strategic information sharing in a supply chain

European Journal of Operational Research 174 (2006) 1567–1579

www.elsevier.com/locate/ejor

Production, Manufacturing and Logistics

Strategic information sharing in a supply chain

Wai Hung Julius Chu a,*, Ching Chyi Lee b

a Emerson Electric Asia-Pacific, Suite 6701, Central Plaza, 18 Harbour Road, Wanchai, Hong Kongb Faculty of Business Administration, Department of Decision Sciences and Managerial Economics,

The Chinese University of Hong Kong, Shatin, NT, Hong Kong

Received 29 April 2003; accepted 16 February 2005Available online 17 May 2005

Abstract

We consider a two-member supply chain that manufactures and sells newsboy-type products and comprises a down-stream retailer and an upstream vendor. In this supply chain, the vendor is responsible for making stock-level decisionsand holding the inventory, and the retailer is better informed about market demand. In each period, the retailer receivesa signal about market demand before the actual demand is realized, and must decide whether to reveal the informationto the vendor, at a cost, before the vendor starts production. We assume that any information that the retailer reveals istruthful. We model the situation as a Bayesian game, and find that, in equilibrium, whether the retailer reveals or with-holds the information depends on two things—the cost of revealing the information and the nature of market demandsignal that the retailer receives. If the cost of sharing the information is sufficiently large, then the retailer will withholdthe information from the vendor regardless of the type of signal that is received. If the cost of sharing the information issmall, then the retailer will reveal the information to the vendor if a high demand is signaled, but will withhold it from thevendor if a low demand is signaled. In general, reducing the cost of sharing information and increasing the profit marginof either the retailer or the vendor (or reducing the cost of the vendor or retailer) will facilitate information sharing.� 2005 Elsevier B.V. All rights reserved.

Keywords: Information sharing; Supply chain; Asymmetric information; Game theory

1. Introduction

Information sharing is an important issue in supply chain management, particularly in some of the newsupply chain practices that have recently become popular, such as vendor managed inventories (VMI), clickand mortar, drop shipping, and vendor hubs. These new supply chain practices have one thing in

0377-2217/$ - see front matter � 2005 Elsevier B.V. All rights reserved.doi:10.1016/j.ejor.2005.02.053

* Corresponding author. Fax: +852 28272168.E-mail address: [email protected] (W.H.J. Chu).

mailto:[email protected]

1568 W.H.J. Chu, C.C. Lee / European Journal of Operational Research 174 (2006) 1567–1579

common—the stock level of the supply chain is determined by the upstream members of the supply chain,who are usually less informed than the downstream members about market demand. Thus, to guarantee thesuccess of these new supply chain management practices, it is essential that the better-informed downstreammembers of the chain share their demand information effectively and efficiently with the less-informed upstream members. Advocates of these new practices often emphasize the importance ofinformation sharing in the supply chain.

There is no doubt that effective information sharing allows a supply chain to operate more efficiently, andhence generate a higher overall supply chain profit. However, information sharing often involves cost. If thecost of information sharing is solely born by the informed party, and if, in addition, there is no pre-definedmechanism to distribute some of the additional profit that is generated through the information sharing to theinformed party, then it is debatable whether the informed party has any incentive to share information withthe uninformed party. In fact, researchers have noticed that many members of supply chains are doubtfulabout information sharing. Clark and Hammond (1997) report that:

Retailers generally acknowledged that providing additional information to manufacturers would offersome savings to the manufacturers, but many retailers were skeptical about the benefits for their firmsin sharing information with manufacturers.

Cost is one of the key factors that may hinder information sharing. The main purpose of this paper is there-fore to study how the incentive to share information is related to the cost of that sharing in the specific contextof a supply chain that manufactures and sells newsboy-type products. The supply chain has two members—the upstream vendor (V) and the downstream retailer (R). In this supply chain, there is no cost for the retailerfor overstocking because the vendor makes the stock level decisions and keeps the inventory. In each period,the retailer receives a signal about market demand before the actual demand is realized, and must then decidewhether to reveal it voluntarily to the vendor at a cost before production begins, or whether to withhold theinformation. We assume any information that the retailer decides to reveal is truthful. We model the situationas a Bayesian game and find that, in equilibrium, whether or not the retailer reveals the information to thevendor depends on two things—the cost of revealing the information, and the nature of the market demandsignal that is received. If the cost of sharing the information is sufficiently large, then the retailer will withholdthe demand information from the vendor regardless of the type of signal that is received. When the cost ofsharing information is smaller, the retailer will reveal the information to the vendor if a high demand is sig-naled, but will withhold it if a low demand is indicated. The latter result is driven by the fact that the retailerbears no overstock cost, and hence would like the vendor to stock as much inventory as possible. If the retailerknows that the demand is likely to be high, then he would want to ensure that the vendor receives the signalcorrectly and consequently stocks a high level of inventory. If the retailer knows that the demand is likely tobe low, then there will be no incentive to reveal the information to the vendor, even though the vendor may beable to partially infer from the retailer�s action that the demand is low. Basically, there is a cutoff value ofmarket demand that separates these two cases. Further study on this cutoff yields some interesting managerialimplications. In general, reducing information sharing cost and increasing the profit margin of either the ven-dor or the retailer (or reducing their costs) will facilitate information sharing.

The rest of this paper is organized as follows. The next section provides a brief survey of the related lit-erature. The model is described in Section 3, and the analysis of the model is given in Section 4. Section 5offers some concluding remarks.

2. Related literature

There is no lack of literature about information sharing in supply chains. Lee and Whang (2000) providesome real life examples of information sharing in a supply chain, and Bourland et al. (1996) and Chen

W.H.J. Chu, C.C. Lee / European Journal of Operational Research 174 (2006) 1567–1579 1569

(1998) develop theoretical models of sharing stationary stochastic downstream demand and inventory datato improve stock level decisions of the upstream. Lee et al. (1997a,b) address the bullwhip effect and Lee etal. (2000) consider the value of information sharing under a known autoregressive demand process. Gavirn-eni et al. (1999) and Cachon and Fisher (2000) study and quantify the value of sharing sales information toovercome demand distortion due to order batching, and Chen et al. (2000) analyze the effects of the fore-casting process on information sharing.

All of these papers report that there are some benefits to sharing demand information, although thesebenefits vary substantially. Gavirneni et al. (1999) conclude that information sharing is more beneficialwhen the capacity of the upstream members of a supply chain is unlimited. Moreover, Lee et al. (2000) sug-gest that the value of sharing demand information can be quite high, especially when the underlying de-mand is significantly correlated over time, when demand is highly variable, or when there is a longreplenishment lead-time. However, Raghunathan (2001) revisits their model and shows that the value ofinformation sharing is insignificant when the upstream members reduce the variance of the demand forecastby analyzing the entire order history. Hence, information sharing is valuable only if the information cannotbe inferred by the receiving party.

In another group of studies, the sharing of accurate demand information through contracts is examined,and readers are referred to Tsay (2000) for a recent review of these studies. Cachon and Lariviere (2001)study contracts that induce credible information sharing when there is asymmetric information. Even whenthe downstream members of a supply chain have an incentive to provide an overly optimistic demand fore-cast, they identify contracts that ensure credible information sharing.

Our model differs from those that have been developed in previous research in one major aspect. Wedo not take information sharing in a supply chain for granted. We recognize the fact that even thoughinformation sharing may be beneficial to the supply chain as a whole, the better-informed party willhave no incentive to share the information with the uninformed party if there is no benefit for themin doing so. In our model, the informed party (the retailer) bears the cost of the information sharingalone, and the passing of information from the informed party to the uninformed party (the vendor)is undertaken voluntarily and truthfully. The informed party does not receive any side payment fromthe uninformed party for the information transfer. The only benefit that the informed party may obtainfrom sharing the information is a possible increase in payoff due to the better stock level decisions thatwould be made by the uninformed party as a result of the information. However, such a benefit must beat least greater in value than the cost of sharing the information to justify the action. Hence, the deci-sion of whether or not to reveal the information to the uninformed party is made strategically by theinformed party.

3. The model

We consider a supply chain that consists of two members—the downstream retailer R and the upstreamvendor V. V supplies R with newsboy-type products to be sold to the end market. This means that the fol-lowing assumptions hold. First, the market demand in all periods is independent and identically distributed.Second, all of the cost and price parameters remain fixed from period to period. Third, backordering is notallowed, and finally, no unsold item in a given period has any value in future periods. These assumptionseffectively reduce a multi-period problem to a single period problem. We assume that all members are riskneutral, and have a zero-order setup cost.

The market demand is denoted as Y = X + H, where X and H are independent variables. X is a randomvariable having support on [0,1) and is governed by a continuously differentiable probability density func-tion f(x), with the corresponding cumulative probability function being F(x). H, which is a random variablethat represents the minimum market demand, is governed by a continuously differentiable probability


density function g(h) with support on [a, b], where a P 0. The corresponding cumulative function of g(h) isG(h). In each period, R receives a signal that indicates the actual value of H before the realization of Y, andmust decide whether to reveal this information to V before V makes a stock decision. Assuming that thesignal received by R is h, then the conditional probability of Y given h is denoted as Fh(y), with the corre-sponding density function being fh(y). Note that Fh(y) = Prob (yjh) = Prob (x + hjh) = F(x) = F(y � h),and similarly that fh(y) = f(y � h). Also note that once it is known that H = h, then E(Y) is known tobe equal to E(X) + h. Thus, although our model can be interpreted as R receiving a signal about minimumdemand, it can also be interpreted as R receiving a signal about mean demand. Except for the actual valueof H which is only known by R before the realization of the actual demand, all of the parameters and prob-ability distribution functions are assumed to be common knowledge.

3.1. Chronology of events

For any given period, the chronology of events is as follows:

1. R receives a signal h and must then decide whether to reveal it to V. We assume that any informationthat R reveals is truthful. Moreover, we assume that there is a non-negative operating cost for R inrevealing the information. The cost of revealing the information is denoted as k.

2. If R chooses to reveal the actual value of h to V in the previous step, then V will become fully informed ofthe distribution of Y, and will then choose a stock level qh. Note here that the subscript h of qh indicatesthat V�s stock level decision in this case is dependent on h. If, on the other hand, R chooses to withholdthe information, then V will make the stock level decision based on incomplete information about Y. Wedenote the stock level that is chosen by V in this case as ~q. Note that as V does not know the actual valueof h when ~q is chosen, ~q does not depend on h. Instead, ~q depends on V�s posterior belief about h. Theunit production cost of V is cV.

3. Demand y is realized. If V�s stock level is higher than or equal to the demand, then V supplies R with y

units of goods at a unit price of pV, and the excess inventory has a residual value of rV per unit. If V�sstock level is lower than the demand, then V supplies R with all of the units of goods that are produced ata unit price pV.

4. R sells the goods to the market at a unit price pR. The unit cost of R is cR = pV + wR, where wR can beinterpreted generally as the unit transaction cost that is necessary to bring the goods from the upstreamto the downstream.

3.2. Assumptions

To make the analysis non-trivial, we assume that pi > ci > ri P 0 (i = V, R) and that wR P 0. The for-mer is simply a standard assumption of the newsboy problem and the latter ensures that R�s transactioncost is non-negative. For technical reason and to simplify the analysis, we further assume that the proba-bility function for H satisfies the following:

A1 g(h)/G(h) is strictly decreasing in h.

This assumption, which is quite similar to the standard monotone hazard rate assumption, is often re-ferred to as the monotone reversed hazard rate assumption (Shaked and Shanthikumar, 1994). Amongthe commonly used distribution functions, the exponential function and the family of power functions,F ðxÞ ¼ ðx�a

b�a Þm, where m P 1 and x 2 [a, b], both satisfy this assumption. Note that uniform distribution

is a member of the power function family (m = 1).


Finally, as H is assumed to be a continuous variable, we impose the following tiebreak rule.

A2 If R is indifferent between revealing and withholding the information, then he will withhold the demandsignal from V.

This sequence of events is very typical in environments such as the supply chains of fast moving con-sumer goods (FMCG), consumer packaged goods (Kumar, 2004), and passive electronic components(Kopczak, 1997, 1998). In these kinds of supply chains, the products that are involved are typicallyshort-lived (newsboy-type products) and the upstream members of the chain are responsible for the stocklevel decisions.

4. The analysis

As the model that has been described is an incomplete information game, in this section, we will char-acterize the perfect Bayesian equilibrium of the game. For a detailed definition of perfect Bayesian equilib-rium, we refer the reader to Fudenberg and Tirole (1991). We focus here only on pure strategy equilibrium.

We first consider the case in which R reveals information to V.If R chooses to reveal h to V, then V will become fully informed of the distribution of Y, and will then

choose the stock level qh to maximize his expected profit PV(qh), where

PV ðqhÞ ¼ pV Ey minðqh; yÞ � cV qh þ rV Eyðqh � yÞþ

¼ pV hþ Ex min ðqh � hÞ; x½ �f g � cV qh þ rV Ex qh � ðxþ hÞ½ �þ. ð1Þ

Throughout the paper, the operator (a)+ is used to indicate the maximum of a and zero, and hence[qh � (x + h)]+ represents the excess inventory. This is basically a newsboy problem, and V�s optimal choiceof qh in this case is

q�h ¼ F �1 pV � cV

pV � rV

� �þ h ¼ F �1 KVU

KVU þ KVO

� �þ h ¼ F �1ðnV Þ þ h. ð2Þ

Here, KVO = (cV � rV) is the cost of overstocking and KVU = (pV � cV) the cost of understocking for V,and nV = (KVU/KVU + KVO) is the critical fractile ratio. Substituting q�h into (1), and after simplification,we obtain V�s maximum expected profit when R reveals h

PV ðq�hÞ ¼ KVU q�h � ðKVO þ KVU ÞZ ðq�h�hÞ

0

F ðxÞdx. ð3Þ

In addition, R�s expected profit in this case is

PRðq�h; hÞ ¼ ðpR � cRÞEy minðq�h; yÞ � k ¼ KRU q�h �Z ðq�h�hÞ

0

F ðxÞdx� �

� k ð4Þ

where KRU = (pR � cR) is R�s cost of understocking.Before we proceed to the analysis of the case in which R withholds the information, we introduce the

following lemma.

Lemma 1. In any pure strategy equilibrium, if R is supposed to reveal the information when he receives a

demand signal h 0, then he will also reveal it when he receives any other demand signal h00 > h 0. On the other

hand, if R is supposed to withhold the information when he receives a demand signal h 0, then he will also

withhold the information when he receives any other demand signal h00 < h 0.

Proof. Please refer to Appendix 1 for the proof. h


Lemma 1 has an important implication that greatly simplifies our later analysis. If, in any equilibrium,R�s revelation of the signal to V depends on the signal h that is received, then it must be the case that R willreveal the information only when h has a relatively large value. Let h be the specific value of the demandsignal that leads R to be indifferent between revealing and withholding the information. Then, by Lemma 1,R will reveal h to V if and only if h > h. Note that there may not exist any h in the interval [a, b] when k issufficiently large, because h would have to be greater than b, the upper bound of its support, for the indif-ference to hold. This means that, in equilibrium, R will always withhold the information, regardless of thesignal h that is received.

Let us assume that an h exists in the interval [a, b]. When R withholds the information, V can theninfer that the actual value of h must be between a and h, and V�s posterior belief about h is thereforeupdated to

ghðhÞ ¼ gðhÞ=GðhÞ 8h 2 ½a; b�. ð5Þ
The corresponding cumulative function is
GhðhÞ ¼ GðhÞ=GðhÞ 8h 2 ½a; b�. ð6Þ
Thus, if R withholds the information, then given h 2 ½a; b� and the posterior belief ghðhÞ, V will choose thestock level ~q to maximize his expected profit ePV ð~qÞ, where ePV ð~qÞ ¼ Eh pV Ey minð~q; yÞ � cV ~qþ rV Eyð~q� yÞþ
� �¼Z h

a

Z ~q

hKVU y � KVOð~q� yÞ½ �fhðyÞdy þ

Z 1

~qKVU ~qfhðyÞdy

� �ghðhÞdh. ð7Þ

The first-order condition for the maximum of ePV ð~qÞ is

d ePV ð~qÞd~q

¼Z h

aKVU � KVO þ KVUð ÞF hð~qÞ½ �ghðhÞdh ¼ 0. ð8Þ

Define

UhðyÞ ¼Z h

aF hðyÞghðhÞdh. ð9Þ

Note that UhðyÞ is simply a conjugated probability distribution function, and thus it is easy to verify thatUhðyÞ satisfies all of the basic probability axioms. Substituting (9) into (8), we find that V�s optimal choice ofstock level ~q�h must satisfy

~q�h ¼ U�1h

pV � cV

pV � rV

� �¼ U�1

h ðnV Þ. ð10Þ

Using (9), the condition that is given in (10) can also be written as

Uh ~q�h�

¼Z h

aF h ~q�h�

ghðhÞdh ¼ nV . ð11Þ

Here, the subscript h of ~q�h is used to indicate that ~q�h is actually dependent on h.Substituting ~q�h into (7), and after simplification, V�s maximum expected profit can be shown to be equal

to

ePV ~q�h�

¼ KVU ~q�h � KVO þ KVUð ÞZ h

a

Z ~q�h

hF hðyÞghðhÞdy dh. ð12Þ


Thus, R�s expected profit if the information is withheld is

ePR ~q�h; h�

¼ pR � cRð ÞEy min ~q�h; y�

¼ KRU ~q�h �Z ~q�

h�h

�0

F ðxÞdx

264375. ð13Þ

By comparing (4) and (13), we can see that R will withhold the demand signal h from V if and only if

ePRð~q�h; hÞP PRðq�h; hÞ () KRU ~q�h �Z ð~q�

h�hÞ

0

F ðxÞdx� �

P KRU q�h �Z ðq�h�hÞ

0

F ðxÞdx� �

� k

() k P KRU

Z q�h�h

~q�h�h½1� F ðxÞ�dx ¼ KRU

Z F�1ðnV Þ

~q�h�h

½1� F ðxÞ�dx. ð14Þ

The last equality results from the fact that, by (2), q�h ¼ F �1ðnV Þ þ h.There is an intuitive explanation for (14). As q�h is the level of stock that R expects V to choose when the

information is revealed, ~q�h is the level of stock that R expects V to choose when the information is withheld,and KRU is R�s cost of understocking, then the right-hand side of (14) is the reduction in R�s expected cost ofunderstocking if the information is revealed (compared with the case if the information is withheld). Thus,if the cost of revealing information, k, is higher than the reduction in the expected cost of understocking,then clearly, R will withhold the information. Note that ~q�h may be larger than q�h. In this case, (14) willclearly hold, because the expected cost of understocking increases rather than decreases when R revealsthe information. This happens when R expects V to choose a higher stock level when the demand informa-tion is withheld than when the information is revealed. As R has no cost associated with overstocking, R

clearly prefers a higher stock level, and thus in this case will withhold the information.When h ¼ h, by the definition of h, R is indifferent between revealing and withholding the information.

Hence, h must satisfy

k ¼ KRU

Z q�h�h


Z F�1ðnV Þ

~q�h�h

½1� F ðxÞ�dx. ð15Þ

We now introduce the following lemma.

Lemma 2. Given assumption A1, ~q�h� h is continuous and strictly decreasing in h for all h 2 ½a; b�.

Proof. Please refer to Appendix 2 for the proof. h

We are now ready for our first result, which states that when k is sufficiently large, then R will neverreveal the actual value of h to V in equilibrium.

Proposition 1. If the cost of revealing information k is sufficiently large such that

k P KRU

Z F�1ðnV Þ

~q�b�b½1� F ðxÞ�dx;

then there exists a unique pure strategy perfect Bayesian equilibrium in which R always withholds the infor-

mation, regardless of the signal h that is received.

Proof. Note that, by (14), k P KRU

R F�1ðnV Þ~q�b�b ½1� F ðxÞ�dx implies that ePRð~q�b; bÞP PRðq�b; bÞ.

This means that if R expects V to choose the stock level ~q�b when the information is withheld, then R willnot deem it worthwhile to reveal the information even when the demand signal is h = b. By Lemma 1, as R


will withhold the information when the signal is h = b, R will also withhold it when the signal is h < b.Thus, for the given condition, R will withhold the information regardless of the value of h.

Now, given that R will always withhold the information regardless of the value of h, V�s posterior beliefabout h remains the same as his prior belief when he finds that the information is being withheld by R.Thus, believing that h 2 [a, b] (* h ¼ bÞ, V chooses the optimal stock level accordingly, which is ~q�b. So, thegiven condition indeed leads to a pure strategy equilibrium.

To check that this is the only equilibrium, let us assume that another equilibrium exists in which R willreveal the information if and only if h > h, where a 6 h < b. In such an equilibrium, as is explained in (15),because R is indifferent between revealing and withholding the information when the signal h ¼ h isreceived, the following must hold:

k ¼ KRU

Z F�1ðnV Þ

~q�h�h

½1� F ðxÞ�dx.

As ~q�b � b < ~q�h � h by Lemma 2 (* h < b), we therefore have

k < KRU

Z F�1ðnV Þ


which violates the given condition. Thus, such an equilibrium cannot exist, and the equilibrium that is de-scribed in the proposition is indeed the only possible pure strategy equilibrium. h

Proposition 1 describes the condition under which R always withholds the information in equilibrium.We now consider the case in which

k < KRU

Z F�1ðnV Þ

~q�b�b½1� F ðxÞ�dx. ð16Þ

In this case, the condition that is given in Proposition 1 is violated, and hence the equilibrium that isdescribed in the proposition is no longer valid.

Lemma 2 states that ~q�h � h is continuous and strictly decreasing in h for all h 2 ½a; b�. Hence, if (16)holds, then there must exist a unique h 2 ½a; b� such that (15) holds, i.e.,

k ¼ KRU

Z q�h�h


Z F�1ðnV Þ

~q�h�h

½1� F ðxÞ�dx.

As has been explained, given that R expects V to choose stock level ~q�h if the information is withheld, andexpects V to choose q�h if the information is revealed, then the aforementioned equality means that R isindifferent between revealing and withholding the information when the signal is h ¼ h. Hence, by Lemma1, R will withhold the information if the signal is h 6 h, and will reveal the information if the signal is h > h.

Given the strategy of R that has just been described, V�s posterior belief about h becomes GhðhÞ when R

withholds the demand information. In this case, believing that h 2 ½a; h�, V chooses the optimal stock level~q�h accordingly. Thus, condition (16) also leads to a pure strategy equilibrium. In addition, given that thereis only one h that satisfies (15), the equilibrium described above must be unique.

We now summarize the above discussions into the following proposition.

Proposition 2. If the cost of revealing information, k, satisfies

k < KRU

Z F�1ðnV Þ



then there exists a unique pure strategy perfect Bayesian equilibrium in which R will reveal the demand signal h

to V if and only if h > h, where h satisfies (15).

Proof. See the previous discussions. h

4.1. Properties of h

Note that, in equilibrium, h and ~q�h must satisfy (15). As KRU = pR�cR = pR � (pV + wR), and lettingx* = F�1(nV), Eq. (15) can be rewritten as:

k ¼ KRU

Z F�1ðnV Þ

~q�h�h

½1� F ðxÞ�dx ¼ ðpR � pV � wRÞZ x�

~q�h�h½1� F ðxÞ�dx. ð17Þ

We now investigate the way in which h changes with k, pV, cV, rV, pR, and wR.Differentiating both sides of Eq. (17) with respect to k, we obtain

dhdk¼ K�1

RU 1� F ~q�h � h �h i�1

1�d~q�hdh

� ��1

. ð18Þ

Becaused~q�

h

dh< 1 by Lemma 2, it must be the case that dh

dk > 0.Differentiating both sides of Eq. (17) with respect to pV, we obtain

0 ¼ �Z x�

~q�h�h½1� F ðxÞ�dxþ ðpR � pV � wRÞ ½1� F ðx�Þ� dx�

dpV

þ ½1� F ð~q�h � hÞ� dhdpV

1�d~q�hdh

� �( ). ð19Þ

Note that as F ðx�Þ ¼ nV ¼ pV �cV

pV �rV; dx�

dpV¼ cV �rV

f ðx�ÞðpV �rV Þ2> 0ð* cV > rV Þ. As the first term on the right-hand side of

(19) is negative, the sign of dhdpV

cannot be determined immediately, because pR � pV � wR > 0; dx�

dpV> 0 and

d~q�h

dh< 1 (by Lemma 2). However, it can be shown that dh

dpV? 0 if k � ðpR � pV � wRÞ2½1� F ðx�Þ� dx�

dpV? 0. Thus,

dhdpV

> 0 for a relatively large k and dhdpV

< 0 for a relatively small k.

Differentiating both sides of Eq. (17) with respect to cV, we obtain

0 ¼ ðpR � pV � wRÞ ½1� F ðx�Þ� dx�

dcVþ ½1� F ð~q�h � hÞ� dh

dcV1�

d~q�hdh

� �( ). ð20Þ

As dx�

dcV¼ �1

f ðx�ÞðpV �rV Þ < 0ð* pV > rV Þ andd~q�

h

dh< 1, we must have dh

dcV> 0.

Differentiating both sides of Eq. (17) with respect to rV, we obtain

0 ¼ ðpR � pV � wRÞ ½1� F ðx�Þ� dx�drVþ ½1� F ð~q�h � hÞ� dh

drV1�

d~q�hdh

� �( ). ð21Þ

As dx�

drV¼ pV �cV

f ðx�ÞðpV �rV Þ2> 0 ð* pV > cV Þ and

d~q�h


drV< 0.

Differentiating both sides of Eq. (17) with respect to pR, we obtain

0 ¼Z x�

~q�h�h½1� F ðxÞ�dxþ ðpR � pV � wRÞ½1� F ð~q�h � hÞ� dh

dpR

1�d~q�hdh

� �. ð22Þ

As the first term on the right-hand side of (22) is positive, andd~q�

h


dpR< 0.


Finally, differentiating both sides of Eq. (17) with respect to wR, we obtain

0 ¼ �Z x�

~q�h�h½1� F ðxÞ�dxþ ðpR � pV � wRÞ½1� F ð~q�h � hÞ� dh

dwR1�

d~q�hdh

� �. ð23Þ

As the first term on the right-hand side of (23) is negative andd~q�

h


dwR< 0.

We can now summarize these results.

1. Because dh=dk > 0, as k increases, the likelihood that R will reveal the demand information decreases.By contrast, as k decreases, the likelihood that R will reveal the demand information increases.

2. As dh=dcV > 0, an increase in V�s production cost will decrease the likelihood that R will reveal thedemand information, or to put it differently, a decrease in V�s production cost can increase the likelihoodthat R will reveal the demand information.

3. As dh=drV < 0, an increase in V�s salvage value will increase the likelihood that R will reveal the demandinformation.

4. As dh=dpR < 0, an increase in R�s price (retailer price) will increase the likelihood that R will reveal thedemand information.

5. As dh=dwR > 0, an increase in R�s transaction cost will decrease the likelihood that R will reveal thedemand information, or to put it differently, a decrease in R�s transaction cost will increase the likelihoodthat R will reveal the demand information.

6. As a change in pV will affect the profit margins of both V and R, the effect of a change in pV on the like-lihood that R will reveal the demand information is less clear. Depending on the values of the otherparameters, a change in pV may increase or decrease the likelihood that R will reveal the demandinformation.

In general, with the exception of a change in pV, we can conclude that a decrease in information sharingcost or an increase in the profit margin of either V or R (a decrease in cV, an increase in rV, an increase in pR,or a decrease in wR) will increase the likelihood that R will reveal the demand information.

5. Conclusion

In the preceding sections, we consider voluntary information sharing between a pair of asymmetricallyinformed members of a supply chain in which the less-informed upstream vendor V makes the stock leveldecision, and the better-informed downstream retailer R must decide whether or not to reveal the marketdemand information to the vendor before the vendor makes the stock level decision. We model the situa-tion as a Bayesian game and find that, in equilibrium, whether the retailer reveals or withholds the infor-mation depends on two things—the cost of revealing the information, and the nature of the market demandsignal that is received. If the cost of information sharing is sufficiently large, then the retailer will withholdthe information from vendor regardless of the nature of the signal that is received. If the cost of sharinginformation is smaller, then the retailer will reveal the information to the vendor if a high demand is sig-naled, but will withhold it if a low demand is signaled. In general, reducing the cost of information sharingor increasing the profit margin of either the retailer or the vendor (or reducing the costs of either) will facil-itate information sharing.

Because the vendor can expect to make better stock level decisions and achieve higher expected profits ifbetter information about the market demand can be obtained, then the vendor should have an incentive tohelp to reduce the cost to the retailer of revealing information. The adoption of information technology(IT) with adequate system integration, for example, can clearly help to reduce the cost to retailers of reveal-


ing information, and would hence promote information sharing. This may explain why IT has become animportant enabler in many new supply chain practices. However, IT investment must be economically jus-tifiable. To help reduce the retailer�s cost, the vendor could share part of the IT implementation cost. Ourmodel can be used to help evaluate the benefit of information sharing to justify an investment decision. Forexample, if a company intends to install Radio Frequency Identification (RFID) to facilitate the transfer ofinformation, then our model can be used to evaluate its cost and benefit. If the cost outweighs the benefit,then our model can be used to evaluate the extent to which the vendor could help to share the cost to makeRFID investment an economically viable option.

Furthermore, some types of information cost more to reveal than others. If there are different types ofinformation that all serve the same purpose, then the information that is the least costly should be used. Forexample, it is often more costly to share point-of-sale (POS) data than aggregated data. Thus, if aggregateddata is sufficient for the purpose, then there is little value in sharing POS data. To conclude, by reducing thecost of revealing information, the incentive for the downstream members of a supply chain to share infor-mation will increase, and thus the upstream members will have a better chance of obtaining valuable infor-mation from the downstream members.

Our analysis shows that a lower operating cost facilitates information sharing, and thus the upstreammembers of a supply chain should develop lean business processes to reduce internal operating cost, whichin turn will encourage voluntary information sharing on the part of the downstream members.

Finally, there are some possible extensions to this paper. Our model can also be generalized to consider acase in which the delivery from the upstream members of a supply chain to the downstream members is notinstantaneous. In such a case, the single period demand distribution of our model needs to be transformedto a demand distribution that covers the demand during the lead-time. Although the algebra may be moretedious, we expect to obtain similar results. Another possible extension would be to consider the differenttypes of information that may be shared. In our model, we assume that the information to be shared is theminimum demand (or the mean demand), but in reality, there are many different types of information, suchas POS data, aggregated demand data, aggregated forecasts, promotion plans, and process constraints, thatdownstream members can share with upstream members. As different types of shared information willclearly have different impacts on the decisions that take place upstream, the incentive for the downstreammembers to share information may also depend on the type of information that is being shared.

Appendix 1. Proof of Lemma 1

In any pure strategy equilibrium, if R reveals the information when the signal h is received, then his ex-pected payoff, as defined in (4), is

PRðq�h; hÞ ¼ KRU q�h �Z q�h�hð Þ

0

F ðxÞdx

" #� k;

where q�h, as defined in (2), is V�s choice of optimal stock level if R reveals the information about the signal h

that is received. Let ~q be V�s choice of optimal stock level if R withholds the information. Note that ~q doesnot depend on h because V does not know the value of h when ~q is chosen. Thus, R�s expected payoff whenthe information is withheld is

ePRð~q; hÞ ¼ ðpR � cRÞEy minð~q; yÞ ¼ KRU ~q�Z ~q�hð Þ

0

F ðxÞdx� �

.

In equilibrium, R will reveal the information if PRðq�h; hÞ � ePRð~q; hÞ > 0; otherwise, the information will bewithheld. We now show that PRðq�h; hÞ � ePRð~q; hÞ is monotonically increasing in h.


PRðq�h; hÞ � ePRð~q; hÞ ¼ KRU q�h � ~q�Z ðq�h�hÞ

ð~q�hÞF ðxÞdx

" #� k:

By (2), q�h ¼ F �1ðnV Þ þ h. Let x* = F�1(nV), and hence q�h ¼ x� þ h. We can then rewrite the aboveexpression as

PRðq�h; hÞ � ePRð~q; hÞ ¼ KRU x� þ h� ~q�Z x�

ð~q�hÞF ðxÞdx

" #� k.

By Leibniz�s rule, the first derivative of the above function with respect to h is KRU ½1� F ð~q� hÞ�, whichis greater than zero, and thus PRðq�h; hÞ � ePRð~q; hÞ is monotonically increasing in h. Hence, PRðq�h0 ; h

0Þ �ePRð~q; h0Þ > 0 implies that PRðq�h00 ; h00Þ � ePRð~q; h00Þ > 0 for all h00 > h 0. That is, in equilibrium, if R is sup-

posed to reveal the information when he receives the signal h0, then he will also reveal it when he receives

the signal h00. However, PRðq�h0 ; h0Þ � ePRð~q; h0Þ < 0 implies that PRðq�h00 ; h

00Þ � ePRð~q; h00Þ < 0 for all h00 < h 0,or in other words, if R is supposed to withhold the information in equilibrium when he receives the signalh 0, then he will also withhold the information when he receives the signal h00. h

Appendix 2. Proof of Lemma 2

For the equilibrium in which R does not reveal if the signal h that he received is less than or equal to h,V�s optimal stock level ~q�h, as defined in (11), must satisfy

Uhð~q�hÞ ¼Z h

aF h ~q�h�

ghðhÞdh ¼ nV . ðiÞ� �

To show that ~q�h � h is decreasing in h, it suffices to show thatd~q

h

dh< 1. Note that

d~qh

dhexits because, as can

be seen from (i), Uhð~qÞ is obviously differentiable at every point in the domain of ~q, and dUd~q is never zero. This

also means that ~q�h � h is continuous in h for h 2 ½a; b�.As ghðhÞ ¼

gðhÞGðhÞ, Eq. (i) can be rewritten as
Z h
aF ð~q�h � hÞgðhÞdh ¼ nV GðhÞ. ðiiÞ

Taking the derivative of (ii) with respect to h, we obtain

F ð~q�h � hÞgðhÞ þZ h

af ð~q�h � hÞgðhÞ

d~q�hdh

dh ¼ nV gðhÞ.

Hence,

d~q�hdh¼

gðhÞ½nV � F ð~q�h � hÞ�R ha f ð~q�h � hÞgðhÞdh

. ðiiiÞ

By (i),

Uhð~q�hÞ ¼Z h

aF h ~q�h�

ghðhÞdh ¼Z h

aF ð~q�h � hÞghðhÞdh ¼ nV

() nV ¼ F ð~q�h � hÞ þZ h

aGhðhÞf ð~q�h � hÞdh

()Z h

a

GðhÞGðhÞ

f ð~q�h � hÞdh ¼ nV � F ð~q�h � hÞ. ðivÞ


Substituting (iv) into (iii), we have

d~q�hdh¼

gðhÞR h

aGðhÞGðhÞ f ð~q

�h � hÞdhR h

a f ð~q�h � hÞgðhÞdh¼R h

a gðhÞGðhÞf ð~q�h � hÞdhR ha gðhÞGðhÞf ð~q�h � hÞdh

< 1.

The last inequality holds because of Assumption A1. As g(h)/G(h) is strictly decreasing in h,

gðhÞ=GðhÞ > gðhÞ=GðhÞ for all h < h. Therefore, gðhÞGðhÞ < gðhÞGðhÞ. h

References

Bourland, K., Powell, S., Pyke, D., 1996. Exploiting timely demand information to reduce inventories. European Journal ofOperational Research 92, 239–253.

Cachon, G., Fisher, M., 2000. Supply chain inventory management and the value of shared information. Management Science 46 (8),1032–1048.

Cachon, G., Lariviere, M., 2001. Contracting to assure supply: How to share demand forecasts in a supply chain. Management Science47 (5), 629–646.

Chen, F., 1998. Echelon reorder points, installation reorder points, and the value of centralized demand information. ManagementSciences 44 (12), S221–S234.

Chen, F., Drezner, Z., Ryan, J.K., Simchi-Levi, D., 2000. Quantifying the bullwhip effect in a simple supply chain: The impact offorecasting, lead times, and information. Management Science 46 (3), 436–443.

Clark, T.H., Hammond, J.H., 1997. Reengineering channel reordering processes to improve total supply chain performance.Production and Operations Management 6 (3), 248–265.

Fudenberg, D., Tirole, J., 1991. Game Theory. MIT Press, Cambridge, MA.Gavirneni, S., Kapuscinski, R., Tayur, S., 1999. The value of information in a capacitated supply chain. Management Science 45 (1),

16–24.Kopczak, L.R., 1997. Logistics partnerships and supply chain restructuring: Survey results from the U.S. computer industry.

Production and Operations Management 6 (3), 226–247.Kopczak, L.R., 1998. How computer companies use logistics partnerships: A snapshot of the present and a view of the future. Global

Supply Chain and Technology Management 1, 91–111.Kumar, D., 2004. Beyond the low-hanging fruit. Industrial Engineer (May), 44–48.Lee, H.L., Padmanabhan, V., Whang, S., 1997a. Information distortion in a supply chain: The bullwhip effect. Management Science 43

(4), 546–558.Lee, H.L., Padmanabhan, V., Whang, S., 1997b. The bullwhip effect in supply chains. Sloan Management Review 38 (3), 93–102.Lee, H.L., So, K.C., Tang, C., 2000. The value of information sharing in a two-level supply chain. Management Science 46 (5), 626–

643.Lee, H.L., Whang, S., 2000. Information sharing in a supply chain. International Journal of Manufacturing Technology and

Management 1 (1), 79–93.Raghunathan, S., 2001. Information sharing in a supply chain: A note on its value when demand is nonstationary. Management

Science 47 (4), 605–610.Shaked, M., Shanthikumar, J., 1994. Stochastic Orders and Their Applications. Academic Press, London.Tsay, A., 2000. The quantity flexibility contract and supplier–customer incentives. Management Science 46 (10), 1509–1522.

strategic information sharing in a supply chain

Documents