This summary provides the key points from the document in 3 sentences: The document presents a model of partial information sharing in a supply chain with one manufacturer and two retailers. It uses a price discrimination strategy to incentivize one retailer to share uncertain demand information. The research finds that information sharing only provides value under certain conditions when using price discrimination, and develops strict constraints for an improved information sharing incentive model.

1. An Incentive Model of Partial Information Sharing in Supply Chain
Xiongwei Zhou, Feicheng Ma, Xueying Wang
Abstract- Considering one manufacturer and two retailers
in supply chain based on part of retailers to participate in
information sharing, we use price discrimination strategy to
design an incentive mechanism which motivates retailers to
share uncertain demand information with manufacturer. The
research results show that information sharing may be
value-added to add their profits only in under certain conditions
using price discrimination strategies. And then we put forward
the strict constraints and improve the information sharing
incentive model under demand uncertain environment. When
the retailers' external environment and their capacity are the
same, i.e., they are perfect competition, the full information
sharing is stable Pareto optimal equilibrium in the improved
incentive model.
I. INTRODUCTION
There is always not the actual consuming demand
information for upstream enterprise in the supply chain.
Known as the bullwhip effect [1,2] is the phenomenon caused
by demand information distortion to expand demand
variability. How to reduce the bullwhip effect in supply chain
has become a hot study issue, and information sharing is seen
as the main strategy to offset the bullwhip effect. Many
researchers have pointed out that information sharing can
offset the "bullwhip effect" and improve performance to
reduce costs and inventory [3,4,5] in supply chain. According to
master-slave Stackelberg game model, through considering
the upper suppliers' profits and approximately calculating by
the expectations of uncertain demand information with
normal distribution in supply chain, the literature [6] draws
the conclusions that information sharing doesn't need make
the whole supply chain optimal performance, and the total
revenue does not increase but also strictly decreases with
sharing uncertain demand information, and the value of
information sharing must be specifically analyzed. But the
optimal constraint conditions are not given in the literature.
Information sharing can often be divided into full
information sharing and partial information sharing from the
company quantity of participating in information sharing.
The partial information sharing refers to that not all retailers
are involved in participating in information sharing, but only
partial retailers to participate in information sharing. The
partial information sharing becomes a new research direction.
Literature [4,5] simulate the partial retailers to share demand
Manuscript received February 22, 2009. This work was supported in part
by the National Natural Science Foundation ofChina under Grant 70833005.
x. Z. is with the School ofInformation Management ofWuhan University
Wuhan, Hubei 430072 China (corresponding author to provide phone:
086-027-61091616; fax: 086-027-68457571; e-mail: daweycs@126.com,).
F.M. is with the School ofInformation Management ofWuhan University
Wuhan, Hubei 430072 China (e-mail: fchma@whu.edu.cn).
X.W.is with the School ofInformation Management ofWuhan University
Wuhan, Hubei 430072 China (e-mail:wangsusie@hotmail.com).
978-1-4244-3541-8/09/$25.00 ©2009 IEEE
information in supply chain, and demonstrate that
information sharing is beneficial to manufacturers and
wholesalers to increase their income, but almost no impact on
retailers. So retailers are not willing to share their private
information, and we must design an appropriate incentive
mechanism to make retailers willing to participate in
information sharing. Literature [7] firstly puts forward using
price discrimination strategy on partial retailers to share
information, but the authors believe that suppliers have not
incentive to use this strategy in the one-sided pursuit of their
maximizing profits, and in order to motivate retailers to
participate in the demand information sharing they pay
certain information cost and achieve the optimal balance
policy through calculating expectations. Considering
suppliers' profits and two level decentralized supply chain
composed of one supplier and many retailers, The literature
[8] further uses price discrimination strategy to encourage
retailers to participate in information sharing based on
maximizing corporate profits, which can lead to achieve the
final stability Pareto optimal equilibrium ofthe overall supply
chain effectiveness. However, the study does not analyze
what private information to share can add members' profits in
supply chain. Literature [9] further study that the
manufacturers adopt price discrimination strategy to share
information from them to partial retailers, and the results
show that manufacturers are more willing to share
information demand information with partial retailers when
information sharing need dissemination costs.
II. THE PARTIAL INFORMATION SHARING INCENTIVE MODEL
In this study, we consider one manufacturer and two
retailers, only one of retailers to participate in uncertain
demand information sharing in supply chain systems. The
price discrimination strategy is used in the information
sharing incentive model. The price discrimination strategy
refers to that retailers to participate in information sharing can
win at lower wholesale prices than retailers not to participate
in information sharing.
We assume our notation in the model as follows: 1!} is the
profits of retailer R}, 1!2 is the profits of retailer R2, 1!3 is
profits ofmanufacturer R3; d1 is the demand ofretailer R1, d2
is the demand ofretailer R2;PJ is the sales price ofretailer R1,
P2 is the sales prices of retailer R2; Cl is the marginal cost of
retailer R1, C2 is the marginal cost of retailer R2, C3 is the
marginal cost of manufacturer R3; WI is the wholesale prices
of retailer R1 to provide information sharing, W2 is the
wholesale prices of retailer R2 not to provide information
sharing; t, reflects the retailer's market signal of demand
uncertainty, where its value is also small when the demand is
58

2. small. t, is random variable of i.i.d. normal distribution with
mean zero and variance 0'2 , namelyti
'"" N (0, a), i = 1,2.
The demand function of retailer RI to participate in
information sharing can be expressed as
dl = DI (PI,/I) = 01 - bPI +II·
The demand function of retailer R2 not to participate in
information sharing can be expressed as
d2 =D2(P 2, /2)=a2 -bp2 +t2·
The profit function of retailer RI to participate in
information sharing is fulfilled with
1fI = (PI - WI - cI)dl •
The profit function of retailer R2 to participate in
information sharing is fulfilled with
!i2 =(P2 -w2 -c2)d 2·
The profit function ofmanufacturer R3 is fulfilled with
!i3 = (WI -c3)d I +(W2 -c3)d 2·
Where, a., b is positive constants, PI, P21 CI, C2, C3, WI and
W2 are positive constants and their relationships meet to
make III
,1l2
and 113
are all positive.
The game process of partial information sharing model is
the process of repeated games, in which every game is as
follows:
1) Manufacturer makes the wholesale prices decision
according to maximize his own profits requirement and
whether retailers participate in information sharing, in which
the wholesale prices is WI for retailer to participate in
information sharing while it is instead ofW2 for retailer not to
participate in information sharing.
2) Retailers determine whether they participate in
information sharing in accordance with the manufacturer
make the wholesale price and their own capacity.
3) Retailers respectively determine the sales prices in
accordance with the principle of maximizing their own
profits. The sales price is PI for retailer to participate in
information sharing and the sales price isP2for retailer not to
share information.
III. MODEL SOLUTION
According to reverse analysis method in game theory and
specific different uncertain private information, the following
expression is fulfilled to solve the model:
ma~ =wI -C3)(~ -bPi+/I)+(W2-C3)(~ -bp2)
s.t, max s. = (al - bPI +tl )(PI - WI - CI ) ,
PI
max s- =(a2-bp2 +t2)(P2-W2-c2) ·
P2
Because the retailer R2 owns private uncertain demand
information12
and doesn't share with supplier, the supplier
can not accurately gain it so that only its expectation can be
used to estimate itselfwhen supplier make his decision.
A. The Retailers' Decision-making
As for the retailer Rl and R2 both have the private
uncertain demand information, so their values are identified
and it is simple to solve their sale prices of decision-making.
According to reverse analysis method, we firstly separately
solve max1f1 and max1f2 • Therefore, we have the
PI P2
following proposition.
Proposition LWhen retailer RI participates in information
sharing with supplier while retailer R2 doesn't share
information with supplier, their sales price of optimal
* *equilibrium PI and P2 are respectively as follows:
* a+bw+bc+t (1) * a2+bw+bS+t2 (2)
PI = I I
2b
I I P2 2
2h
.
B. The manufacturer's Decision-making
Then we use the constraints conditions of max H
3
to
solve manufacturer's decision making. The retailer R2 owns
private demand information 12
and doesn't share it with
supplier, while supplier can't accurately catch it, so supplier
only can use its expectation to approximately calculate the
demand function and the optimal price when he
solves max H 3
•
Proposition 2. When retailer RI participates in information
sharing with supplier while retailer R2 doesn't share
information with supplier, supplier's wholesale price of
* *optimal equilibrium WI and w2 based on price
discrimination strategies and the retailers' optimal polices are
respectively as follows:
* al -b(cI-C3 )+tI * a2 -b(c2 -c3 )
W= w=-----I 2b 2 2b
* 3aI +b(CI +C3 ) +311 * 3a2 +b(C2 +C3 ) +212
~ = 4b P2= 4b .
Proof. Because £(t2
) =0,
* a2+bw +bc2+t2 a2 +bw +bc2E(p ) = E( 2 ) = 2 ,
2 2b 2b
E(d2) =E(a2- bp2 + t2) =a2- bp2·
Retailer RI shares information with supplier, so uncertain
demand information sharing t1 can directly substitute into
demand function and the optimal price. Then K 3 can be
calculated as follows:
113 =(111-S)(q-bn+tI)+(~ -S)(~-bR)
=(lIj ---s)~-.!.(q+blf+b,,+t)+t)+(~---s)~-.!.(t;+bw+bC;))(3).
2 2 2
1 1
=2(lIj---s)qnf+b,,-q-tJt
2(~ ---s)(b~+bc;-t;)
Then a1i3 =a+tl -b(2w1 +c -C3 ) , a21i
3 =-b < 0
a~ 2 a~2
59

3. alr3 =a2 -b(2w2 +C2 -c3 ) , (j2
ff; = -b < o·
aW2 2 dW2
Let aJl'3 =al +tl -b(2wI +cI -c3 ) =oand
aWl 2
aJl'3 =a2-b(2w2+C2-C3)=oto be simultaneous
aW2 2
equations and solve the WI, W2 optimal equilibrium
ofmax 1r3 •
* al - b(CI - c3 ) +II * a2 - b(C2 - c3 ) (4)
WI = 2b w2 = 2b
Substitute the values of WI, W2 into the front of(1) and (2)
to get the optimal equilibrium solution ofPI and P2:
P
* _ 3al +b(cI +c3)+3/1 p* 3a2 +b(c2 +c3)+212 (5).
1- 4b 2 4b
C. The Profit Distribution Mechanism
Proposition 3. The optimal profits ofthe manufacture and
the retailers are:
* (al - b(cI + c3 ) + tl ) 2
Jr=----.;;.---"""'------~
I 16b
* (a2 - b(c2 +c3 ) +212)2
Jr - ----=.----=--=----~
2 - 16b
* (al -b(CI +C3)+tl ) 2 +(b(c2 +c3)-a2 ) 2
Jl'3 8b
IV. MODEL ANALYSIS AND DISCUSSION
A. The Equilibrium Conditions' Stability Based on Price
Discrimination Strategy
Proposition 4. The price discrimination strategy achieves a
stable incentive and restrictive equilibrium conditions for
retailer only if
(al -a2 )- b(cI -C2 )+tl <0 (6)
2b
((al -a2)-b(cI -C2)+tl -2t2 ) ) (7).
(al +a2 -b(cI +c2 +2c3)+tl +2t2)/16b>0
The conditions (6) satisfy WI <W2 in order to encourage
information sharing through using the price discrimination
strategy. Therefore inequality (6) is the basic constraint
condition in the incentive model using price discrimination
strategy to meet information sharing incentives for retailers.
The retailer to participate in information sharing enjoys
preferential policies to get a lower purchase price because his
information sharing can reduce manufacturer's costs to
increase his profits; while retailer not to participate in
information sharing accepts that he catch a higher purchase
price and maintain cost unchanged.
The information sharing incentive model makes price
discrimination strategy achieve a stable equilibrium, that
is 111
> 1l2
, only if the profits of retailer to participate in
information sharing is greater than the profits ofretailer not to
participate in information sharing. The condition (7) is more
incentive and restrictive condition to satisfy 111
>112
•
B. When al = a2 andc1 =c2 ' the Effective Analysis to the
Information sharing Incentive Mechanism
Proposition 5. When al
= a2
and CI = c2
' II < 0 is satisfied.
When al
= a2
and CI
= C2
' that is to say the environment and
entrepreneurial capacity retailer Rl and retailer R2 are almost
identical, II < 0 can be deduced from the basic conditions (6)
of the price discrimination strategy to motivate retailers
information sharing. In other words, only if II < 0 is the
condition of WI <W2 satisfied. This illustrates that if using
price discrimination strategy sets up an incentive mechanism
to share uncertain demand information with normal
distribution, only when the retailer's demand information to
reflect the uncertain signal is negative can information
sharing make lower wholesale prices for retailer; otherwise
retailers to provide information sharing obtain rather than
higher wholesale prices, which is not in line with the purposes
of the price discrimination strategy to stimulate information
sharing. Hence the information sharing incentives mechanism
must be appropriately amended.
V. THE IMPROVED INFORMATION SHARING INCENTIVE
MECHANISM
According to Proposition 5, we improve the information
sharing incentives mechanism as follows: When II ~ 0, let
w* = al -b(cI -c3 ) to satisfy w; = w; in order to motivate
I 2b
retailers to participate in information sharing. Besides, the
mechanism does not allow retailers to participate in
information sharing in order to obtain low-cost wholesale
prices to inform tl
< 0 instead of tl
;;::: 0 because (I is the
actual needs ofthe retailer, and then false information reduces
their sales and their own profits. That is,
* _ al -b(cI -c3 ) t > O·
WI - 1- ,
2b
* al -b(cI -C3 )+tl 0
WI = 11 < .
2b
Because the role ofinformation sharing is mainly to reduce
production and inventory costs in the supply chain,
manufacturer and retailer can increase their effectiveness. If
II < 0, the demand information is critical for manufacturer to
reduce production and make manufacturer and retailer reduce
inventory costs, thereby increasing the overall efficiency, so
the manufacturer shares the profit-added of information
sharing with retailer to participate in information sharing. If
tl
;;::: 0, on the contrary, the demand information is not so
important during the overproduction, and it plays almost little
role to reduce production and inventory costs, so that
manufacturer does not have incentive to use price
discrimination strategy. Therefore the improved mechanism
is also fully consistent with the actual situation.
Proposition 6. When al
= a2
and CI
= C
2
' the improved
information sharing incentive mechanism is effective to use
price discrimination strategy in supply chain.
60

4. Proof. According to the improved information sharing
incentive mechanism, when II ~ 0, then w; =w;, in fact it
does not use price discrimination strategies to incentive
information sharing, and retailers comply with the same
policy to obtain the same benefits whether they participate in
information sharing. Therefore, we only need to consider if
11 < 0 whether III
> 112
• Then only if
* * (al -b(ci +C3) +tl ) 2 (a2 -h(c2 +C3) +2t2 ) 2
JZi >112 161 > 161
Because al
= a2
and CI
= C2
' then
al -b(cI +C3) =a2 -b(c2 +C3) •
Also because dl = al - bPI +II >0 ,
PI - WI - cI > 0 and WI - C3 > 0 as well as
d2 =a2 - bp2 +12 >0 , and P2 - w2 - c2 > 0 and W2 - C3 > 0,
So it can be launched
al -b(cI +C3)+/1 > Oandzz, -b(c2 +C3)+/2 > O.
It is apparently
al - b(cI +c3 ) =a2 - b(c2 +c3 ) > 0 by 11 < o.
So as long as
al -b(cI + C3) + /I >1 a2-b(c2 + C3) + 2/2 1,it meets 111 > 1l2 •
Assume tl =t2 ' then the real value of a2 - b(c2 +c3 ) +2/2
is often greater than 0, so it is obvious for 111
> 112
.Therefore it
is effective to design information sharing incentive
mechanism using price discrimination strategy in supply
chain.
Proposition 7. When al
= a2
and C
I
= C
2
' the improved
information sharing incentive mechanism make both retailers
eventually reach complete information sharing stable
equilibrium.
Proof.At the same time it can be seen by the optimal retail
price of the retailer Rl and R2, that is the expression of (5),
when al =a2 and c1 =c2 ' and 11 < 0 :
* 3~ +b(cI +C3) +3/1 * 3~ +b(c2 +C3)+2t2
A ~ <A ~ .
And WI <W2 and 1l1
>112
based on Proposition 6, there is
directly perfect competition between the retail Rl andR2. So
the price ofretailer Rl to participate in information sharing is
obvious competition advantages, which attracts more
customers for retailer Rland ultimately forces the retailer R2
to participate in information sharing, and eventually reaches
complete information sharing stable equilibrium of both
retailers to participate in information sharing.
VI. CONCLUSION
Information asymmetry in the supply chain is very
common. Retailers often have uncertain demand private
information. But many studies show that information sharing
does not improve the effectiveness of retailers. How to
motivate retailers willing to share their private information
has become a hot research issue. In this paper, we design the
information sharing incentive mechanism based on partial
retailers to participate in information sharing and price
discrimination strategy.
In the study we use the actual value rather than
approximate expectations to solve. The solution further
demonstrates that only when information sharing is strictly
bound in certain conditions does it add profit ofsupply chain.
This result shows that information with value-added is very
important whether retailers share information in the supply
chain. We design information sharing incentive mechanism
and improve it based on price discrimination strategy
according to the certain range and conditions of information
sharing with value added. The analysis shows they are
effective.
The next step is to conduct empirical research and
introduce our research methods into the electronic direct
marketing environment to design information sharing
incentive mechanism in a dual-channel supply chain.
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