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Supplier Encroachment Under Asymmetric InformationZhuoxin Li, Stephen M. Gilbert, Guoming Lai
To cite this article:Zhuoxin Li, Stephen M. Gilbert, Guoming Lai (2014) Supplier Encroachment Under Asymmetric Information. ManagementScience 60(2):449-462. http://dx.doi.org/10.1287/mnsc.2013.1780
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MANAGEMENT SCIENCEVol. 60, No. 2, February 2014, pp. 449–462ISSN 0025-1909 (print) � ISSN 1526-5501 (online) http://dx.doi.org/10.1287/mnsc.2013.1780
© 2014 INFORMS
Supplier Encroachment UnderAsymmetric Information
Zhuoxin Li, Stephen M. Gilbert, Guoming LaiMcCombs School of Business, University of Texas at Austin, Austin, Texas 78712
{[email protected], [email protected], [email protected]}
Prior literature has shown that, for a symmetric information setting, supplier encroachment into a reseller’smarket can mitigate double marginalization and benefit both the supplier and the reseller. This paper
extends the investigation of supplier encroachment to the environment where the reseller might be betterinformed than the supplier. We find that the launch of the supplier’s direct channel can result in costly signalingbehavior on the part of the reseller, in which he reduces his order quantity when the market size is small. Sucha downward order distortion can amplify double marginalization. As a result, in addition to the “win–win”and “win–lose” outcomes for the supplier and the reseller, supplier encroachment can also lead to “lose–lose”and “lose–win” outcomes, particularly when the reseller has a significant efficiency advantage in the sellingprocess and the prior probability of a large market is low. We further explore the implications of those findingsfor information management in supply chains. Complementing the conventional understanding, we show thatwith the ability to encroach, the supplier may prefer to sell to either a better informed or an uninformed resellerin different scenarios. On the other hand, as a result of a supplier developing encroachment capability, a resellereither may choose not to develop an advanced informational capability or may become more willing to find ameans of credibly sharing his information.
Keywords : direct and indirect channel; information asymmetry; supplier encroachmentHistory : Received March 13, 2012; accepted May 12, 2013, by Yossi Aviv, operations management. Published
online in Articles in Advance November 4, 2013.
1. IntroductionMany upstream manufacturers have invested indirect channels such as online stores, catalog sales,and factory outlets (Nair and Pleasance 2005). Withthese established direct channels, manufacturers maysell their products directly as well as indirectlythrough the reselling channels (e.g., distributors,wholesalers, retailers). Consequently, competitioncan arise between the resellers and their suppli-ers, a phenomenon often referred to as “supplierencroachment.”
Whereas retail competition (competition amongresellers) has been extensively studied and wellunderstood, supplier encroachment has receivedmuch less attention and has distinct features. A studyby Arya et al. (2007) shows that supplier encroach-ment endows the supplier with a mechanism tocontrol the selling price in the retail market, andconsequently motivates her to reduce her wholesaleprice. The combination of these two effects mitigatesdouble marginalization and can benefit both the sup-plier and the reseller when the latter has a significantefficiency advantage in the retail process. Whereasthe existing literature has considered various elementsthat may influence the effects of supplier encroach-ment, the information structure is often assumed to
be symmetric in the supply chain. In practice, resellersoften have better knowledge of the market potentialthan the upstream suppliers, due to their expertiseand superior forecasting ability in the selling process,as well as rich first-hand sales data. Although conven-tional wisdom holds that resellers necessarily bene-fit from having access to private market information,our results demonstrate that this is not always thecase when the supplier has developed its own directchannel.
In this paper, we build upon the supplier encroach-ment framework based on Cournot competition fromArya et al. (2007) by incorporating an asymmetricinformation structure, where the reseller knows therealization of the market size but the encroachingsupplier knows only the prior distribution of themarket size. Credible information communication isnot available. In the face of information disadvan-tage, the supplier wants to infer the true market sizefrom the reseller’s order quantity to more properlydecide the direct selling quantity. Anticipating thesupplier’s strategy, the reseller may purposely distorthis order quantity for his own benefit. The interactionbetween the supplier’s and the reseller’s incentivescan result in an inefficient downstream signaling out-come. Regardless of which market size is observed by
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the reseller, he would like the supplier to believe itis small. Consequently, when the reseller observes asmall market, he may need to distort his order quan-tity downward in order to send a credible signal thatthe market size is small. This downward distortion, ifit occurs, amplifies double marginalization and mayhurt both the supplier and the reseller. As a result,we find that, in the presence of asymmetric infor-mation, the supplier’s development of encroachmentcapability can lead to “lose–win” or “lose–lose” out-comes for the supplier and the reseller in additionto the “win–win” and “win–lose” outcomes that arereported in Arya et al. (2007).
We then explore the implications of supplierencroachment for information management in supplychains. Prior literature has shown that with a resellingchannel alone, the supplier is indifferent between areseller who is better informed or equally informed.However, we find that when the supplier has the abil-ity to encroach, she strictly prefers to sell to a better-informed reseller when her efficiency disadvantage inthe selling process is not large; otherwise, she prefersto sell to an equally informed reseller. On the otherhand, prior literature shows that without the sup-plier’s direct channel, the reseller always prefers to bebetter informed. Whereas, after the supplier launchesher direct channel, the incumbent reseller can be dis-couraged from obtaining advanced information in awide range of parameters. While this prevents down-ward distortion of the reseller’s order quantity andbenefits the supplier, it expands the range of param-eters for which total supply chain profits are lowerunder encroachment. Our analysis also provides aninteresting implication on information sharing. It iswell known in the literature that, in standard bi-lateral monopoly settings in which production costsare linear, the supplier is restricted to setting a lin-ear wholesale price, and the reseller determines theoutput quantity, the reseller benefits from having pri-vate information about demand. In contrast, we findthat in the presence of the supplier’s direct channel,the reseller may prefer that the supplier has access tothe same information that he has over being privatelyinformed.
The remainder of our paper is organized as fol-lows. Section 2 reviews the related literature. In §3,we describe the model. We provide the analysis of themodel in §4, and in §5, we discuss the implications forsupply chain information management. Finally, in §6,we discuss the limitations of our analysis and direc-tions for future research.
2. Literature ReviewThe effects of supplier encroachment have been dis-cussed in the literature. Empirical studies find that
supplier encroachment can possibly lower a reseller’seffort to sell a product (Fein and Anderson 1997)and it can also affect brand image (Frazier andLassar 1996). However, several analytical studies haveshown that supplier encroachment can mitigate dou-ble marginalization and thus benefit both the supplierand the reseller. For example, Chiang et al. (2003)demonstrate that a supplier’s threat to sell through adirect channel causes the reseller to lower his sellingprice, which can benefit both parties. In another study,Tsay and Agrawal (2004) incorporate sales efforts thatcan be exerted by the supplier as well as the reseller,and show that in such a context, the launch of asupplier direct channel can still benefit both parties.The effect of mitigating double marginalization is alsofound by Cattani et al. (2006), based on a model withhorizontal differentiation. They reveal that supplierencroachment can benefit both the supplier and thereseller if the supplier commits to the same sellingprice and the direct channel is not as convenient forconsumers as is the existing reselling channel. Simi-larly, Arya et al. (2007) demonstrate based on a quan-tity competition model that the supplier’s direct salenot only adds another source of revenue for her butalso motivates her to offer a lower wholesale priceto the reseller. Consequently, encroachment has thepotential to benefit the supplier as well as the reseller,especially when the latter enjoys a significant costadvantage in the selling process. Our work comple-ments this stream of research by allowing for thereseller to have private information about the marketsize, and this leads to results that are quite differentfrom those found in the literature, including the factthat supplier encroachment can sometimes amplifydouble marginalization and hurt both the supplierand the reseller when the latter is privately informedabout demand.
Our work is also related to the literature that inves-tigates the incentives of information sharing in supplychains. Cachon and Lariviere (2001) explore contractsthrough which a downstream buyer can crediblyshare private demand information with a supplier.Li (2002) and Zhang (2002) investigate informationsharing in a setting where a central supplier sells tomultiple competing resellers and they show that with-out particular incentives, the resellers will withholdtheir private demand information instead of shar-ing it with the supplier in equilibrium. With a con-fidential agreement by which the supplier does notleak received information, competing resellers mightbe willing to share their private demand informationwith the supplier, which can drive down the whole-sale price. Ha and Tong (2008) and Ha et al. (2011)study the incentives of information sharing withintwo competing supply chains, considering the effectsof information accuracy, nonlinear production costs,
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and a nonlinear pricing schedule. Two recent papersare similar to ours in considering how a reseller’sconcern over leaking his private demand informationmay affect how he orders from a supplier. Anandand Goyal (2009) and Kong et al. (2013) investi-gate a one supplier–two reseller setting where thesupplier may leak the market information learnedfrom the incumbent reseller’s order quantity to anentrant reseller. Anand and Goyal (2009) show underan exogenous wholesale-price contract that the sup-plier always leaks information to stimulate down-stream order quantity. Consequently, the incumbentreseller may purposely block information dissemina-tion by ordering the same quantity for any marketsize. Kong et al. (2013) consider a similar setting, butdemonstrate that a revenue-sharing scheme may pre-vent the supplier from leaking information, and con-sequently can result in Pareto gains for all parties.Similar to this latter paper, we allow for an endoge-nous wholesale price, but we consider a setting inwhich the supplier’s own direct channel, rather thana second reseller, is the potential beneficiary of infor-mation gained from the informed reseller. In addition,we consider the effect that a supplier’s developmentof a direct channel can have upon her own, as wellas the reseller’s, preferences among different informa-tion structures, and we find that encroachment mayencourage the reseller to share his private informa-tion with the supplier. Consequently, our perspectiveof analyzing how supplier encroachment affects theflows of materials and information in a supply chainis quite different from either of these papers.
Finally, our work is related to the recent work ofJiang et al. (2011). In their study, an independentseller sells a product through a platform. The plat-form owner can also acquire the product and hasmonopolistic control over the access to the market.In particular, the platform owner can incur a fixedcost, to sell the independent seller’s product and takeaway all of the demand from the latter if strong salesare revealed. They show a pooling outcome wherethe independent seller’s incentive to hide the pri-vate demand information by exerting the same sell-ing effort may hurt the platform owner, but benefithimself. In contrast, we assume that both firms haveaccess to the market, but the supplier has full con-trol over the access to the product (i.e., the resellerhas no alternative source of supply). For this setting,we show that no pooling equilibrium can survive theintuitive criterion, and that in the resulting separatingequilibria, supplier encroachment can either benefit orhurt the two firms.
3. The ModelWe consider a supplier (she) that sells a productthrough a reseller (he), but she also has her own
direct channel and may sell the product directly toconsumers. We normalize both the production costof the supplier and the selling cost for the resellerto zero. To allow for the possibility that the sup-plier may be less efficient in retail operations thanis the reseller, we assume that the supplier incursa per-unit selling cost of c for each unit that shesells directly to consumers. Consumer demand fol-lows a linear, downward-sloping demand function,P = a−Q, where Q is the total number of the productdeployed for sale, P is the market clearing price, anda represents the market size. Note that it is withoutfurther loss of generality that we have normalized theslope of this demand function to be −1.
The above setup is nearly identical to that of Aryaet al. (2007). However, to capture the notion that thereseller is closer to the market and may also havebetter expertise in forecasting the demand than thesupplier, we assume that the market size a is, ex ante,random which can be either large (a= aH ) with proba-bility � and small (a= aL) with probability 1−�, whereaH > aL > 0; the reseller can observe the true mar-ket size privately, before ordering from the supplier,whereas the supplier knows only the prior distributionof the market size.1 Let �= �aH + 41 −�5aL, represent-ing the expected market size, and �2 = �4aH − �52 +
41 − �54aL − �52 be the variance of the market sizedistribution. We restrict our attention to the cases inwhich aL > �/2, so that, as we will show later, thereseller’s equilibrium order quantity is strictly posi-tive for both market sizes without supplier encroach-ment. Such an assumption will simplify the analysisand can also highlight the contrast between the caseswith and without supplier encroachment. Finally, weassume that the supplier uses a linear wholesale-price-only contract. Linear pricing schemes are widely usedin practice and also are commonly assumed in the lit-erature that studies channel structure (e.g., McGuireand Staelin 1983, Lariviere and Porteus 2001, Cachon2003, Arya et al. 2007). Similar results hold even if thesupplier can implement nonlinear pricing through amenu of contracts.
Figure 1 details the timeline of the model. First,the supplier offers a wholesale contract to the reseller,which contains a unit wholesale price w. The resellerwho has observed the true market size, a = aH ora= aL, orders qR units from the supplier. The supplierthen decides the quantity qS , which she sells throughher direct channel. The market clearing price P is real-ized according to P = ai − 4qR + qS5 for i ∈ 8H1L9, and
1 For simplicity, we assume here that the reseller learns the marketsize perfectly, whereas the supplier only has the prior knowledge.The insights we reveal, however, will continue to hold, even ifboth of them receive noisy signals of the market size, as long asthe reseller is more precisely informed about the demand than thesupplier.
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Figure 1 Timeline of the Model
The supplier offers awholesale contract
The supplier decides the stockinglevel for her direct channel
The market clearing price is realized, as arethe profits of the reseller and the supplier
The reseller who observes the marketsize decides the order quantity
the two parties obtain their final profits.2 The assump-tion that the reseller orders before the supplier deter-mines her order quantity is justified by the fact thatthe supplier has no way to credibly commit to refrainfrom revising her own order quantity after receivingthe reseller’s order.
4. AnalysisBefore beginning our analysis of how the develop-ment of supplier encroachment capability (i.e., thelaunch of the direct channel) affects the interactionsbetween a supplier and a reseller, we first present thebenchmark in which the supplier lacks this capabilityand sells the product only through the reseller.
4.1. Benchmark Without EncroachmentWhen the supplier lacks the infrastructure of a directchannel, she has effectively provided a credible com-mitment that she will not encroach. Then, given thewholesale price w and the market size ai1 i ∈ 8H1L9,the reseller determines his order quantity as the solu-tion to
maxqR
6ai − qR −w7qR0
It is easy to obtain the optimal order quantity of thereseller for each market size ai, i ∈ 8H1L9:
qNR 4w3ai5=ai −w
20
Recall that the supplier does not observe the truemarket size, but anticipates the reseller’s decision.Thus, the supplier chooses her wholesale price as thesolution to
maxw
E6qNR 4w3a5w70
In equilibrium, the supplier’s optimal wholesale priceis wN = �/2, and the expected profits of the resellerand the supplier are, respectively,
�R =�2 + 4�2
16and �S =
�2
81 (1)
where the lowercase � indicates that there is noencroachment.
2 This inverse demand function implicitly assumes that consumersperceive the two channels to be perfect substitutes. Although allow-ing for partial substitutability would complicate the analysis, itwould not provide additional insights.
4.2. Encroachment AnalysisLet us now enhance the model to allow for sup-plier encroachment, by which we mean the sup-plier has her direct channel in place and can chooseto sell directly. Since the supplier does not observethe market demand directly, she will use the infor-mation revealed from the reseller’s order quantityto make her decision on the direct sale quantity.Because the reseller anticipates the supplier’s reac-tion to his order, a signaling game may arise inwhich the reseller may purposely alter his orderquantity. In particular, as is often the case, there aretwo mutually exclusive types of equilibria that mightarise. In the first, the reseller orders a distinct quan-tity for each market size, and his order perfectlyreveals the market size to the supplier. In the sec-ond, he orders the same quantity for both marketsizes, and his order is uninformative. The former caserepresents a separating outcome, whereas the lattercorresponds to a pooling outcome. Typically, such sig-naling games can have multiple equilibria depend-ing on the players’ belief specification. However, thisobstacle can be overcome by using the intuitive cri-terion, which is a classical equilibrium refinementdeveloped by Cho and Kreps (1987). Because we canshow (see Online Appendix D, available at http://ssrn.com/abstract_id=2340117) that pooling equilib-rium cannot survive the intuitive criterion in ourmodel, we focus directly on separating equilibrium.That is, all of the formulation and analysis presentedbelow are based on the fact that the supplier can per-fectly infer the market size from the reseller’s orderquantity. Furthermore, we confine our formulationand analysis to those cases (with respect to c, �, aH ,and aL) where the supplier optimally sells a positivequantity for each market size. (The boundary condi-tion is provided when we characterize the equilib-rium.) Displaying the full analysis for the cases wherethe supplier optimally chooses not to encroach wouldcomplicate the exposition without adding any inter-esting insights.
We first formulate the supplier’s belief. We use aj4qR5to indicate the market size that the supplier believesafter receiving an order quantity qR from the reseller.It is intuitive that the reseller will order more whenthe true market size is large than when the marketsize is small. Thus, we apply the following belief
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structure depending on a threshold order quantityqR4w5 for a given wholesale price w. (Other belief for-mulations exist that can lead to the same equilibriumresult.)
j4qR5=
{
H if qR > qR4w51
L otherwise0
That is, the supplier believes that the market size islarge if the reseller’s order quantity qR > qR4w5 andsmall otherwise. Then, after observing the reseller’sorder quantity qR, the supplier determines her directselling quantity by solving
maxqS
6aj4qR5 − qR − qS − c7qS1
which yields the optimal direct selling quantity:
qS4qR5=aj4qR5 − qR − c
20
In anticipation of the supplier’s belief and reaction,the reseller, who knows the true market size ai, i ∈
8H1L9, solves
maxqR
6ai − qR − qS4qR5−w7qR0 (2)
Let qR4w3ai5 denote the optimal solution of (2). Noticethat for a given order quantity, the reseller wouldbe better off if the supplier believed the market sizewere small than if she believed it were large. Thus,the reseller may purposely order a lower quantity toinduce the supplier to believe the market size is small.The supplier will adjust qR4w5 taking the reseller’sincentive into account. To solve this problem, wedefine the following equilibrium concept.
Definition 1. Given any wholesale price w, a per-fect Bayesian separating equilibrium is reached ifaj4qR4w3ai55
= ai for each market size ai, i ∈ 8H1L9; that is,there exists a qR4w5 such that qR4w3aH 5 > qR4w5 whileqR4w3aL5≤ qR4w5.
To facilitate the characterization of the equilibrium,we define the following functions:
Vij4qR5=
[
ai−qR−aj − qR − c
2−w
]
qR1 ∀ i1 j ∈ 8H1L91
where Vij4qR5 is the reseller’s profit if the true marketsize is ai, while, given the reseller’s order quantity qR,the supplier believes that the market size is aj .
Lemma 1. The function Vij4qR5 is concave in qR for anyi1 j ∈ 8H1L9, and there is a unique maximizer of Vii4qR5;that is, qR = 44ai − 2w+ c5/25+, for each i ∈ 8H1L9.
All proofs are provided in Online Appendix A.Figure 2 illustrates the reseller’s possible profit
functions, Vij4qR5. From Lemma 1, we can clearly seethat if the supplier could also observe the market size,
Figure 2 Demonstration of the Reseller’s Possible Profit Functionsand the Threshold qR4w5
VHL qR
VHH qR
VLL qR
VLH
qR
qR
qR w aL w c aH w c
Notes. The parameters are �= 003, aH = 102, aL = 1, w = 002, and c = 002.In this example, w < w = 0055.
then the reseller would order qR = 44ai − 2w+ c5/25+
for each market size ai. When the supplier doesnot have complete information, the reseller mayhave an incentive to place an order lower than44ai − 2w+ c5/25+. It is easy to see that the supplierwould never benefit from setting a wholesale price,w ≥ 4aH + c5/2, since this would prevent the resellerfrom ordering anything for each market size. There-fore, we implicitly assume w < 4aH + c5/2 for all theanalysis below.
Lemma 2. For any qR > 0, VHL4qR5 > VHH 4qR5, andthere exists
qR4w5
=2aH −aL−2w+c−
√
4aH −aL543aH −aL−4w+2c52
<aH −2w+c
2
such that VHL4qR4w55 = VHH 44aH − 2w+ c5/25, VHL4qR5< VHH 44aH − 2w+ c5/25 when qR < qR4w5, andVHL4qR5 > VHH 44aH − 2w+ c5/25 when qR4w5 < qR <4aH − 2w+ c5/2. Furthermore, let w = 43aL − aH + 2c5/4.Then, qR4w5Ó 44aL − 2w+ c5/25+ when wÓ w.
Figure 2 provides an illustration of the resultsof Lemma 2 and the threshold qR4w5. Lemma 2implies that if the threshold qR4w5 in the supplier’sbelief structure is above qR4w5, then if the resellerobserves a large market he would order less than4aH − 2w+ c5/2, to induce the supplier to believe that
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the market size is small. Therefore, for a separatingequilibrium to exist, qR4w5 cannot be greater thanqR4w5. With this intuition, the following propositioncharacterizes a unique separating equilibrium thatsurvives the intuitive criterion.
Proposition 1. There exists a unique perfect Bayesianseparating equilibrium that survives the intuitive cri-terion, in which the reseller’s order quantity satisfiesqR4w3aH 5 = 4aH − 2w+ c5/2 and qR4w3aL5 = qR4w5 =
min844aL − 2w+ c5/25+1 qR4w59, and the supplier’s directselling quantity is qS4qR4w3ai55 = 4ai − qR4w3ai5− c5/2,∀ i ∈ 8H1L90
In this equilibrium, the reseller orders 4aH −
2w + c5/2 when the market size is large, which coin-cides with the optimal quantity he would order ifthe supplier also observes the market size. In otherwords, for the large market size, the reseller’s orderquantity will not be distorted as the information ofthe market size becomes private to the reseller. How-ever, when the market size is small, distortion ofthe reseller’s order quantity can arise due to infor-mation asymmetry. We can observe from Lemma 2that only when w ≥ w would qR4w3aL5 coincidewith 44aL − 2w+ c5/25+, and when w< w, qR4w3aL5 <44aL − 2w+ c5/25+. That is, if the wholesale pricew< w, then for the small market size, the reseller willorder less in the presence of asymmetric informationthan he would if the market size were observable tothe supplier. To credibly signal that the market sizeis small, the reseller needs to downward distort theorder quantity to such a level that he would haveno incentive to mimic when observing the large mar-ket size, even if that would allow him to deceive thesupplier. Consequently, in equilibrium, the suppliercan always learn the market size from the reseller’sorder quantity and determine her direct selling quan-tity accordingly.
Recall from Arya et al. (2007) that the potentialfor mutual benefit from encroachment arises becausethe supplier lowers the wholesale price at the sametime that she stimulates the volume of sales throughthe reseller with the threat of her own direct sales.However, in the presence of asymmetric informa-tion, the reseller’s propensity to downward distorthis order quantity when the wholesale price is lowcan dampen the supplier’s willingness to reduce herwholesale price. Consequently, informational asym-metry can reduce or eliminate the potential for mutualbenefit from encroachment.
A deeper investigation of the reseller’s order quan-tity for the small market size can draw the followingconclusion.
Lemma 3. The reseller’s equilibrium order quantity forthe small market size satisfies �4dqR4w3aL55/dw� = 1 whenw ≤ w <4aL + c5/2 and �4dqR4w3aL55/dw� < 1 whenw< w.
Lemma 3 asserts that the reseller’s equilibriumorder quantity under a small market size, qR4w3aL5,will be less responsive to the wholesale price (i.e.,the order quantity increases at a slower rate as thewholesale price decreases) in the region with a dis-tortion than in a region without. As we will see later(at Proposition 2), the point where w drops below wcorresponds to a discontinuous drop in the price elas-ticity of the reseller’s order quantity and can driveup the supplier’s wholesale price and thus amplifydouble marginalization.
The supplier’s wholesale pricing decision, inanticipation of the subsequent subgames, can be ex-pressed as
maxw
E[
qR4w3a5w+ 4a− qR4w3a5− qS4qR4w3a55− c5
· qS4qR4w3a55]
0 (3)
Proposition 2 provides the solution to (3) and the cor-responding subgame equilibrium for the cases wherethe supplier encroaches for both market sizes.
Proposition 2. Given aH and aL, for any � ∈ 40115,there exists a threshold c4�5 such that in equilibrium,3
(1) the supplier’s optimal wholesale price and thereseller’s order quantity follow:
(i) if c ∈ 401 43√�4aH − aL55/47, then w∗ = 43aH −
c5/6, qR4w∗3aH 5= 4aH − 2w∗ + c5/2, and qR4w∗3aL5= 0;
(ii) if c ∈ 443√�4aH − aL55/41min84341 + 2�54aH −
aL55/81 c4�597, then w∗ = 43�− c5/6, qR4w∗3aH 5= 4aH −
2w∗ + c5/2, and qR4w∗3aL5= 4aL − 2w∗ + c5/2;
(iii) if c ∈ 4min84341+2�54aH −aL55/81 c4�591 c4�55,then w∗ = min8w1wf 9, where wf > 43�− c5/6 is thesmallest solution of the first-order condition of (3),4
qR4w∗3aH 5= 4aH − 2w∗ + c5/2 and qR4w
∗3aL5= qR4w∗5;
(2) the supplier’s direct selling quantity followsqS4qR4w
∗3ai55 = 4ai − qR4w∗3ai5 − c5/2, ∀ i ∈ 8H1L9,
which is positive for c ∈ 401 c4�55.
Proposition 2 shows that when the supplier’sselling cost is relatively small, i.e., 0 < c ≤
43√�4aH − aL55/4, she chooses the wholesale price at a
level such that the reseller orders a positive quantityonly if the market size is large. With an intermediateselling cost, 43
√�4aH − aL55/4 < c ≤ min84341 + 2�5 ·
4aH − aL55/81 c4�59, the supplier’s optimal wholesaleprice induces the reseller to order a positive quan-tity for each market size. Furthermore, the resellerwho observes high demand will have no incentiveto attempt to mimic even the undistorted quan-tity that he would order with a small market size.
3 The threshold, c4�5, is the selling cost above which the supplier’sdirect selling quantity under at least one market size reaches zeroin equilibrium.4 The first-order condition of (3) is �43aH − c − 6w5 + 41 − �54aH +
2aL − c− 6w541 −√
4aH − aL5/43aH − aL + 2c− 4w55= 0.
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Consequently, when the supplier’s selling cost isintermediate, we will see a natural separating equilib-rium in which there is no distortion of the reseller’sorder quantity when the true market size is small.However, when the supplier’s selling cost is relativelylarge, min84341 + 2�54aH − aL55/81 c4�59 < c < c4�5, thereseller who observes a large market size would havean incentive to mimic an undistorted small orderquantity to deceive the supplier. As a result, thereseller will have to distort his order quantity down-ward when he truly observes a small market size,to credibly reveal the information to the supplier. Inanticipation of this quantity distortion, the supplier’soptimal wholesale price will exceed the 43�− c5/6that she would otherwise offer in the absence of quan-tity distortion. Note that this is a direct outcome of thediscontinuous reduction in the price elasticity of thereseller’s order quantity as discussed after Lemma 3.Finally, note that we have restricted our analysis tothe cases where c < c4�5 for which the supplier willsell a positive quantity through her direct channel foreach market size. For c ≥ c4�5, the analysis becomesquite complex because there may be cases in whichthe supplier sells nothing through her direct channelfor either the small or the large market size. Becausefurther analysis of these cases is unlikely to yieldadditional insights, we have restricted our attention tothose cases for which the supplier always encroaches.
With Proposition 2, we can assess the impact ofsupplier encroachment on the supplier’s as well asthe reseller’s profitability. Let us denote by uppercaseçR and çS the equilibrium profits of the resellerand the supplier under encroachment when only thereseller knows the true realization of market size.We first focus on the cases with small and interme-diate direct selling costs, i.e., c ∈ 401min84341 + 2�5 ·4aH − aL55/81 c4�597.
Proposition 3. The supplier is always better off inexpectation by encroachment (i.e., çS > �S) when c ∈
401min84341 + 2�54aH − aL55/81 c4�595.
Proposition 3 shows that when the supplier’sselling cost is relatively small or intermediate,encroachment always increases the supplier’s profit.In particular, when the direct selling cost is small,0 < c ≤ 43
√�4aH − aL55/4, by encroachment, the sup-
plier can set a wholesale price, w∗ = 43aH − c5/6,more appropriately targeting the large market sizethan what she would offer without encroachment; onthe other hand, having the ability to sell the prod-uct directly with a small cost limits the potential lossif the reseller does not order when the market sizeis small. When the direct selling cost is intermedi-ate, 43
√�4aH −aL55/4 < c < min84341+2�54aH −aL55/81
c4�59, the situation faced by the supplier in ourmodel is the most similar to what has been explored
in Arya et al. (2007). In particular, the reseller isinduced to order a positive but distinct quantity foreach market size without any intentional distortion.Supplier encroachment not only introduces anotherstream of revenues to the supplier but also endowsthe supplier with a mechanism to control the sell-ing price in the retail market, which mitigates doublemarginalization.
For the reseller, although supplier encroachmentcauses him to lose the monopoly power in his mar-ket, it may also lead to a lower wholesale price. Asrevealed in Arya et al. (2007), with symmetric and fulldemand information, supplier encroachment can ben-efit or hurt the reseller depending on the supplier’sdirect selling cost. We find a similar result with asym-metric information.
Proposition 4. Given aH and aL, for any � ∈ 40115,there exists a threshold cR4�5 such that the reseller is worseoff in expectation by supplier encroachment (i.e., çR <�R)when c ∈ 401 cR4�55 and better off (i.e., çR > �R) whenc ∈ 4cR4�51min84341 + 2�54aH − aL55/81 c4�597.
Proposition 4 shows the existence of a threshold,cR4�5, with respect to the supplier’s direct sellingcost. When the supplier’s direct selling cost, c, islower than this threshold, the reseller is made worseoff from losing the monopoly position in the down-stream market as the supplier encroaches. In con-trast, when the supplier’s selling cost exceeds thisthreshold, the reseller enjoys a large efficiency advan-tage in the selling process, which helps him to gainmore profit with a lower wholesale price offeredby an encroaching supplier. The benefit from thereduction of the wholesale price outweighs the lossof demand due to the supplier’s direct competitionunder encroachment. In particular, it can be shownthat when �→ 0, cR4�5→ 43
√2aL5/8, and when �→ 1,
cR4�5 → 43√
2aH 5/8, which coincides with the thres-hold characterized in Arya et al. (2007) (with the mar-ket size a defined in their study being equal to eitheraL or aH ). Therefore, supplier encroachment can stilllead to a win–win outcome for the supplier and thereseller, even under the setting with asymmetric mar-ket information in the channel.
The above analysis focuses on the cases where thesupplier has a relatively small or intermediate sell-ing cost. In such cases, the reseller has no incen-tive to purposely distort his order quantity under thesupplier’s optimal wholesale price. However, as weobserve from Proposition 2, when the supplier’s sell-ing cost is relatively large, the supplier will set awholesale price under which the reseller will down-ward distort his order quantity if the market size issmall. Such a distortion can take a toll on both thesupplier and the reseller.
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Remark 1. There exist aH , aL, �, and c ∈ 4min84341+
2�54aH −aL55/81 c4�591 c4�55 such that both the supplierand the reseller are worse off in expectation by sup-plier encroachment.
Although it is challenging to derive the suffi-cient and necessary condition under which havingthe ability to encroach hurts the supplier herself aswell as the reseller, as a consequence of the factthat the supplier’s optimal wholesale price takesa complex implicit form when c ∈ 4min84341 + 2�54aH − aL55/81 c4�591 c4�55, Remark 1 asserts the exis-tence of such scenarios. With information asymme-try, the reseller observing a large market size has theincentive to order less to pretend to have observeda small market to induce the supplier to sell lessin her direct channel. For a sufficiently small whole-sale price, this incentive can cause the reseller tolower his order quantity to credibly signal his infor-mation when the market size is truly small. Recallfrom Lemma 3 that in the range of w for whichdistortion occurs, there is a reduction in the mag-nitude of the price elasticity of the reseller’s orderquantity. As a result, the anticipation of the reseller’spotential distortion can cause the supplier to offera higher wholesale price, which consequently ampli-fies double marginalization in the indirect channel.In contrast to the win–win outcome revealed in theearlier discussion, a lose–lose outcome can also ariseif the supplier possesses the ability to encroach whileshe has an intermediate selling cost and the proba-bility of a large market is low. This result does notoccur in the analysis of Arya et al. (2007) becauseit is driven by the information asymmetry betweenthe reseller and the supplier. It sounds an alarmover upstream encroachment when the downstreamis better informed. Supplier encroachment can create
Figure 3 Demonstration of the Impacts of Supplier Encroachment on the Supplier’s and the Reseller’s Profits with Symmetric and AsymmetricInformation Settings
0.11
0.13
0.15
0.17
0.19
0.21
0.23
0.25
0.27
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
c
Supp
lier
prof
its
Encroachment with
symmetric information
Encroachment withasymmetric information
No encroachment
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
c
Encroachment with
symmetric information
Encroach
ment with
asymmetr
ic informatio
n
No encroachment
Res
elle
r pr
ofits
Note. In this example, aH = 1035, aL = 1, and �= 0010.
downstream ordering distortion amid informationdissemination, which harms channel efficiency.
To gain a deeper intuition, we further conduct anumerical analysis to reveal all possible outcomes.First, we find that the presence of information asym-metry can have a significant impact on the benefits ofencroachment for both the supplier and the reseller,and in general, this impact is stronger when the sup-plier’s direct selling cost c becomes larger (see Fig-ure 3). However, for some range of c, the presenceof information asymmetry can also make supplierencroachment benefit the reseller more compared tothe corresponding case with symmetric information.This is because an uninformed supplier cannot tai-lor her optimal wholesale price to the realized marketsize. Second, and more interestingly, we can observefrom Figure 4 that in the presence of informationasymmetry, supplier encroachment can still lead toeither a win–win or a win–lose outcome for the sup-plier and reseller, respectively, but a lose–win or alose–lose outcome is also possible. Recall from Aryaet al. (2007) that neither of these latter two outcomesarises as a result of the development of encroach-ment capability under symmetric information. Specif-ically, even though the supplier benefits from havingencroachment capability for a relatively wide range ofparameters, she can still be worse off with a relativelysmall � (the prior probability of the large market size)when her direct selling cost is intermediate (see theleft subplot of Figure 4) or the ratio of the two mar-ket sizes is neither very large nor very small (seethe right subplot of Figure 4). For the reseller, hewill benefit from the supplier’s ability to encroachonly if he enjoys a relatively large advantage in theselling process while the ratio of the two marketsizes is small. Note that the equilibrium result in our
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Figure 4 Demonstration of the Impacts of Supplier Encroachment on the Supplier’s and the Reseller’s Profitability
0
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0.7
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Reseller better offby supplier encroachment
Supplier worse off withthe ability to encroach
c
win–lose
lose–lose
win–winSupplier does not sell when a = aL
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
aH
/aL
Reseller better offby supplier encroachment
Supplier worse off withthe ability to encroach
win–lose
lose–lose
lose–winwin–win
lose–win
� �
Notes. In this example, aL = 100. In the left plot, aH = 1035; in the right plot, c = 006.
study converges to that in Arya et al. (2007) as aH/aLapproaches 1 so that there is no information asymme-try and the signaling game does not occur. Althoughour results also converge perfectly to their results as �approaches 1, we will not have similar convergence as� becomes arbitrarily small, since the signaling gamewill always arise and there will be a discontinuitybetween the equilibrium result in our study and thatin Arya et al. (2007). Such a discontinuity is com-mon among signaling games and is not unique to ourmodel.
5. Implications for InformationManagement
Throughout the previous analysis, we have assumedthat the reseller is endowed with a better knowledgeof the market scenario than that of the supplier. In thissubsection, we explore how the supplier’s develop-ment of encroachment capability alters the extent towhich the supplier and the reseller benefit from thepossession of information. We explore this issue fromthree different perspectives. First, we take the per-spective of a supplier that may be able to chooseamong several resellers with which to do business,and we address the issue of whether the suppliershould prefer to interact with a more or less infor-mationally capable reseller (i.e., who can be betterinformed than the supplier or just equally informed).Second, we take the perspective of a supplier whois in a bilateral monopoly relationship with a singlereseller, in which the reseller’s decision to developinfrastructure to enhance his informational capabil-ity is an endogenous decision. Here, we addressthe question of how such an endogenized informa-tional strategy affects the equilibrium profits of thesupplier and the reseller. Finally, we consider the
possibility that the reseller can share demand infor-mation with the supplier, and we address the ques-tion of whether encroachment impedes or facilitatesinformation sharing.
5.1. PreliminariesTo address the questions above, we must first performsome preliminary analysis to characterize the prof-its of the supplier and the reseller with and withoutencroachment capability under two additional infor-mation structures: one in which neither firm knowsthe realized market size, and another in which bothfirms know the realized market size. As before, weuse �R and �S (çR and çS) to denote the profits ofthe reseller and the supplier without (with) supplierencroachment capability.
In the absence of encroachment, it is straightfor-ward to show that when neither the supplier nor thereseller knows the realization of the market size, theirequilibrium expected profits can be characterized as
�NIR =
�2
16and �NI
S =�2
81 (4)
where NI indicates no information. Similarly, ifboth the reseller and the supplier can observe therealization of the market size, presumably throughsome credible information-sharing mechanism, thentheir expected profits can be expressed as
�SIR =
�2 +�2
16and �SI
S =�2 +�2
81 (5)
where SI indicates shared information. Recall from§4.1 that when the reseller has private information,the profits of the reseller and the supplier are �R =
4�2 + 4�25/16 and �S = �2/8, respectively. Therefore,in the absence of supplier encroachment, we have
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that �R ≥ �SIR ≥ �NI
R while �SIS ≥ �S = �NI
S , where theinequalities are strict if and only if � > 0. That is,the reseller prefers to be privately informed to hav-ing shared information, and prefers shared informa-tion to no information. Although the supplier prefershaving shared information to either no information orhaving a privately informed reseller, she is indiffer-ent between the latter two. This finding has also beenestablished in the literature (Li and Zhang 2002).
We now provide the profits of the firms for thecase where the supplier has encroachment capabil-ity. (The detailed derivation is provided in OnlineAppendix B.) In particular, if neither firm has infor-mation about the realization of demand, then thereseller’s and the supplier’s expected profits follow:
çNIR =
2c2
9and çNI
S =3�2 − 6�c+ 7c2
120
In contrast, if they both have information about thetrue market size, then their expected profits are
çSIR =
2c2
9and
çSIS = �
3a2H − 6aHc+ 7c2
12+ 41 −�5
3a2L − 6aLc+ 7c2
120
Note that for both of the above cases of encroach-ment under symmetric information, the expectedprofit of the reseller is independent of the mar-ket size and depends only on the supplier’s rela-tive inefficiency, c.5 The reason for this is that, withsymmetric information, the supplier’s equilibriumwholesale price induces the reseller to respond byordering a quantity equal to 42c5/3, and the suppliersubsequently sets her own quantity to ensure thatthe reseller’s expected per-unit profit margin is c/3.As a result, the supplier’s development of encroach-ment capability alters the reseller’s preferences so thatinstead of preferring shared information to no infor-mation, he is indifferent between the two.
However, when the reseller has private informa-tion, an encroaching supplier can no longer ensurethat the reseller’s order quantity and profit margin areinvariant with respect to the market size, and it is notobvious whether the reseller’s having private infor-mation affects the expected profits of the supplier orthe reseller. Recall that çS and çR are the expectedprofits for the supplier and reseller under encroach-ment when the reseller has private information thatwe analyzed in §4. In what follows, we compare theseto the profit functions above and discuss the manage-rial implications.
5 This is also the case in Arya et al. (2007), though they do notdiscuss it.
5.2. Supplier Preference for an InformationallyMore or Less Capable Reseller
In settings in which a supplier can choose fromamong multiple potential resellers, it is of interest tounderstand the conditions under which she shouldprefer a reseller who is more or less capable of learn-ing the market demand. Specifically, we consider thecase where the supplier must choose between onereseller who is informationally more capable andknows the market size perfectly, and another whois less capable who has the same knowledge of themarket size as the supplier. While such a choice isstylized, it reflects the reality that resellers are nothomogenous in their abilities to collect and interpretdata for the purpose of forecasting demand. Recallthat, in the absence of encroachment, the supplieris indifferent regarding the reseller’s informationalcapability. However, when the supplier has encroach-ment capability, we have the following result:
Proposition 5. The supplier prefers a better-informedreseller if c < min84341 + 2�54aH − aL55/81 c4�59.
Once the supplier develops the ability to encroachupon the reseller’s market, the reseller’s knowledgeof the true market size matters to the supplier. Aslong as her own direct selling operations are not tooinefficient relative to those of the reseller, she prefersto interact with a reseller who has better knowl-edge of the market. Note that the condition (i.e., c <min84341 + 2�54aH − aL55/81 c4�59) specified in Propo-sition 5 serves as a sufficient condition. From ournumerical analysis (see Figure 5), however, we canmake the following observation:
Observation 1. When the supplier’s direct sellingcost exceeds a threshold level of inefficiency, she may
Figure 5 Demonstration of the Impact of Downstream InformationAdvantage on the Supplier’s Profitability in the Presence ofSupplier Encroachment
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
c
Supplier worse off witha betterinformed reseller
Supplier does not sell when a = aL
Supplier better off witha betterinformed reseller
�
Note. In this example, aH = 1035 and aL = 1.
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prefer to interact with a reseller whose information isidentical to her own to avoid the adverse effects ofdownward distortion that would arise with a better-informed reseller.
The above result is related to that of Taylor andXiao (2010), who show that for a supplier selling toa newsvendor, the supplier may or may not prefer tohave a better-informed reseller. However, our resultis driven by entirely different forces that exist only inthe presence of supplier encroachment.
5.3. Endogenous Encroachment andInformation Strategies
We now consider how a supplier’s decision todevelop encroachment capability affects the decisionof an existing reseller to develop/maintain the infras-tructure that provides him with better knowledge ofthe market demand. Specifically, we consider the fol-lowing sequence of events: First, the supplier deter-mines whether to develop encroachment capability bydeveloping the infrastructure for a direct channel, andthis decision is publicly observed. Second, the resellerdecides whether to develop advanced informationalcapability. Third, the supplier observes the reseller’sinformational capability and sets the wholesale price.Fourth, the reseller responds with an order quantity.Finally, if the supplier has a direct channel, she deter-mines her own volume of direct sales. Note that analternative sequence of events would be to assumethat the reseller decides whether to acquire spe-cific market information after the wholesale price isannounced. However, the sequence that we have pro-posed is more reasonable in environments where thereseller’s information advantage is generated fromhis informational capability and expertise in predict-ing the demand, so that even if the supplier andthe reseller receive the same data about the mar-ket demand, an informationally more capable resellermight be better able to interpret it and thus havea more accurate prediction of the true market size.To gain such informational capability would requirea relatively long-term development of infrastructure,e.g., software, data structures, human resource capa-bility; whereas, the wholesale price and ordering deci-sions can be made instantaneously. For simplicity, wenormalize to zero the cost incurred by the resellerto develop informational capability (introducing afixed cost would not change our results qualitatively).To understand how the reseller will choose his infor-mation strategy when the supplier develops encroach-ment capability, we need to compare his expectedprofits with private information, çR, from §4.2 withhis expected profits without information, çNI
R .
Proposition 6. If c ∈ 443√�4aH − aL55/41min84341 +
2�54aH − aL55/81 c4�595, then the reseller will develop
advanced informational capability relative to the supplier,which benefits both himself and the supplier (i.e., çR >çNI
R
and çS > çNIS ). Otherwise, if c ∈ 401 43
√�4aH − aL55/47
or c ∈ 4min84341 + 3� + 4√�54aH − aL55/81 c4�591 c4�55,
then çR <çNIR and the reseller will choose not to develop
advanced informational capability.
Proposition 6 confirms that even if the supplier hasencroachment capability, the reseller can still benefitfrom having better knowledge of the demand, butonly when his efficiency advantage in the selling pro-cess is intermediate so that he can avoid substantialdistortion of his order quantity. In such a scenario,the dominant effect of private information is that itallows the reseller to tailor his order quantity to therealized market size. Furthermore, the supplier alsostrictly benefits from the reseller’s endogenous deci-sion to be better informed. Recall from the results ofLi and Zhang (2002) that this will never occur in theabsence of encroachment.
However, Proposition 6 also affirms that under sup-plier encroachment, the reseller is worse off by havingbetter knowledge when his advantage in the sellingprocess is either small or large. In particular, whenc ∈ 401 43
√�4aH − aL55/47, the supplier will set a high
wholesale price for a privately informed reseller thatinduces him to order a positive quantity only if themarket size is large. Because the supplier is onlyslightly less efficient than the reseller, she is willingto monopolize the market when demand is small inreturn for setting a wholesale price that is more pre-cisely targeted at the large market size. This moreprecisely targeted (higher) wholesale price hurts thereseller. At the other extreme, when the reseller’sselling cost advantage is large, i.e., c ∈ 4min84341 +
3� + 4√�54aH − aL55/81 c4�591 c4�55, access to private
demand information causes him to substantially dis-tort his ordering quantity under low demand, whichcan result in his earning lower profit in expecta-tion than if he did not have access to the informa-tion. Note that to compare the reseller’s profits withand without advanced informational capability whenc ∈ 4min84341 + 2�54aH − aL55/81 c4�591min84341 + 3�+
4√�54aH −aL55/81 c4�595 is technically challenging, but
we observe from our numerical analysis (see Figure 6)that, within this region, there exists a threshold on thecost, c, above (below) which the reseller is worse off(better off) with advanced informational capability.
To understand the impact of a reseller’s endoge-nous information strategy upon the supplier’s deci-sion about whether to develop encroachment capa-bility, we resort to a numerical investigation. For theexample depicted in Figure 6, where aH = 1035 andaL = 1, the reseller develops advanced informationalcapability for only a relatively small range of parame-ters. However, this is not enough to deter the supplier
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Figure 6 Demonstration of the Impact of Endogenous DownstreamInformation Strategy on the Reseller’s Profitability in thePresence of Supplier Encroachment
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c
Reseller develops advanced
informational capability
Supplier does not sellReseller better off
by supplier encroachment
�
Note. In this example, aH = 1035 and aL = 1.
from encroaching. Regardless of the value of �, thesupplier benefits from encroachment over the entirerange of c for which she would exercise her ability toencroach if she could.
To further explore how the development of en-croachment capability affects the profits of the sup-plier and the reseller, we have plotted the ratio of prof-its with encroachment capability to profits withoutencroachment capability for the supplier, the reseller,and the supply chain in Figure 7. (A profit ratio largerthan unity implies a benefit from encroachment capa-bility.) Notice that in all three subfigures, curves arenot smooth. In particular, the plots of the profit ratiosshift upward when there is positive variance and c isin the range for which the reseller develops informa-tional capability. This occurs for c ∈ 4001810035 for �2 =
0003 and for c ∈ 40028100485 for �2 = 0007.There are several things worth noting in these
plots. First, observe that for the supplier, the profit
Figure 7 Impact of Demand Uncertainty on the Efficiency of the Supply Chain
1.0
1.2
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1.8
2.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6c
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0.0 0.1 0.2 0.3 0.4 0.5 0.6c
Res
elle
r pr
ofit
ratio
(Π
R/π
R)
0
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0.8
1.0
1.2
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1.1
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Supp
lier
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it ra
tio (
ΠS/
π S)
Supp
ly c
hain
pro
fit r
atio
(ΠS
+ Π
R/π
S +
πR)
�2 = 0�2 = 0.03�2 = 0.07
Note. In this example, � = 005; aH = aL = 10175 for the scenario with � 2 = 0; aH = 1035 and aL = 1 for the scenario with � 2 = 0003; and aH = 1045 andaL = 009 for the scenario with � 2 = 0007.
ratio is greater than one over the entire range of c;i.e., she benefits from having encroachment capabilityeven when it discourages the reseller from develop-ing advanced informational capability. Second, noticethat for the reseller, outside of the range of c forwhich he is better informed, greater demand variancereduces his profit ratio; i.e., he does not benefit asmuch from demand variance under encroachment ashe does without it. As a consequence, we can see thatas demand variance increases, there is a reduction inthe range of c for which the reseller benefits fromencroachment, i.e., where his profit ratio exceeds 1.Also note that in the range of c for which the reselleris better informed under �2 = 0003 (and �2 = 0007),his profit ratio exceeds that for �2 = 0. This is becausewhen the reseller endogenously develops advancedinformational capability, there is little or no orderingdistortion, and demand variance reduces the extent towhich he is harmed by encroachment, though not byenough to allow him to benefit.
Finally, we can observe that the range of c for whichthe entire supply chain is harmed by the supplier’sdevelopment of encroachment capability is increasingin demand variance. This can be confirmed by the factthat, as �2 increases, a larger portion of the supplychain profit ratio curve lies below 1.0. This is a resultof the fact that encroachment discourages the devel-opment of advanced informational capability at thereseller, whereas in the absence of encroachment, thetotal supply chain profit increases when the resellerdevelops advanced informational capability.
5.4. Credible Information SharingThus far, we have assumed that there does not exista credible mechanism for information sharing. Let usnow relax this assumption and consider how the sup-plier’s development of encroachment capability mightaffect the incentives for both firms to pursue a meansfor credibly sharing information.
It is well established in the literature that, in theabsence of supplier encroachment, �R ≥ �SI
R , while
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�SIS ≥ �S ; i.e., the reseller prefers being privately
informed over having shared information with thesupplier, while the supplier would prefer shared infor-mation over the reseller’s having private information(see, e.g., Li and Zhang 2002). However, once the sup-plier has encroachment capability, both the supplier’sand the reseller’s preferences between informationstructures can change as described in the followingproposition.
Proposition 7. (i) When the supplier has encroach-ment capability, information sharing always benefits thesupplier (i.e., çSI
S ≥çS).(ii) However, the reseller prefers to share his informa-
tion (i.e., çSIR > çR) when c ∈ 401 43
√�4aH − aL55/47
or c ∈ 4min84341 + 3� + 4√�54aH − aL55/81 c4�591 c4�55,
and she prefers not to share his information (i.e., çR >çSI
R ) when c ∈ 443√�4aH − aL55/41min84341 + 2�54aH −
aL55/81 c4�595.
Knowing the exact market scenario always benefitsthe supplier because she can set a targeted wholesaleprice for each market size and avoid reseller order dis-tortion. However, for the reseller, having shared infor-mation with the supplier is a double-edged sword.On one hand, shared information allows the sup-plier to optimize the wholesale price for each marketsize. Of course, this hurts the reseller as a conse-quence of the fact that his profit function is con-cave in the wholesale price. On the other hand, whenan encroaching supplier obtains access to the samemarket information as the reseller, it alters her strat-egy in setting the wholesale price, so the reseller isinduced to sell a positive quantity even when the mar-ket size is small and the supplier’s cost disadvantageis small (i.e., c ∈ 401 43
√�4aH − aL55/45); furthermore,
information sharing will also cure the reseller’s incen-tive to distort his order quantity when the supplier’sdirect selling cost is large (e.g., c ∈ 4min84341 + 3� +
4√�54aH −aL55/81 c4�591 c4�55), which will improve the
efficiency. As a result, in contrast to the case with-out supplier encroachment, Proposition 7 asserts thatunder supplier encroachment, both the supplier andthe reseller may benefit from the development ofsome means by which the reseller can credibly shareits demand information. In other words, once thesupplier has encroachment capability, a shift from aninformation structure in which the reseller is privatelyinformed to one in which both firms have sharedinformation is Pareto improving. This is not the casewithout encroachment, and suggests that the devel-opment of mechanisms for credibly sharing informa-tion might be more likely to occur in supply chains inwhich the supplier has its own direct channel.
6. Discussion and ConclusionIn this paper, we investigate supplier encroachmentin the presence of information asymmetry where the
reseller has private information about the market size.We show that in such a setting, if the supplier usesa linear wholesale price, supplier encroachment cancause the reseller to practice costly signaling anddistort his order quantity downward. In addition,the supplier may increase her wholesale price andthus amplify double marginalization. Consequently,there are parameters for which supplier encroachmentleads to win–win, win–lose, lose–win, and lose–loseoutcomes for the supplier and the reseller. These find-ings complement existing results that show how sup-plier encroachment mitigates double marginalizationwhen both firms have the same information.
We also demonstrate that supplier encroachmentcan have significant implications for informationmanagement in supply chains. We find that when thesupplier has the ability to encroach, she will strictlyprefer to sell to a better-informed reseller when herefficiency disadvantage in the selling process is notlarge; otherwise, she will prefer to sell to an equallyinformed reseller. This result complements prior lit-erature that has shown that with a reselling channelalone, the supplier is indifferent toward the reseller’sstate of information. On the other hand, we findthat when the supplier has encroachment capability,the reseller may prefer to remain uninformed aboutdemand, which contrasts with existing results thathave been obtained without encroachment. We fur-ther show that even though encroachment alwaysbenefits the supplier after the reseller’s informationstrategy is endogenized, it can hurt the total supplychain performance because the reseller is discouragedfrom obtaining advanced information. Finally, ourstudy reveals that both the supplier and the resellermay benefit from the development of a mechanismthat will allow the reseller to credibly reveal his pri-vate demand information, which does not happen inthe absence of encroachment.
Of course, our model also has some limitations.First, to avoid unnecessary complications, we haveassumed that the reseller releases to the market all ofthe units that he orders, even if it might be ex postsuboptimal to do so. If we were to allow the resellera free-disposal option, this will tend to undermine thereseller’s ability to commit to a sales quantity, butonly when the wholesale price is relatively high. Con-sequently, a free-disposal option plays a role onlywhen both the ratio aH/aL is large and the probabil-ity of a large market, �, is sufficiently small. When itdoes play a role, it causes the reseller to order less forthe large market size, and forces him to further distorthis order quantity for the small market size. How-ever, our main insights are robust to the free-disposaloption. For further discussion of this, we refer readersto Online Appendix C.
A second limitation is the fact that we do not con-sider the possibility thatonce the supplier develops a
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direct channel, she may have access to a new sourceof information. In Online Appendix C, we extend ourmodel to allow for the supplier to receive a noisy sig-nal about demand if she develops encroachment capa-bility. This enables the supplier to tailor her wholesaleprice according to the signal that she receives. How-ever, so long as the signal is imperfect, the signalinggame between the supplier and reseller always arises,and all of our main results continue to hold quali-tatively. Of course, it is also possible that both thesupplier and the reseller may have imperfect signalsabout demand. Because it would introduce the possi-bility of signaling behavior for both the supplier andthe reseller, this may alter the dynamics, which is aworthy subject for future research.
Finally, our model assumes that the supplier is lim-ited to a linear wholesale price. Because linear whole-sale prices are common in practice and are standardin the literature, it is useful to focus on them initially.However, it is also of interest to understand the impli-cations of encroachment when a supplier can use amore sophisticated pricing mechanism. Under a non-linear pricing policy, the issues shift from signallingto screening. The analysis and insights are fundamen-tally different, as revealed in Li et al. (2013).
AcknowledgmentsThe authors are grateful to the department editor, the asso-ciate editor, and the referees for their thoughtful commentsand suggestions that improved this paper.
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