquire informationwhen the information state is I = y. The manufacturer’sequilibrium ex ante payoff is higher than that without infor-mation sharing (i.e., �ns) if and only if

4�l − 2��3−��h

2�l + 1−��4−��!�h

< � <2�

1+�

and

2��l−��h�

�1−�� 2−��+�!

<d<min{

� ��2−��+�!�h

2��2−�� 2−��+�!��l−��h�

2��1−��

}�

and (weakly) lower if otherwise.

Two interesting results pertaining to the effects ofthe flexibility in information sharing emerge fromthis proposition. First, in contrast to the manda-tory information sharing case, acquiring informationis the equilibrium strategy under voluntary shar-ing when information acquisition is inflexible. Thisimplies that the manufacturer would acquire informa-tion when it is not bound to disclose all the acquiredinformation. Intuitively, when information sharing ismandatory, the manufacturer is committed to discloseunfavorable information, which may be undesirablefrom an ex ante perspective. However, when informa-tion sharing is voluntary, the manufacturer can with-hold ex post unfavorable information but disclose

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only favorable information. It is this ex post flexibil-ity that induces the manufacturer to acquire (perfect)information.

Second, the manufacturer may or may not bene-fit from the flexibility to selectively disclose informa-tion. This is driven by the two counteracting effectsexerted by voluntary disclosure that, in contrast tomandatory sharing, results in equilibrium (perfect)information collection. On the one hand, acquiringinformation can lead to a positive payoff effect whenthe acquired information is favorable such that theconsumer segments are more likely to be served thanwhen no information is acquired; i.e., �r�1� = 1 > �.On the other hand, the low-segment consumers maybe unserved when the acquired information conveysnegative news and may be otherwise served when theprior belief is maintained by the retailer under zeroinformation acquisition; i.e., �r�⊗� < �. As a result,there may be a market recession effect of informationacquisition. Note that this market recession effect mayarise even in the scenario when no useful informationis available (i.e., I = �y). This is because the retailercannot distinguish between the scenarios when use-ful information is unavailable and when unfavorableinformation is strategically withheld.

The net effect of the flexibility in information shar-ing on the manufacturer’s ex ante payoff hence hingeson whether on average higher equilibrium marketcoverage is induced. Intuitively, voluntary disclosureis beneficial if and only if the equilibrium market cov-erage is increased when the acquired information isfavorable but not lowered when the information isunfavorable. This requires that the prior belief is inan intermediate range.16 On the one hand, � cannotbe too small, because both the probability that favor-able information would be acquired (i.e., �/2), andthe retailer’s posterior belief when no useful infor-mation is available or when unfavorable informa-tion is acquired (i.e., �r�⊗�), increase with �. On theother hand, the prior belief cannot be too large either,because the potential benefit from inducing highermarket coverage would become less important as �approaches �r�1� = 1. Moreover, for voluntary shar-ing to be beneficial, the competitive margin d shouldtake intermediate values as well. When d is too small,the manufacturer is constrained to set low wholesaleprices such that both consumer segments are servedin equilibrium even under mandatory sharing. Con-versely, when d is sufficiently large, excessively highwholesale prices would be charged in equilibrium,

16 Nevertheless, when the low-segment consumers become suffi-ciently unimportant (i.e., 4�l − 2��3 − ��h < 0) such that marketrecession is less of a concern, voluntary sharing can be beneficialeven when � goes to zero.

such that no consumer would be served when theretailer’s updated posterior belief is �r�⊗�, or only thehigh segment would be covered even when �r = 1, orboth.

5.2. Sequential (Flexible) Information Acquisition

5.2.1. Optimal Information Acquisition and Shar-ing Strategies. When useful information is available,the manufacturer sequentially decides whether to ter-minate the information acquisition process at eachupdated posterior belief �m and then determineswhether to share the acquired information with theretailer. Note that at the time when the sharing deci-sion is made, the manufacturer’s updated posteriorbelief is given by �m ∈ �� ̄�, where � ∈ 0��! and�̄ ∈ ��1! are the boundary points characterizing theoptimal stopping rule for information collection. Thisimplies that the manufacturer’s optimal disclosurestrategy is influenced by its stopping rule for informa-tion acquisition, which is in turn affected by whetherthe manufacturer would choose to disclose the col-lected information.

As in the mandatory sharing case in §4�2, the man-ufacturer will not acquire more information whenever�m ≥ �h, or �m ≥ �l and �h > 1, and will continue theinformation acquisition process whenever �m < �l, or�l < �m < �h ≤ 1, irrespective of the retailer’s updatedposterior belief �r�⊗�. In contrast, the manufacturerwould prefer to collect more information when �m

reaches �l, if and only if �r�⊗� ≥ �l and �h ≤ 1. Thisis because now the manufacturer can strategicallycontrol the disclosure of information to prevent thereduction in retail ordering even when unfavorableinformation is generated (i.e., �m = 0).

We can then determine the manufacturer’s equilib-rium information acquisition and sharing decisionsand the retailer’s equilibrium posterior belief �r�⊗�.First, it is straightforward that when � ≥ �h (or � ≥�l, and �h > 1), in equilibrium the manufacturer willnot start the information collection process and thus�r�⊗� = �. Next, consider the equilibrium wherebythe manufacturer continues to acquire informationuntil either �h or zero is reached. For this to bean equilibrium, the necessary and sufficient condi-tion is �r�⊗� ≥ �l and � < �h ≤ 1. Note also that themanufacturer would disclose the acquired informa-tion when �m = �h is reached and withhold the infor-mation when �m = 0 is reached. Therefore, the mes-sage m=⊗ would be sent by the manufacturer whenand only when (1) the information state is I = �y, or(2) the information state is I = y and the manufac-turer’s updated belief reaches �m = 0. Noticing thatthe ex ante probabilities for these two scenarios are

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1/2 and 1 − *�� 0��h�!/2 = �1 − �/�h�/2, respec-tively, we can obtain

�r�⊗� = �/21/2+ �1−�/�h�/2

= �1−��

2�1−��−��l −��h�� (3)

which sustains �r�⊗� ≥ �l if and only if � ≥2�1−��/��l + �1− 2��h�.

Consider then the equilibrium whereby informa-tion collection is terminated at either �m = �l or�m = 0, which is to be respectively disclosed orconcealed. Given the manufacturer’s strategies, notethat we have �r�⊗� = ��/2�/�1/2+ �1−�/�l�/2� =��/�2�−��h�, which is less than �l if and only if� < �l. This implies that this equilibrium would ariseif and only if � < �l. Moreover, unlike the manda-tory sharing case, there does not exist an equilibriumwhereby the manufacturer continues to acquire infor-mation until either �h or �l is reached. If otherwise,it must be the case that �l ≤ � < �h ≤ 1, which in turnimplies �r�⊗� ≥ �l. However, then it is better off forthe manufacturer to continue information acquisitionwhen arriving at �m = �l.

It follows that there does not exist a pure-strategyequilibrium when �l ≤ � < 2�1−��/��l + �1− 2��h�(and �h ≤ 1). In the mixed-strategy equilibrium, itmust be that (1) the manufacturer is indifferent andrandomizes between continuing and stopping infor-mation acquisition when its updated belief reaches�l, and (2) the retailer is indifferent and randomizesbetween ordering � and zero when it receives noinformation from the manufacturer. Let us define theprobability as 1 that the manufacturer continues toaccumulate signals when �m = �l, and the probabilityas 2 (or 1− 2) that the retailer orders x = � (or x = 0)when m=⊗. The mixed-strategy equilibrium requires

��=*��l � 0��h��+ 1−*��l � 0��h�!2�� (4)

�r�⊗�= �/21/2+1�1−�/�h�/2

= �l� (5)

which lead to

2= ��h −�l

��h −�l�= ��2−��h − �l

��h − �l�∈ �0�1��

and

1= �h��−�l�

�l��h −��= �1−��h −��

�1−��−��l −��h�∈ 0�1��

respectively. Summarizing the above discussion, weobtain the following proposition:

Proposition 5. Under ex post voluntary informationsharing and when information acquisition is sequential,

the optimal stopping rule of information acquisition whenI = y is characterized by two boundary points, � ∈ 0��!

and �̄ ∈ ��1!, such that the manufacturer continues tocollect information unless the updated posterior belief �m

reaches either � or �̄; the optimal disclosure strategyis characterized by m�� ∈ ��⊗� and m��̄� = �̄, whenthe manufacturer stops information acquisition at � or�̄, respectively; and the retailer’s updated belief is givenby �r�m� = m if m �= ⊗, and by �r�⊗� if m = ⊗. Inparticular,

(i) If �≤ ��l−��h�/�1−��, then �= �̄= �, m��=�r�⊗�= �, �′ =�, and � ′ = ��l −�;(ii) If

��l −��h�

1−�< �≤min

{� �l + �1− 2��h!

2�1−��

�l −��h

1−�

}�

then � = 0, �̄ = �h, m�� = ⊗, �r�⊗� = �1−��/�2�1−��−��l −��h��, �′ = ��l − ��h� + ��, and� ′ = ��h −��;

(iii) If

min{

� �l + �1− 2��h!

2�1−��

�l −��h

1−�

}

< �≤min{��h�

�l −��h

1−�

}�

then � = 0 or � = �l with probability 1 = �h��− �l�/

��l��h −�� or 1−1, respectively, �̄= �h, m�0�=⊗,

m��l�= �r�⊗�= �l�

�′ = �1−��h��l −��h�

�h − �l

+ ��2−��h − �l!�

�h − �l

�

and � ′ = �2�h + �1− 2��l!��h −��/��h − �l�;(iv) If ��l −��h�/�1−�� < � ≤ ��h, then � = �̄ = �,

m��= �r�⊗�= �, �′ = ��, and � ′ = ��h −��; and(v) If � > ��h, then �= 0, �̄= �l, m��=⊗, �r�⊗�=

��/�2�−��h�, �′ = ��h, and � ′ = 0.

In comparison to mandatory sharing (i.e., Propo-sition 2), voluntary sharing leads the manufacturerto generate a larger amount of information.17 Thisimplies that, similar to the cases when informa-tion acquisition is inflexible (i.e., §§4�1 and 5�1),the manufacturer’s flexibility to selectively discloseits acquired information can promote more infor-mation acquisition. When ��l −��h�/�1−�� < � ≤min��h� ��l −��h��1−��, for example, the lowerbound at which the manufacturer stops collecting

17 This can be seen by comparing the amount of information acqui-sition in Proposition 5(ii) and (iii) under voluntary sharing to that inProposition 2(ii) under mandatory sharing. In addition, the respec-tive parameter ranges (on �) and the amount of information acqui-sition in the other parts are identical in both propositions.

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information is � = �l under mandatory sharing butcan be extended to �= 0 if information sharing is vol-untary. This is because, if information collection con-tinues when the updated posterior belief is at �m = �l,the acquired unfavorable information (i.e., �m = 0) canbe strategically withheld and therefore does not nec-essarily induce less retail ordering.

Interestingly, there may exist a mixed-strategy equi-librium (i.e., Proposition 5(iii)) where the manu-facturer randomizes the lower bound of stoppinginformation acquisition between � = �l and � = 0.This mixed-strategy equilibrium arises because theretailer’s belief when it does not receive any infor-mation from the manufacturer, �r�⊗�, is positivelyinfluenced by the equilibrium lower bound of infor-mation acquisition. If the lower bound were placedat �l for sure, the retailer’s updated posterior belief�r�⊗� would be above �l. However, then it is bet-ter off for the manufacturer to deviate and (secretly)decrease the lower bound of information acquisition.On the other hand, if the lower bound were placed atzero for sure, the retailer would update its posteriorbelief �r�⊗� sufficiently downward and below �l andthus would order zero amount for sure if no infor-mation is received from the manufacturer. However,this discourages the manufacturer from extending thelower bound of information acquisition toward �= 0.

Nevertheless, the flexibility to sequentially deter-mine how much information to acquire does not nec-essarily promote the amount of information generatedin equilibrium. Whether it does so depends on the for-mat of information sharing. Looking first at voluntarysharing, recall from Proposition 4 that when informa-tion acquisition is inflexible and the manufacturer isconstrained to acquire either none or perfect informa-tion, acquiring information is the dominant strategyfor the manufacturer. Thus, the equilibrium amountof information generated decreases from perfect infor-mation when information acquisition is inflexible toless than perfect information when the manufac-turer can sequentially decide how much informa-tion to acquire. This result stands in contrast to the

Figure 4 The Firms’ Expected Payoffs Under Voluntary Sharing �< ��l − ��h�/��1− ��h�

d, w d, w

Π�

Π(w)

Π′′Π′

��

� (w)

� ′′�′

��h��h

��h

�(�l – ��h)

1 – �

�[�l + (1– 2�)�h]

2(1 – �)

�[�l + (1– 2�)�h]

2(1 – �)

�(�l – ��h)

1 – �

�(�l – ��h)

1 – �

case of mandatory sharing, where the equilibriumamount of information generated increases from zerowhen information acquisition is inflexible (i.e., Propo-sition 1) to a positive amount when the manufac-turer can sequentially decide how much informationto acquire (i.e., Proposition 2). Overall, our analysissuggests that the equilibrium amount of informationacquired depends on the interaction between the flex-ibility in information acquisition (sequential versusinflexible) and the flexibility in information sharing(voluntary versus mandatory).

5.2.2. Equilibrium Ex Ante Profits. The firms’equilibrium ex ante payoffs under voluntary shar-ing are shown in Figure 4 for the case when � <��l − ��h�/��1−��h�. We will focus on the compari-son with the mandatory sharing case in §4�2.

Proposition 6. Under ex post voluntary informationsharing and when information acquisition is sequential:(i) if both � and d are intermediate, the manufacturer’sequilibrium ex ante payoff is higher than that undermandatory information sharing; and (ii) if � is sufficientlysmall, the manufacturer’s (retailer’s) equilibrium ex antepayoff can be lower (higher) than that under mandatoryinformation sharing.

This proposition indicates that, when informationacquisition is sequential, voluntary sharing can benefitthe manufacturer in comparison to mandatory shar-ing only if the prior belief � is intermediate but canhurt the manufacturer if the prior belief is sufficientlylow. To understand this result, note that the flexi-bility under voluntary sharing can induce the man-ufacturer to collect more (unfavorable) information,extending the lower bound of information acquisitionto � = 0. This increase in information generation hastwo offsetting effects on the manufacturer’s ex antepayoff. On the one hand, it escalates the likelihoodthat the upper bound of information acquisition is

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reached in which case the retailer would order x = 1;i.e., *�� ̄� = ��−��/��̄−�� decreases with thelower bound �. This implies an increase in the man-ufacturer’s expected payoff �′ when the informationstate is I = y. On the other hand, collecting more unfa-vorable information may drive down the retailer’supdated posterior belief when no information is dis-closed by the manufacturer. That is, �r�⊗� is lowerwhen the lower bound is extended to �= 0. This inturn has a negative effect on the retailer’s orderingquantity and thus on �′′ when the information stateis I = �y.

Therefore, whether voluntary sharing leads to ahigher equilibrium ex ante payoff for the manufac-turer hinges on whether the retailer is not induced toorder less when its updated posterior belief is givenby �r�⊗�. Note that �r�⊗� is positively related to theprior belief �. As a result, when � is not sufficientlysmall, the increase in the acquired information undervoluntary sharing does not lead to lower retail order-ing because the mixed-strategy equilibrium will notarise. However, when the prior belief � becomes suf-ficiently large, the maximum ordering of one unitwould be induced in equilibrium even under manda-tory sharing. Thus, it is only when � is in an interme-diate range that the manufacturer is better off undervoluntary sharing.

In contrast, when � is sufficiently small, the mixed-strategy equilibrium will occur in which case theretailer would order less, hurting the manufacturer’sequilibrium ex ante profit. As the proof shows, this isespecially the case when the low-segment consumers’valuation �l is relatively high. Moreover, when thiseffect becomes sufficiently severe, the manufacturer inequilibrium charges a lower wholesale price than itscompetitive margin d to cope with this demand reces-sion problem. However, in the corresponding scenariounder mandatory sharing, the manufacturer wouldin equilibrium charge �= d. This explains why theremay exist equilibrium conditions under which themanufacturer is worse off, while the retailer is bet-ter off, when the former can selectively disclose itsacquired information, i.e., a lose-win situation.

In summary, the economic forces underlying theeffect of the flexibility in information sharing on themanufacturer’s equilibrium ex ante profits are simi-lar to those when information acquisition is inflexible(i.e., §5�1): sharing information voluntarily with theretailer leads to an increasing incentive for the manu-facturer to acquire information, but generating moreinformation is a double-edged sword that can in equi-librium improve the manufacturer’s ex ante payoffwhen and only when on average more retail orderingis induced.

6. Extensions and Robustness ofResults

6.1. Flexible Wholesale PriceIn the base model the choice of the wholesale priceprecedes the manufacturer’s information acquisitionand hence does not respond to the acquired informa-tion. Our intention in assuming this timing was torule out the efficiency effect of information acquisitionon the manufacturer’s decision on wholesale price,and rather to focus on the strategic effect of informa-tion acquisition on retailer behavior. We now consideran alternative model timing whereby the wholesaleprice is decided in the third stage of the game.18 Otherassumptions in the base model are maintained.

We start with deriving the optimal wholesale price,conditional on d and the retailer’s updated pos-terior belief �r following the manufacturer’s infor-mation acquisition/disclosure decisions. Given theretailer’s optimal behavior as laid out in §3�1, it isstraightforward that the optimal wholesale price is� = mind� �r��l −��h�/�1−�� if d ≤ �r��l −��h�/��1−��, and � = mind� �r�h� if otherwise. As aresult, the manufacturer’s equilibrium sub-game pay-off in Stage 3 is given by

�� r�=

�mind� �r�h�� if �r ≤��1−��d

�l−��h

%

min{d�

�r��l−��h�

1−�

}� if otherwise�

(6)

Define �L ≡ d/�h and �H ≡ �1−��d/��l −��h�. Weconcentrate on the interesting scenario � < �H ≤ 1: themanufacturer will surely stop information acquisitionwhen its (prior or updated) belief is not lower than�H . We provide the full characterization of the man-ufacturer’s equilibrium information acquisition andsharing strategies in the electronic companion (avail-able as part of the online version that can be foundat http://mktsci.pubs.informs.org) and show that thekey results are qualitatively similar to those in thebase model. In particular, when information acquisi-tion is inflexible, the manufacturer decides to (decidesnot to) acquire information if sharing is voluntary(mandatory). In addition, when information acqui-sition is sequential and sharing is mandatory, themanufacturer continues to collect information untilthe firms’ (symmetric) posterior belief reaches �H ,�L, or zero. In contrast, when information acquisi-tion is sequential and sharing is voluntary, the man-ufacturer may continue information collection even

18 It does not matter whether information sharing and the wholesaleprice are determined simultaneously or sequentially in the thirdstage. Nevertheless, to facilitate exposition, the analysis will pro-ceed as if the wholesale price is set after the information disclosuredecision is made.

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when its posterior belief arrives at �L. This is becausethe manufacturer can ex post withhold unfavorableinformation, leading to an increasing ex ante incen-tive for information acquisition. Indeed, this informa-tion withholding effect is stronger here than in thebase model, because the concern about acquiring badsignals can be mitigated when the wholesale priceis adjusted in response to the acquired information.Therefore, flexible wholesale prices can in equilibriumresult in more information acquisition than when thewholesale prices are chosen before the informationacquisition.

6.2. Retailer Information AcquisitionIn the base model the retailer does not acquire anyinformation but relies on the disclosure by the man-ufacturer. However, in many real market situations,the retailer may also acquire useful information aboutdemand uncertainty. As indicated in Gal-Or et al.(2008), this may be particularly true in the case of exante data pooling arrangements such as collaborativeplanning, forecasting, and replenishment. Considernow the case when the retailer also has the ability toacquire information and be informed of the perceivedproduct fit at an acquisition cost c. Let this acquisitioncost take two possible values, i.e., c ∈ ch� cl�, where ch

is prohibitively high and cl is negligible. The probabil-ity for cl and ch are 4 and 1−4, respectively, where 4 ∈�0�1�. The retailer’s information acquisition cost (andthus whether the retailer is informed) is unknown tothe manufacturer. For example, retailers can analyzesales data they possess or collect local market infor-mation to improve their knowledge about consumerpreference, where c can represent the retailer’s oppor-tunity cost to process and analyze sales data, to con-duct market research, or to transmit the derived infor-mation to decision makers in the organization (e.g.,procurement manager).19 Under this extension, it isstraightforward to show that the manufacturer’s equi-librium information acquisition and sharing strategiesremain the same as in the base model. Nevertheless,the ex ante probability that the retailer’s behaviorcan be strategically manipulated by the manufactureris reduced when 4 becomes higher. As a result, themanufacturer’s economic rents derived from sequen-tially controlling the information acquisition processare reduced as 4 increases but do not collapse tozero as long as the retailer’s information acquisitionis imperfect (i.e., 4 < 1).

6.3. Continuous DemandThe two-segment assumption in the base modelresults in a discrete demand function. Consider now

19 Alternatively, we can assume zero retailer acquisition costs andinterpret 4 as the degree of informativeness of the retailer’s data.

an alternative setup in which aggregate consumerdemand is continuous and given by

D�p�= a− bp� (7)

where a > 0 denotes market potential, p is the retailerprice, and b > 0 captures price sensitivity. Akin tothe base model, market potential is uncertain and cantake two possible values, a ∈ ah� al�. The firms havecommon prior belief about the realization of marketpotential: Pr�a= ah�= � and Pr�a= al�= 1−�, where� ∈ �0�1�. The manufacturer can acquire (imperfect)signals to resolve the uncertainty about market poten-tial, in the same manner as in the base model. To facil-itate exposition without sacrificing conceptual gist, wefocus on the scenario when 0 < ah − al < al and b issufficiently low relative to a.

As we show in the electronic companion, the maininsights in the base model also hold for this alterna-tive demand setup, irrespective of whether the whole-sale price is set before or after information acqui-sition. The manufacturer may not acquire perfectinformation even though doing so is costless, whenit can collect information in a sequential manner.Moreover, the flexibility in information acquisition canresult in a larger (smaller) amount of informationgenerated when sharing is mandatory (voluntary).In contrast, the flexibility in information sharing canunambiguously induce the manufacturer to acquiremore information.

We also consider an alternative model in which theprior probability � of perceived product fit followsa continuous distribution (for example, a uniform ora Beta distribution) over which the parties integratefor decision making. The manufacturer sequentiallyacquires informative signals about the underlyingproduct fit that are independently generated from thetrue states exactly as in the base model. It can thenbe shown, given risk neutrality of the parties, that allthe results of the paper are robust to this extension ofthe basic model with a continuous prior on �.

More generally, consider realized retail demandD�p�Q� that is positively influenced by the product fitQ which has a prior probability �. Let � be the firms’(posterior) belief after information acquisition thatthe product fits consumer preference. The expecteddemand will be based on the updated belief � andwill influence retail ordering. Suppose the retailer’soptimal ordering decision is x� ��, which is an increas-ing, continuous, and twice-differentiable function of �.The other assumptions are the same as in the basemodel. We can then characterize the manufacturer’soptimal information acquisition and sharing strate-gies, which are qualitatively similar to the base model.For example, suppose that x�·� is S-shaped: x�·� is con-vex when � ∈ 0� �′! and concave when � ∈ �′�1!.

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Under sequential information acquisition and manda-tory sharing, the manufacturer will continue to col-lect information if and only if the posterior belief isin �0� �̄�, where the upper bound �̄ is determinedby 'x��̄�/�'�̄� = �x��̄�− x�0��/�̄, and �̄ > �′. The casewhen acquisition is sequential and sharing is vol-untary is similar, except that now �̄ is determinedby solving 'x��̄�/�'�̄� = �x��̄�− x� �r�⊗��/�̄, where�r�⊗�= ��/2�/�1/2+ �1−�/�̄�/2�. Alternatively, if x�·�is first concave and subsequently convex, then we willget through similar arguments that the manufacturerwill continue information collection (in the mandatorycase) if and only if the posterior belief is in ��1�,where the lower bound � is determined by solving'x��/�'�� = �x�1�− x��/�1−��. Therefore, we con-clude that our results are robust to a fairly general setof demand setups.

7. ConclusionIn many markets characterized by fashion or sea-sonal cycles, short product life span, new prod-uct proliferation, and the resulting uncertainty aboutconsumer preferences or market demand, firms invertical relationships can benefit from uncertainty-resolving information. We investigate a manufac-turer’s optimal information acquisition and sharingdecisions in exerting strategic influence on its down-stream retailer’s behavior. Our paper departs fromextant studies that focus mainly on either nonsequen-tial information acquisition or mandatory sharing,each of which is typically analyzed in isolation andusually in the context of horizontal oligopolies. Ouranalysis is the first to jointly examine both informa-tion acquisition and sharing by a manufacturer in avertical system. This allows us to uncover the strate-gic interaction between these two decisions and exam-ine how it is influenced by both the flexibility ininformation acquisition and the flexibility in sharingformat.

7.1. Implications of the Key FindingsThis paper obtains several results that provide usefulmanagerial insights into strategic information man-agement in vertical relationships. We demonstratethat a manufacturer can wield information powerover its downstream retailer not only through selec-tively withholding unfavorable information, but alsothrough strategically controlling the generation ofinformation. First, when information acquisition issequential, the manufacturer should exercise self-restriction in information acquisition and refrain fromacquiring perfect information, even if it is costless todo so. To influence the retailer’s belief, the manu-facturer may terminate information collection eitherwhen the acquired information is sufficiently favor-able or before an overly adverse outcome arises. As

such, we identify “strategic ignorance” in informationacquisition as a new mechanism that can be used byfirms to manage channel relationships. The analysissuggests that manufacturers should take this strate-gic impact into account in their endeavors to resolveuncertainty about consumer preferences, which is par-ticularly relevant as sequential monitoring of infor-mation acquisition becomes increasingly prevalent(e.g., online research instruments, syndicated con-sumer databases).

Interestingly, we show that the manufacturer shouldcollect either more or less information as sequentialinformation acquisition becomes increasingly feasi-ble, depending on the format of information shar-ing. Under mandatory sharing, the manufacturer canmanipulate the retailer’s belief only through the con-trol over the information acquisition process, and thusshould acquire information only when this strategiccontrol is available. Conversely, voluntary sharing per-mits the manufacturer to manipulate the retailer’sbelief through the ex post control over the shared infor-mation, which thus motivates the manufacturer to exante acquire more information. As a result, the impactof the flexibility in information acquisition on the man-ufacturer’s optimal acquisition strategy is moderatedby the flexibility in information sharing. In contrast,irrespective of the level of flexibility in informationacquisition, the flexibility to selectively decide whetherto share the acquired information should generallylead the manufacturer to collect more information,which follows from the manufacturer’s ability undervoluntary sharing to disclose favorable informationwhile credibly withholding unfavorable information.

The above insights provide useful prescriptionson how manufacturers should respond to changesin information collection technologies and in infor-mation sharing arrangements. When manufacturersmove increasingly from standard information collec-tion technologies (e.g., mail surveys, mall intercepts,field testing) to those that allow for sequential mon-itoring (e.g., online surveys, syndicated databases),how should they adjust their information acquisitionpolicies? The results above suggest that manufactur-ers may indeed strive to collect more informationwhen they have committed ex ante to mandatorilyshare the information. In addition, for manufactur-ers who have set up more formal arrangementsto mandatorily share information with downstreamfirms (e.g., Procter & Gamble, Warner-Lambert),greater scrutiny should be employed regarding theamount of information to generate than their counter-parts who rely primarily on ex post voluntary sharingfor channel communication. They should generally bemore conservative in information acquisition, espe-cially when they do not have access to information

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collection technologies that afford sequential controlover the data generation process.

Moreover, we investigate the conditions underwhich the manufacturer should pursue the ex postflexibility in disclosing its acquired information to theretailer. Counterintuitively, the manufacturer may notnecessarily prefer to maintain its flexibility in infor-mation sharing. In particular, our results suggest thatthe manufacturer’s preference for the ex ante commit-ment to mandatorily share information is influencedby the prior belief on consumer preference. When theprior belief is sufficiently low and thus the product ismore likely to be perceived as a bad fit, the manufac-turer may want to commit to mandatorily share theacquired information and thereby choose to give upthe flexibility to voluntarily disclose information (i.e.,the ex post strategic influence over the retailer). Com-mitting to mandatorily disclose the collected infor-mation can then serve as a self-disciplining deviceto acquire less information, which may paradoxicallyinduce the retailer to order higher amounts whenthe likelihood of product failure is high. For exam-ple, in many fashion markets only a small fraction ofdesigns may ultimately succeed in any given season.In such environments, ex ante commitments by man-ufacturers to share the to-be-acquired information canbe valuable. Not surprisingly, a number of successfulmandatory information sharing arrangements havebeen documented in markets such as fashion appareland consumer electronics (Hammond et al. 1991).

7.2. Discussion and Future ResearchOne implicit assumption in our model is that con-sumer preference does not change throughout thegame and that retail ordering does not occur beforeinformation acquisition (either inflexible or sequen-tial) can be completed.20 This will be the case if abun-dant information can be gathered in a relatively shorttime period (e.g., online surveys, subscription to syn-dicated databases) and if there is significant lead timebetween upstream production and downstream sell-ing (i.e., new market, product entry). For example,consumer tastes in most markets are relatively sta-ble in the short run and sequential market researchstudies can be run before the start of retail ordertaking during a fashion or season cycle (Doeringerand Crean 2006). Note also that a finite number ofsignals are sufficient to reasonably resolve the firms’uncertainty—the marginal information contained ineach additional signal is decreasing. Nevertheless, theresults of this paper will continue to hold, even inscenarios when consumers change their preferencesindependently or market demand (and thus retail

20 We thank the review team for inspiring some of the discussionsin this section.

ordering) arises in each period in which one piece ofinformation can be acquired. However, an interestingcase for future research is when consumers changetheir preferences systematically over time because ofsome endogenous mechanism such as social commu-nication or learning from experiences. In these casesthe manufacturer’s sequential information acquisitionstrategy will be more involved because it is condi-tional not only on the updated posterior belief butalso on time.

It is instructive to discuss other (nonstrategic) con-siderations that may influence a manufacturer’s rel-ative preference for the different information sharingformats. First, mandatory sharing is normally imple-mented through data pooling systems that involvebilateral information exchange by both upstream anddownstream firms. As a result, a manufacturer maybenefit from such systems if the information providedfrom downstream can improve the efficiency of themanufacturer’s decision making. The current analysiscan thus be seen as isolating the commitment from theefficiency effect of such systems. Second, the sharingformats may involve different cost implications. Gen-erally, data pooling arrangements involve fixed setupcosts, whereas voluntary sharing decisions may incuronly marginal costs. Interestingly, however, a lowermarginal cost of information sharing does not neces-sarily lead to a higher ex ante preference for volun-tary sharing. This is because a higher marginal costof information sharing can facilitate strategic informa-tion concealment under voluntary sharing, leading toa nonmonotonic net effect on ex ante payoffs (Guo2009). Moreover, mandatory sharing is more likely tobe preferred in environments with higher marginalcosts of information acquisition, because the manufac-turer’s expected payoff is hurt more under voluntarysharing that involves more equilibrium informationcollection.

Another problem that seems to be a good candi-date for future investigation is the role of explicitand costly mechanisms that will induce truth tellingin ex post voluntary sharing arrangements (Ziv1993). One can also investigate bilateral informationexchange in a more comprehensive framework inwhich both firms in a vertical system can acquire andshare information to influence each other’s decisionmaking. The analysis will be similar to this paper ifeach firm has exclusive access to information on dif-ferent types of uncertainty (e.g., product fit versusdemand). Conversely, if the firms can acquire infor-mation on the same type of uncertainty, their optimalinformation acquisition and sharing strategies willinteract with each other. Interestingly, however, onemay conjecture that a firm may have an incentiveto stop the information acquisition process in orderto mitigate the chance that the (common) posterior

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belief is updated by the other firm’s acquired signalstoward the undesirable direction. Of course, all theseissues pertaining to sequential information acquisi-tion and sharing that are currently studied in thispaper, are not necessarily unique to vertical relation-ships and can be examined analogously in the contextof horizontal oligopolies.

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

AcknowledgmentsThe authors thank the editor, the area editor, two anony-mous reviewers, Tony Cui, Anthony Dukes, RaphaelThomadsen, and seminar participants at Cheung KongGraduate School of Business, Summer Institute in Com-petitive Strategy 2008, Beijing University, and MarketingScholar Forum 2009 for valuable comments. The usual dis-claimer applies.

Appendix.Proof of Lemma 1. Let us define

+S�N�≡*S� ��N� � �L� �H�

as the conditional probability (on S ∈ G�B�) that the netnumber of good signals reaches NH before NL, as a func-tion of the starting point N ∈ NL�NH!. Note that by defini-tion +G�N� = �+G�N + 1� + �1− ��+G�N − 1�� where N ∈NL +1� � � � �NH −1�. This is a second-order difference equa-tion, where the boundary conditions are +G�NL� = 0 and+G�NH�= 1. We can then obtain the solution:

+G�N�= 1− ��1−��/��N−NL�

1− ��1−��/��NH−NL��

where N ∈ NL� � � � �NH�� (8)

Similarly, the second-order difference equation condi-tional on S = B is +B�N�= �1−��+B�N + 1�+�+B�N − 1�,where N ∈ NL + 1� � � � �NH − 1�, +B�NL� = 0, and+B�NH�= 1. The solution is

+B�N�= 1− ��/�1−��N−NL�

1− ��/�1−��NH−NL��

where N ∈ NL� � � � �NH�� (9)

Note that by definition

�L ≡ ��NL�=�̇

�̇+ �1− �̇��1−��/��NL�

and�H ≡ ��NH�= �̇

�̇+ �1− �̇��1−��/��NH�

which can be inverted to obtain NL as a function of �L

and NH as a function of �H , respectively. Plugging theseinverted solutions into (8) and (9), respectively, we thereforehave *G��̇ � �L� �H�=+G�0�= �H��̇− �L�/��̇� �H − �L�� and

*B��̇ � �L� �H�=+B�0�= �1− �H��̇− �L�/��1− �̇�� H − �L��.Finally, we obtain *��̇ � �L� �H�≡ �̇*G��̇ � �L� �H�+ �1− �̇� ·*B��̇ � �L� �H�= ��̇− �L�/� �H − �L�. Q.E.D.

Proof of Proposition 1. Suppose that the manufac-turer acquires information when I = y. The manufac-turer’s expected payoff is hence given by � = �� if � ≤��l −��h�/�1−��, � = �� if ��l −��h�/�1−�� < � ≤ �h,and �= 0 if otherwise. This expected payoff is higher thanthat when no information is acquired at all, if and onlyif � > � and ��l −��h�/�1−�� < � ≤ ��l − ��h�/�1−��, or��h < �≤ �h.

Let us then derive the equilibrium wholesale price. Con-sider first the case when d ≤ ��h. If furthermore � < �,the manufacturer’s expected payoff with information acqui-sition is always lower than that when no informationis acquired at all. If instead � > �, information acquisi-tion is desirable if and only if ��l −��h�/�1−�� < � ≤��l −��h�/�1−��. However, charging a wholesale price inthe range � ∈ ��l −��h�/�1−�� l −��h��1−��!, irre-spective of the subsequent information acquisition decision,is ex ante dominated by charging � = ��l −��h�/�1−��.Similarly, in the case d > ��h, it is always dominant for themanufacturer to charge �= ��h. As a result, the equilibriumwholesale price is the same as that in the benchmark with-out information sharing. The proposition follows. Q.E.D.

Proof of Proposition 2. If � ≤ ��l −��h�/�1−�� (i.e.,� ≥ �h), the manufacturer would not start the informationacquisition process and the retailer would order x = 1. Itfollows that �= �̄= �, �′ =�, and � ′ = ��l −�.

If ��l −��h�/�1−�� < � ≤ min��h� ��l −��h�/�1−��(i.e., �l ≤ � < �h ≤ 1), the manufacturer would continuethe information acquisition process until � reaches either� = �l or �̄ = �h. The manufacturer’s expected pay-off is then �′ = *�� l��h�� + 1 − *�� l��h�!�� =�1−��h��l −��h�/��h − �l� + ��2−��h − �l!�/��h − �l�,and the retailer’s is

� ′ = �[*G�� l��h��l + 1−*G�� l��h�!��h

]− [

*�� l��h��+ 1−*�� l��h�!��]

= ��h −��

If ��l −��h�/�1−�� < � ≤ ��h (i.e., �l ≤ � < 1 < �h), themanufacturer would not collect any information and theretailer would order x = �, which leads to � = �̄ = �, �′ =��, and � ′ = ��h −��.

Finally, if � > ��h (i.e., � < �l), the manufacturer wouldcollect information until either it is learned almost withcertainty that S = B or � reaches �l; i.e., �= 0 and�̄ = �l. The manufacturer’s expected payoff is then �′ =*�� 0��l�� = ��h, and the retailer’s is expected payoff� ′ = �*G�� 0��l��h −*�� 0��l��= 0. Q.E.D.

Proof of Proposition 3. When I = �y, no useful infor-mation is available and the manufacturer’s expected payoff,conditional on � ≤ d, is �′′ = � if � ≤ ��l −��h�/�1−��,�′′ = �� if ��l −��h�/�1−�� < � ≤ ��h, and �′′ = 0if otherwise. When I = y, the manufacturer wouldacquire information if and only if ��l −��h�/�1−�� <� ≤ min��h� ��l −��h�/�1−�� or � > ��h, where itsexpected payoff is �′ = �1−��h��l −��h�/��h − �l� + ��2−��h − �l!�/��h − �l� or �′ = ��h, respectively; if oth-erwise, then �′ = �′′. To derive the equilibrium wholesale

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price and the firms’ ex ante payoffs, we consider two alter-native parameter ranges.Range (i): � ≤ ��l −��h��1−��h�. In this case, ��h ≤

��l −��h�/�1−��. Therefore, when ��l −��h�/�1−�� < d ≤��h, the manufacturer would charge �= d if

12

{�1−��h��l −��h�

�h − �l

+ ��2−��h − �l!d

�h − �l

}+ 1

2�d

≥ ��l −��h�

1−��

and �= ��l −��h�/�1−�� if otherwise. The firms’ equilib-rium ex ante payoffs are then given by, respectively,

�mi =

min{d�

��l−��h�

1−�

}�

if d≤ ��l−��h� �1+��2−��h−2�l!

�1−�� 3−��h−�1+��l!%

min{

�1−��h��l−��h�

2��h−�l�

+ ��3−��h−�1+��l!d

2��h−�l��h

}�

if otherwise�

�mi =

��l−min{d�

��l−��h�

1−�

}�

if d≤ ��l−��h� �1+��2−��h−2�l!

�1−�� 3−��h−�1+��l!%

��h−�mind��h�� if otherwise�

Note that �mi > �ns if and only if

��l −��h� �1+��2−��h − 2�l!

�1−�� 3−��h − �1+��l!< d < ��h�

and �mi < �ns if and only if

��l −��h� �1+��2−��h − 2�l!

�1−�� 3−��h − �1+��l!< d <

��l −��h�

��1−��%

if otherwise, then �mi =�ns and �m

i =�ns.Range (ii): � > ��l − ��h�/��1− ��h�. In this case, ��h >

��l −��h�/�1−��. The manufacturer’s expected payoff, con-ditional on �≤ d, is then ��=� if �≤ ��l−��h�/�1−��,

��= �1−��h��l −��h�

2��h − �l�+ ��3−��h − �1+��l!�

2��h − �l�

if��l −��h�

1−�< �≤ �l −��h

1−��

�� = �� if ��l − ��h�/�1 − �� < � ≤ ��h, and �� =��h/2 if � > ��h. Note that

�1−��h��l −��h�

2��h − �l�+ ��3−��h − �1+��l!�

2��h − �l�

is lower than � when � → ��l − ��h�/�1− ��, and higherthan �� when � → ��l − ��h�/�1 − ��. Moreover, thereexists a �̃ ∈ ��l − ��h�/��1− ��h��1�, such that �1− ��h ·��l −��h�/�2��h − �l��+ ��3−��h − �1+��l!�/�2��h − �l��is lower than ��l −��h�/�1−�� when �→ �l −��h/�1−��if and only if � > �̃.

Therefore, if � ≥ �̃, the manufacturer would charge� = ��l − ��h�/�1 − �� when ��l − ��h�/�1 − �� ≤ d ≤

��l − ��h�/��1 − ��. As a result, the manufacturer inequilibrium would not acquire any information even whenI = y, and its equilibrium ex ante payoff �m

ii is the same asthat without information sharing (i.e., �ns). If ��l − ��h�/��1 − ��h� < � < �̃, the manufacturer would charge � =��l −��h�/�1−�� if

��l −��h�

1−�< d ≤ ��l −��h� �1+��2−��h − 2�l!

�1−�� 3−��h − �1+��l!�

�= ��l −��h�/�1−�� if

�l −��h

1−�

< d ≤ ��l −��h� ��3− 2��−�2�1−��+��h − �1+��l!

2��1−��h − �l��

� = ��h if d > ��h, and � = d if otherwise. Thus, when��l − ��h�/��1− ��h� < � < �̃, the manufacturer in equilib-rium would acquire information when I = y if and only if

��l −��h� �1+��2−��h − 2�l!

�1−�� 3−��h − �1+��l!

< d <��l −��h� ��3− 2��−�2�1−��+��h − �1+��l!

2��1−��h − �l��

where its equilibrium ex ante payoff �mii is higher than that

without information sharing (i.e., �ns).When ��l −��h�/��1−��h� < � < �̃ and

max{

�l −��h

1−��

��l −��h�

��1−��

}

< d <��l −��h� ��3− 2��−�2�1−��+��h − �1+��l!

2��1−��h − �l��

note that the optimal wholesale price � = ��l − ��h�/�1−�� is lower than that when information sharing is infea-sible (i.e., w = d). This implies that the retailer’s equilibriumex ante payoff under mandatory information sharing andsequential information acquisition can be higher than thatwithout information sharing (i.e., �ns). Q.E.D.

Proof of Proposition 4. Suppose that the manufactureracquires information when I = y, which leads to �m = 1 or�m = 0, with probability � or 1−�, respectively. Because themanufacturer’s expected payoff increases with the retailer’supdated posterior belief �r , the manufacturer’s optimaldisclosure strategy is m�1�= 1 and m�0�=⊗. Knowing this,the retailer’s updated posterior beliefs are �r�1� = 1 and�r�⊗� = �/�2 − ��. This is because, the message m = ⊗would be delivered either when no useful information isavailable, or when the manufacturer’s updated posteriorbelief is zero (i.e., �m = 0). As a result, it is indeed an equilib-rium strategy for the manufacturer to acquire informationbecause �r�1� > �r�⊗�. To prove the uniqueness of the equi-librium, suppose instead that no information is acquiredwhen I = y, which results in �r�⊗� = �. However, then themanufacturer can benefit from deviating and choosing toacquire information: the manufacturer can send m=⊗ anddo no worse when the acquired information indicates S = B,and can do better when the acquired information indicatesS =G.

The setting of the wholesale price takes into account thesetwo equilibrium scenarios on the retailer’s updated pos-terior belief: �r ∈ 1��/�2 − ��. In particular, when I = y

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and the manufacturer subsequently learns that �m = 1, itwill disclose the information to the retailer whose updatedposterior belief is then �r�1� = 1, the ex ante probabilityof which is �/2. In addition, when I = �y, or when I = yand the manufacturer subsequently learns that �m = 0, theretailer would receive the message m = ⊗ and update itsbelief toward �r�⊗� = �/�2− ��, the ex ante probability ofwhich is 1−�/2.Range (i): � < 2��l − ��h�/��l + �1 − 2��h�. In this case,

�r�⊗��l −��h�/�1−�� < �r�⊗��h < �r�1��l −��h�/�1−�� <�r�1��h. The manufacturer’s expected payoff is �� = �when � ≤ �r�⊗��l − ��h�/�1 − ��. Similarly, the manu-facturer’s expected payoff is �� = ��/2 + ��1 − �/2��when �r�⊗��l − ��h�/�1− �� < � ≤ �r�⊗��h, �� = ��/2when �r�⊗��h < � ≤ �r�1��l − ��h�/�1 − ��, and �� =��/2 when �r�1��l − ��h�/�1 − �� < � ≤ �r�1��h. Notethat the manufacturer’s expected payoff increases with� within each of the above four ranges, and discon-tinuously drops at the boundary points. Note also that�� = � → ��l − ��h�/��1 − ��2 − �� when � →�r�⊗��l −��h�/�1−��,

��= ��/2+��1−�/2��→ � ��2−��+�!�h

2�2−��

when � → �r�⊗��h, �� = ��/2 → ��l − ��h�/�2�1− ��when � → �r�1��l − ��h�/�1 − ��, and �� = ��/2 →��h/2 when �→ �r�1��h. Moreover,

��l −��h�

�1−��2−��<

� ��2−��+�!�h

2�2−��

� ��2−��+�!�h

2�2−��>

��l −��h�

2�1−��

and

� ��2−��+�!�h

2�2−��>

��h

2�

Noticing that

��/2+��1−�/2��= ��l −��h�

�1−��2−��

when�= 2��l −��h�

�1−��2−�� 2−��+�!�

we can then obtain the manufacturer’s equilibrium ex antepayoff, when � < 2��l −��h�/��l + �1− 2��h�:

�ivi =

min{d�

��l −��h�

�1−��2−��

}�

if d ≤ 2��l −��h�

�1−��2−�� 2−��+�!%

min{ ��2−��+�!d/2�

� ��2−��+�!�h

2�2−��

}�

if otherwise�

Comparing �ivi with �ns, we obtain

2��l −��h�

�1−��2−�� 2−��+�!<

��l −��h�

��1−��

��l −��h�

�1−��2−��<

��l −��h�

1−��

��2−��+�!d/2 > �d, � ��2−��+�!�h/�2�2−�� < ��h,and

� ��2−��+�!�h

2�2−��<

��l −��h�

1−�

if and only if � < 4�l − 2��3− ��h/�2�l + 1− ��4− ��!�h�.Moreover, ��2 − �� + �!d/2 > ��l − ��h�/�1 − �� ifand only if d > 2��l − ��h�/��1 − �� 2 − �� + �!�,and � ��2−��+�!�h/�2�2−�� > �d if and only if d <� ��2 − �� + �!�h/�2��2 − ��. Therefore, when � <2��l −��h�/��l + �1− 2��h�, we obtain that �iv

i > �ns if andonly if � > �4�l − 2��3− ��h�/�2�l + 1− ��4 − ��!�h� and2��l −��h�/��1−�� 2−��+�!� < d < � ��2−��+�!�h/�2��2−��.Range (ii): � > 2��l − ��h�/��l + �1 − 2��h�. In this

case, �r�⊗��l − ��h�/�1 − �� < �r�1��l − ��h�/�1 − �� <�r�⊗��h < �r�1��h. Similarly, the manufacturer’s expectedpayoff is ��=� when �≤ �r�⊗��l−��h�/�1−��, ��=��/2 + ��1 − �/2�� when �r�⊗��l − ��h�/�1 − �� < � ≤�r�1��l − ��h�/�1 − ��, �� = �� when �r�1��l − ��h�/�1− �� < � ≤ �r�⊗��h, and �� = ��/2 when �r�⊗��h <� ≤ �r�1��h. Note that �� = � → ��l − ��h�/��1 − �� ·�2− �� when � → �r�⊗��l − ��h�/�1− ��, �� = ��/2+��1 − �/2�� → ��2 − �� + �!��l − ��h�/�2�1 − �� when� → �r�1��l − ��h�/�1 − ��, �� = �� → ��h/�2 − ��when � → �r�⊗��h, and �� = ��/2 → ��h/2 when� → �r�1��h. Moreover, ��l − ��h�/��1 − ��2 − �� <��h/�2−��, and ��h/�2−�� > ��h/2. Therefore, we canobtain the manufacturer’s equilibrium ex ante payoff

�ivii = max

{min

{d�

��l−��h�

�1−��2−��

}�

min{

��2−��+�!d

2�

��2−��+�!��l−��h�

2�1−��

}�

min{�d�

��h

2−�

}}�

Comparing �ivii with �ns, we obtain

��l −��h�

�1−��2−��<

��l −��h�

1−��

��2−��+�!d

2> �d�

��h

2−�< ��h� and ��2−��+�!

�l −��h

2�1−��< ��h�

Therefore, when � > 2��l − ��h�/��l + �1 − 2��h�, �ivii >

�ns if and only if ��2 − �� + �!��l − ��h�/�2�1 − �� >��l − ��h�/�1− ��, ��2− ��+ �!d/2 > ��l − ��h�/�1− ��,and ��2−��+�!��l−��h�/�2�1−��>�d, which give riseto �<2�/�1+��, d > 2��l−��h�/��1−�� 2−��+�!�, andd < ��2−��+�!��l −��h�/�2��1−��, respectively.

Noticing that � ��2 − �� + �!�h/�2��2 − �� > ��2 − ��+ �!��l −��h�/�2��1−�� if and only if �>2��l −��h�/��l + �1− 2��h�, we can combine the ranges (i) and (ii) toobtain that �iv > �ns if and only if �4�l − 2��3 − ��h�/�2�l + 1− ��4− ��!�h� < � < 2�/�1+ �� and 2��l − ��h�/��1 − �� 2 − �� + �!� < d < min� ��2 − �� + �!�h/�2��2−�� 2−��+�!��l −��h�/�2��1−��. Q.E.D.

Proof of Proposition 5. If � ≤ ��l − ��h�/�1− �� (i.e.,� ≥ �h), the manufacturer would not start the informationacquisition process and the retailer would order x = 1. Itfollows that � = �̄ = �, m�� = m��̄� = �r�⊗� = �, �′ = �,and � ′ = ��l −�.

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If��l −��h�

1−�< �≤min

{� �l + �1− 2��h!

2�1−��

�l −��h

1−�

}

(i.e., 2�1 − ��/��l + �1 − 2��h� ≤ � < �h ≤ 1), the man-ufacturer would continue to collect information until itsupdated posterior belief reaches either �m = �h in whichcase the acquired information would be disclosed and theretailer would order x = 1, or �m = 0 in which case theacquired information would be withheld and the retailerwould order x = �. It follows that � = 0, �̄ = �h, m�� =⊗,m��̄�= �̄, and

�r�⊗� = �/21/2+ �1−�/�h�/2

= �1−��

2�1−��−��l −��h�≥ �l�

The manufacturer’s expected payoff is

�′ =*�� 0��h��+ 1−*�� 0��h�!��= ��l −��h�+��

and the retailer’s is

� ′ = �[*G�� 0��h��l + 1−*G�� 0��h�!��h

]−[

*�� 0��h��+ 1−*�� 0��h�!��]

= ��h −��

If min� �l + �1 − 2��h!/�2�1 − �� l − ��h�/�1 − �� <� ≤ min��h� ��l − ��h�/�1 − �� (i.e., �l ≤ � < 2�1 − ��/��l + �1 − 2��h� and �h ≤ 1), then there exists nopure-strategy equilibrium. In the (partially) mixed-strategyequilibrium, the upper bound where the manufacturer stopsinformation acquisition is �̄ = �h, and the manufacturerdiscloses the upper bound to the retailer (i.e., m��̄� = �̄).However, the manufacturer randomizes the lower bound ofinformation acquisition between �= 0 and �= �l. The prob-ability 1 that the manufacturer continues to collect infor-mation until �m = 0 is such that the retailer is indifferentbetween ordering x = � and x = 0 when the message m=⊗is received, i.e., �r�⊗� = ��/2�/�1/2 + 1�1 − �/�h�/2� = �l.This leads to 1= �h��−�l�/��l��h −��= �1−��h −��/��1 − �� − ��l − ��h��. In addition, the manufacturerwould withhold (disclose) the acquired information whenthe lower bound � = 0 (� = �l) is reached, i.e., m�0�=⊗and m��l� = �l. Moreover, when the retailer receives them = ⊗ message, it would randomize between orderingx = � and x = 0, with probability 2 and 1 − 2, respec-tively. To make the manufacturer indifferent between � =0 and � = �l, it is required that �� = *��l � 0��h�� + 1 − *��l � 0��h�!2��, which leads to 2 = ��h − �l�/��h − �l�� = ��2− ��h − �l�/��h − �l��. It follows thatthe manufacturer’s expected profit is

�′ = *�� l��h��+ 1−*�� l��h�!��

= �1−��h

�l −��h

�h − �l

+ ��2−��h − �l!�

�h − �l

�

and the retailer’s is

� ′ = �{1[*G�� 0��h��l+ 1−*G�� 0��h�!��h

]

+�1−1�[*G�� l��h��l+ 1−*G�� l��h�!��h

]}

−[*�� l��h��+ 1−*�� l��h�!��

]= �2�h+�1−2��l!��h−��/��h−�l��

If ��l − ��h�/�1− �� < � ≤ ��h (i.e., �l ≤ � < 1 < �h), themanufacturer would not collect any information and theretailer’s order is x = �, which leads to � = �̄ = �, m�� =m��̄�= �r�⊗�= �, �′ = ��, and � ′ = ��h −��.

Finally, if � > ��h (i.e., � < �l), the manufacturerwould continue information collection until either it islearned almost with certainty that S = B or its updatedposterior belief reaches �l; i.e., � = 0 and �̄ = �l. Inaddition, the manufacturer would withhold (disclose) theacquired information when the lower (upper) bound isreached; i.e., m�� = ⊗ and m��̄� = �̄. This implies that�r�⊗� = ��/2�/�1/2 + �1 − �/�l�/2� = ��/�2� − ��h� <�l. The manufacturer’s expected payoff is then �′ =*�� 0��l�� = ��h, and the retailer’s expected payoff is� ′ = �*G�� 0��l��h −*�� 0��l��= 0. Q.E.D.

Proof of Proposition 6. When I = �y, the manufacturer’sexpected payoff, conditional on � ≤ d, is �′′ = � if � ≤��l −��h�/�1−��, �′′ = �� if

��l −��h�

1−�< �≤min

{� �l + �1− 2��h!

2�1−��

�l −��h

1−�

}or

�l −��h

1−�< �≤ ��h�

�′′ = 2�� if min� �l + �1 − 2��h!/�2�1 − �� l − ��h�/�1 − �� < � ≤ min��h� ��l − ��h�/�1 − ��, where 2 =��2 − ��h − �l�/��h − �l��, and �′′ = 0 if otherwise.When I = y, the manufacturer’s expected payoff is givenin Proposition 5. That is, �′ = � if �≤ ��l −��h�/�1−��,�′ = ��l − ��h� + �� if ��l − ��h�/�1 − �� < � ≤min� �l + �1 − 2��h!/�2�1 − �� l − ��h�/�1 − ��, �′ =�1−��h��l −��h�/��h − �l�+ ��2−��h − �l!�/��h − �l� ifmin� �l + �1− 2��h!/�2�1− �� l − ��h�/�1− �� < � ≤min��h� ��l −��h�/�1−��, �′ = �� if ��l −��h�/�1−�� <�≤ ��h, and �′ = ��h if � > ��h.Range (i): � < ��l − ��h�/��1 − ��h�. In this case, ��h <

��l − ��h�/�1 − ��. The manufacturer’s expected payoff,conditional on � ≤ d, is then �� = � if � ≤ ��l − ��h�/�1−��, ��= ��l −��h�+2��!/2 if ��l −��h�/�1−�� <�≤ � �l+�1−2��h!/�2�1−��, ��= �1−��h��l−��h�/�2��h −�l��+ ��2−��h −�l!�/��h −�l� if � �l + �1−2��h!/�2�1− �� < � ≤ ��h, and �� = ��h/2 if � > ��h. Notethat �� = � → ��l − ��h�/�1− �� when �→��l−��h�/�1−��= ��l−��h�+2��!/2→��l−�2�h�/�2�1−��when �→ � �l + �1− 2��h!/�2�1−��, and

�� = �1−��h

�l −��h

2��h − �l�+

[��2−��h − �l

]�

�h − �l

→ ��h ��3−��h − �1+��l!

2��h − �l�

when �→ ��h. Moreover,

��l −��h�

1−�<

��l −�2�h

2�1−��< ��h�

��h

2<

��h ��3−��h − �1+��l!

2��h − �l�< ��h�

and

��l −�2�h�

2�1−��>

��h ��3−��h − �1+��l!

2��h − �l�

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if 1−√�1−��3!�h < �l < ��2− ��h. Therefore, when 1−√

�1−��3!�h < �l < ��2−��h, the firms’ equilibrium ex anteprofits are given by, respectively,21

�vi =

min{d�

��l −��h�

1−�

}� if d ≤ �1+��l −��h�

2��1−��%

min{ ��l −��h�+ 2�d!/2�

��l −�2�h�

2�1−��

}�

if otherwise�

�vi =

��l−min{d�

��l−��h�

1−�

}� if d≤ �1+��l−��h�

2��1−��%

��h−�min{d�

� �l+�1−2��h!

2�1−��

}� if otherwise�

We can then readily obtain that �vi < �m

i if d is sufficientlylarge. Similarly, we have �v

i > �mi if d > � �l + �1− 2��h!/

�2�1−��. This proves part (ii) of the proposition.Range (ii): � > 2��l − ��h�/��l + �1− 2��h�. In this case,

� �l + �1− 2��h!/�2�1− �� > ��l − ��h�/�1− ��. The man-ufacturer’s expected payoff, conditional on � ≤ d, is then��=� if

�≤ ��l −��h�

1−��

��= ��l −��h�+ 2��

2

if ��l − ��h�/�1 − �� < � ≤ ��l − ��h�/�1 − ��, �� =�� if ��l − ��h�/�1 − �� < � ≤ ��h, and �� = ��h/2 if� > ��h. Note that �� = � → ��l − ��h�/�1 − �� when� → ��l − ��h�/�1 − ��, �� = ��l − ��h� + 2��!/2 → 2� + �1 − ��!��l − ��h�/�2�1 − �� when � → ��l − ��h�/�1− ��, and �� = �� → ��h when � → ��h. Moreover, 2�+�1−��!��l−��h�/�2�1−��<��h given

� >2��l−��h�

�l + �1− 2��h

� and

2�+ �1−��!�l −��h

2�1−��<

��l −��h

1−�

if and only if � > 2�/�1+ ��. Therefore, the manufacturer’equilibrium ex ante payoff is

�vii = max

{mind��l −��h�

1−�

}�min ��l −��h�+ 2�d!

2�

2�+ �1−��!��l −��h�

2�1−��

}�min�d��h�

}�

It is then obvious that given

� >2��l −��h�

�l + �1− 2��h

�

we can obtain that �vii > �m

ii if � < 2�/�1+�� and

�1+��l −��h�

2��1−��< d <

2�+ �1−��!�l −��h

2��1−��

21 The case when ��h < �l < 1−√�1−��3!�h is similar, but the com-

putation is more involved.

and �vii = �m

ii if otherwise. This proves part (i) of theproposition. Q.E.D.

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