American Journal of Operations Research, 2013, 3, 402-412
http://dx.doi.org/10.4236/ajor.2013.34038 Published Online July 2013 (http://www.scirp.org/journal/ajor)
Altruism and Pricing Strategy in Dual-Channel
Supply Chains
Kuiran Shi, Feng Jiang, Qi Ouyang
College of Economics and Management, Nanjing University of Technology, Nanjing, China
Received May 1, 2013; revised June 1, 2013; accepted June 10, 2013
Copyright © 2013 Kuiran Shi et al. This is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
ABSTRACT
With the development of behavioral operational management, human behavior such as altruism, fairness and trust has
received considerable attention. This paper studies the effect of altruism on retailer’s and manufacturer’s pricing strat-
egy in two classic dual-channel supply chains by presenting Stackelberg game models. The analysis shows that the
player’s altruism preference strongly affects their pricing strategies. The more altruistic one player is, the more profits
the other player obtains. Moreover, the effect of manufacturer’s altruistic preference is larger than that of retailer’s. In
addition, online price is always lower than offline price in dual-channel supply chain, which still holds true considering
altruism. The results also reveal that the product web-fit has significant effect on the player’s optimal pricing strategies.
The more compatible with online market the product is, the lower the retail price is set, and the more profit the manu-
facturer obtains whereas the less the retailer gets.
Keywords: Altruism; Dual-Channel Supply Chain; Pricing Strategy; Product Web-Fit
1. Introduction
With the emergence and development of internet, con-
sumers’ demand is increasing at an amazing speed,
which opens an online market with great potential. Ac-
cording statistical data of iResearch, the amount of online
shopping reached 498 billion in 2010, which is predicted
to exceed 1000 billion in the year of 2013. Facing such
temptation, every corporation is eager to share this “big
cake” by adding an online channel besides the traditional
one. According to one survey, about 42% of the top sup-
pliers in a variety of industries such as IBM, Nike, Dell,
Pioneer Electronics and Cisco System are selling directly
to consumers through the direct online channel (see [1]).
In addition, more and more retailers such as Wal-mart,
Gome, Suning and Watsons also successfully opened
their online market. In a word, e-commerce channel is
increasingly adopted in supply chain. Dual-channel sup-
ply chain management is thus paid with high attention in
recent years.
There are two main streams of research related to our
paper, channel management in dual-channel supply chain
and social preference. In the following, we briefly review
the most related research and describe our contributions
with respect to the vast, growing literature.
Contrary to tremendous interest in the dual-channel
distribution strategy, much recent research on dual chan-
nel management tends to focus on pricing strategies
rather than finding an optimal distribution strategy. Ref-
erence [1] shows that a direct online channel plays a role
of exerting potential competition pressure on the existing
retailer by increasing the manufacturer's negotiation
power and reducing the double marginalization in the
retail market even though its profit is non-positive. Ref-
erence [2] concludes that the manufacturer’s optimal
strategy is to charge the same price across both channels.
[3] shows that an equal-pricing strategy—the online
channel and the retail channel are priced the same—is
appropriate as long as the retail channel is significantly
more convenient than the Internet channel. [4] studies the
optimal pricing strategy when a retailer sells its product
through both the internet channel and the traditional
channel. Reference [5] indicates that a manufacturer’s
contract with a wholesale price and a price for the direct
channel can coordinate the dual-channel supply channel,
benefiting the retailer but not the manufacturer. Refer-
ence [6] shows that the optimal pricing decisions are af-
fected by customers’ preference for the direct channel
and the market scale, in both centralized and decentral-
ized dual-channel supply chains. A lot of literature prove
that dual-channel strategy is more preferable under most
C
opyright © 2013 SciRes. AJOR

K. R. SHI ET AL. 403
situation (see [5,7,8]). Retail services are taken into con-
sideration in some literature, e.g. [9,10].
There are other literature studied different factors af-
fecting channel selection by supposing linear function
of retailer’s and manufacturer’s effort in different chan-
nels. Reference [11] finds that channel preference de-
pends on supply chain’s efficiency and marketing capa-
bility. If the manufacturer is willing to reduce the whole-
sale price, both manufacturer and retailer can benefit
from a dual channel. [12] indicates that the most critical
factor in channel selection in a vertically integrated sup-
ply chain is the variable cost per unit of product sold us-
ing the direct vs. the retail channels. In the presence of
independent retailer, the size of the retail-captive con-
sumer segment relative to the size of the hybrid con-
sumer segment becomes a major factor in channel selec-
tion. [13] investigates the impact of channel structures on
the supplier, the retailer, and the entire supply chain in
the context of two single-channel and two dual-channel
supply chains.
Channel competition is always a hot point in dual-
channel supply chain management. Reference [14] looks
at price competition between the two channels using
Bertrand and Stackelberg game models. [15] studies the
impacts of different channel strategies on the total profits
of a firm from a cooperative advertising perspective and
showed that channel cooperation leads to an excess of
profits that can be shared between the online and con-
ventional parties. [16] studies the optimal contract design
problem in a mixed channels supply chain considering
information condition. [17] indicates that the manufac-
turer’s optimal channel strategy depends on the channel
environment. [18] examines the optimal decisions of
delivery lead time and prices in centralized and decen-
tralized dual-channel supply chains. In a Stackelberg
model, [19] compares equilibrium price and profit of
retail and manufacturer in different information condi-
tions, information symmetry and asymmetry. Analysis of
a bargaining model indicates that an information sharing
equilibium can be reached by proper profit sharing.
However, the above papers fail to address product web-
fit, which is well known for its strategic importance for
online sales (see [20-22]). In our study, we incorporate
product web-fit into our channel structure to study the
pricing strategies in two classic dual-channel supply
chains.
On the other hand, the development of behavioral op-
erational management brings challenge to the “homo
economics” hypothesis. Scholars show highly interest in
the role of human behavior in management, which is the
second literature stream related to our study. We only
refer to the effect of social preference in supply chain
management, which is the closest to this paper. For in-
stance, Reference [23] proves that the fairness considera-
tions can coordinate the channel under price-only con-
tract. Assuming a linear demand function, [24] provides
experimental evidence that there exist two contrasting
social preferences that systematically affect economic
decision making in supply chain transactions: while the
relationship preference promotes cooperation, individual
performance, high system efficiency, and sustainable
over time, the status preference induces tough actions
and reduces both system efficiency and individual per-
formance. These authors find considerable support that
the player’s utility is a weighted linear function of each
one’s profit. In the context of SCM, References [25] and
[26] discuss the effect of altruism on strategic behavior
or partnership management. [27] shows that the per-
formance of the supply chain in consideration of altruism
is between those of scenarios under decentralization and
under integration. The paper further point out that a
manufacturer, as a leader, should find an egoistic retailer,
while a retailer, as a follower, should find a manufacturer
with altruistic liability, to form a good chain. Different
from the above literature, this paper explores the effect of
altruistic preference on each player’s pricing strategy in
two classic dual-channel supply chains.
Different channel selection leads to different supply
chain structure. In a two-stage supply chain, according to
which member use the dual-channel (traditional and
online channel coexist), we have two classic dual-chan-
nel supply chain: retailer-dual channel manufacturer-
supply chain (supply chain (a)) and manufacturer-dual
channel retailer-supply chain (supply chain (b)) (see Fig-
ure 1). Most of the literature about channel management
manufacturer
retaile
r
consumer
traditional
channel online channel
Supply chain (a)
manufacturer
retailer
online channel
traditional
channel
consumer
Supply chain (b)
Figure 1. Supply chain’s structure of dual manufacturer
and dual retailer.

K. R. SHI ET AL. 404
studied channel selection and price setting with respect to
the manufacturer or the retailer. By comparing two clas-
sic dual-channel supply chains in the altruism and non-
altruism scenario, this paper tries to explore the effect of
altruism on each player’s pricing strategies. We incorpo-
rate product web-fit into demand function.
Reference [28] indicates that a product bought online
is less valuable to the consumer than an identical product
bought through a traditional retailer. There can be several
reasons for this phenomenon. First, real product can be
touched by consumers in physical stores, which well
conveys product attributes, while online channel cannot.
Second, for the online purchase, possession and gratifi-
cation is delayed, whereas they are instant when the
product is purchased through the traditional channel.
Besides, consumers typically will be charged a transport
fee for online purchases, and returns to online stores are
difficult. All these factors reduce the value of the product
for online purchases.
Suppose that the value of the product is when it is
bought through traditional channel, and the value of the
same product is
v
v


  1 when it is purchased
online. The parameter

is defined as product web-fit,
and is determined by product attributes and the nature of
online marketing. Based on empirical analysis of data,
Reference [21] shows that product web-fit turns out to be
less than one for most product categories (see Table 1).
Therefore, product web-fit varies with product categories
and the value of product web-fit ranges from zero to one
0 < θ < 1. The value of zero signifies that the product is
not compatible with online marketing at all and the value
of one signifies that the product is completely compatible
with online sales. Our paper considers such products
whose web-fit range from zero to one.
In this paper, we present an analytical framework for
product web-fit in a centralized and a decentralized
dual-channel supply chain system. In each system, we
formulate Stackelberg game model to compare two clas-
sic dual-supply chains. In the decentralized system, al-
truism and non-altruism scenario are compared to exam
the effect of altruism on pricing strategy. This paper con-
tributes to the literature in the following three aspects: 1)
we incorporate product web-fit in the demand function,
which is more reasonable in fact; 2) we study the effect
of altruism on each player’s pricing strategies, a new
perspective in dual-channel supply chain management; 3)
two classic dual-channel supply chains are compared.
The reminder of this paper is organized as follows.
Section 2 introduces the notation and formulates the de-
cision models for the manufacturer and the retailer. In
Table 1. Product web-fit

for web-based online channel.
Category Book Shoes ToothpasteDVD player FlowerFood items

0.904 0.769 0.886 0.787 0.7920.784
Sections 3 and 4, we examine the price decisions of the
retailer and the manufacturer in the non-altruism and
altruism scenarios respectively. Section 5 gives numeri-
cal examples to illustrate the influence of altruism and
product web-fit on the retailer’s, the manufacturer’s and
whole supply chain’s profits. We conclude the results
and suggestions for future research in Section 6. All
proofs are in the appendix.
2. The Model
In this paper, we consider a manufacturer who produces
a single product at a unit cost c and distributes it through
an independent retailer channel at a wholesale price w.
The product is sold through online channel at price p1 and
through traditional channel at price p2. Customers can
choose either the traditional retail channel or the online
channel to purchase the product.
We assume that in traditional channel consumers’
evaluation of a product is v, and the retailer’s price is p2,
then those consumers whose evaluation exceed p2 would
purchase the product through traditional channel as they
can get surplus. vr, which equals to p2, is the marginal
valuation for buying from the traditional channel. We
therefore have the demand functiond D = v − p2 when the
retailer sales products only in physical stores.
Now we discuss mixed channel. Product web-fit needs
to be considered. Consumers’ evaluation of a product in
online channel is supposed to be θv, and the product is
sold online at the price of p1, then consumers would pre-
fer to buy the product from online channel if θv > p1 v >
p1/θ as they can get surplus θv − p1·vd, which equals p1/θ,
is the marginal valuation for buying from the online
channel. When facing two channels, consumers would
prefer the channel which brings them more surpluses. So
when
12
vp vp


 , 21
1
pp
v







,
consumers would choose online channel. vdr, which
equals
21
1
pp

,


is the marginal valuation for buying from traditional
channel when comparing consumer surplus. When vd < vr,
then vd < vr < v
dr, and those consumers whose evalua-
tions are in the interval [vd, vdr] would prefer to buy from
the online channel, whose evaluations are in the interval
[vdr, v] would prefer traditional channel. When vd > vr,
then vd > v
r > v dr, and no consumers is willing to buy
from the online channel as traditional channel would
bring more surplus in comparison, those consumers
whose evaluations are in the interval [vr, v] would prefer
to buy from the traditional channel, but those whose

K. R. SHI ET AL. 405
evaluations are in the interval [0, v
r] will not buy the
product from either of the two channels. A similar mar-
ket structure has been used by References [1] and [29].
Thus, the demand functions for the online and traditional
channels, respectively, can be expressed as
21 1
1
ppp
1
d




 (1)
21
1
pp
dv
2


 

22
Apwd
 
21 1
wcdp cd 

2211
B
rpwd pwd
  
(2)
In supply chain (a), the retailer’s and manufacturer’s
profits are determined by
r

A

(3)
m (4)
In supply chain (b), the retailer’s and manufacturer’s
profits are determined by
(5)



12
d d

2211cpcd pcd
  

B
mwc
  (6)
If the dual-channel supply chain is vertically integrated,
then the profit of the centralized dual-supply chain (both
supply chains (a) and (b)) is
(7)
Note that the formulations of supply chains (a) and
(b)’s profits in centralized system are identical. The fol-
lowing section considers a centralized system in which
all the decisions are centralized to maximize the per-
formance of the entire supply chain, that is, the manu-
facturer is vertically integrated with the retailer. She con-
trols both decisions: the retail price and direct sale price.
The centralized system solution serves as a benchmark
for the decentralized setting. Then we consider a decen-
tralized supply chain under the Stackelberg game led by
the manufacturer. For the decentralized situation, two
supply chains ((a) and (b)) are compared in non-altruism
and altruism scenarios respectively.
In supply chain (a), the decision process is assumed to
follow the following sequence: the manufacturer, as the
Stackelberg leader, determines the wholesale price and
direct sale price first, then the retailer as the follower,
sets his own retail price based on the manufacturer’s de-
cisions. Similarly, in supply chain (b), the manufacturer
sets the wholesale price first, and the retailer decides the
traditional and online retail price accordingly.
Here the subscript “m”, ”r”, ”c” means the parameters
corresponding to the manufacturer, the retailer and the
wholesale system; the superscript “c”, “d”, “A” and “B”
means the parameters corresponding to the centralized
and decentralized system, supply chains (a) and (b). In
supply chain (a), we call the online channel as the direct
channel because the manufacturer sells products through
online channel directly.
3. Non-Altruism
In this Section, we discuss the retailer’s and manufac-
turer’s price strategies when both of them are not altruis-
tic.
3.1. Centralized Dual-Channel Supply Chain
Model
The supply chain performs best if the channel is centrally
controlled. Since the wholesale price is only used to di-
vide the profit between the retailer and the manufacture,
w is no longer decision variable in the centralized supply
chain. The decision variable is only p1, p2.
Substituting (1) and (2) into (7), we obtain:

22
1
1
2
11
11
c
pp p
pc
pp
cv p




 





 
 (8) 

Proposition 1. The online price and the traditional
price are given by
12
ccv
p


,22
ccv
p ,
and the total profit πc is given as
222
4
c
cv cv





1
c
p1
c
p
v
1
c
p
.
We easily know and will increase with in-
creasing , which is reasonable because, intuitively, the
higher the consumers’ evaluation for a product is, the
higher its price will be set. In addition, increase
with increasing

while is independent of
1
c
p

.
3.2. Decentralized Dual-Channel Supply Chain
Model
In this Section, we discuss the decentralized system, in
which the retailer and manufacturer maximize their own
profits respectively. We model the decision process as a
sequential, Stackelberg game, with the manufacturer as
the leader and the retailer as the follower. We first give
the retailer’s and the manufacturer’s best response func-
tions, then present the method to decide the Stackelberg
equilibrium strategies of the two players.
3.2.1. Retailer-Dual Channel Manufa c turer-Supply
Chain
Substituting (1) and (2) into (3) and (4), we obtain

21
21
A
r
pp
pwv




 




(9)

2121 1
1
11
A
m
pp ppp
wc vpc 




 



(10)

K. R. SHI ET AL. 406
Proposition 2. In retailer-dual channel manufacturer-
supply chain, the optimal price of manufacturer and re-
tailer are given respectively by
12
dA vc
p


, 2
dA vc
w ,


2
dA
p3
24
v
v


 .
The corresponding profits of manufacturer, retailer and
total supply chain are given as
222 2
24
8
c vc
A
m
vv




 

,
2
1
16
A
r
v  
 
,
22
16
A
c
vv
2 2
348cvc




dA dA
w2
dA
p
1
dA
p
 ,
respectively.
We can easily know that , , all increase
with increasing , which is intuitively reasonable.
also increases with increasing
1
p
v

, while 2 decreases
with increasing
dA
p

, and is independent of
dA
w

. Pro-
position 2 indicates that in supply chain (a), the formula-
tions of the optimal wholesale price and the optimal di-
rect sale price are identical to the optimal traditional
price and the online price in the centralized system. In
other words, compared with the pricing strategies in the
centralized supply chain, the manufacturer should con-
sider the retailer as an end customer and set the whole-
sale price equal to the retail price in the centralized sup-
ply chain, and keep the direct sale price unchanged. Note
that when

is between 0 and 1, 1 is always smaller
than , which would render the retailer order his
products through the online channel instead of the tra-
ditional channel. The extreme case is that the manu-
facturer sells all his products through the online chan-
nel.
dA
p
dA
w
3.2.2. Manufacturer-Dual Channel Retailer-Supply
Chain
Substituting (1) and (2) into (5) and (6), we obtain


21
21 1
1
1
pp
v
pp p

2
1
B
rpw
pw


















(11)
1
p
wc v
B
m



 


(12)
Proposition 3. In Manufacturer-dual channel retailer-
supply chain, the optimal price of manufacturer and re-
tailer are given respectively by
2
dB
wcv


, 14
dB
p3vc


, 2
2
4
dB vc v
p


.
The corresponding profits of manufacturer, retailer and
total supply chain are given as
222
2
8
B
m
ccvv 


,
22
2
16
B
r
ccvv






,
22
36 12
16
B
c
ccvv



 

dB
wdB
pdB p
v
,
respectively.
From Proposition 3, we see that , 1, 2 are
all increasing functions to and

. Not that

is
between 0 and 1, 1 is always smaller than2, that
means, the retailer sets a lower online price to appeal
consumers into online market. Compared with supply
chain (a), the manufacturer sets a smaller wholesale price
in supply chain (b). A reasonable explanation is that
when the retailer opens an online channel, the retailer
benefits from dual-channel while whether the manufac-
turer’s profit will be increased depends on the value of
product web-fit. As a result, the manufacturer in supply
chain B had better to reduce wholesale price, otherwise
the retailer may contact another manufacturer to get
lower wholesale price and higher profit.
dB
pdB p
rrr m
U
4. Altruism
Instead of being purely self-interested, both the manu-
facturer and retailer share some mutual concerns about
the well-being of the others. Using altruistic utility or the
“reciprocity-free” formulation in Reference [30], verified
in the experiments by [24], the retailer’s utility function
is:




(13)


where the coefficient 0,1
r
 
0
r
measures the degree of
altruistic preference of the retailer towards the manufac-
turer. If


, the retailer is purely competitive to-
wards the manufacturer, conversely, if 1
r


r
, the re-
tailer is fully cooperative with the manufacturer. The
larger (less)

is, the more cooperative (competitive)
the retailer towards the manufacturer will be.
Similarly, the manufacturer’s utility is
mmm r
U

 

(14)


where 0,1
m
 
r
is the manufacturer’s altruistic pref-
erence. Note that the retailer’s profit

takes full ac-
count of the inventory risk while m

takes no inventory
risk at all, therefore Um reflects the manufacture willing-
ness to share part of the supply chain inventory risk, and
m

characterizes the degree of this willingness.
4.1. Retailer-Dual Channel
Manufacturer-Supply Chain
Substituting (9) and (10) into (13) and (14), we obtain:

K. R. SHI ET AL.
AJOR
407
  
21 21
2 1
11
r
A
r
pp pp
pwv wUcv 

 
 
  211
1
ppp
pc


 


  

 

 



 (15)
  
2121 1
1
11
A
m m
pp ppp
wc vpcpw21
2
1
pp
Uv








p




 



 (16)
Proposition 4. For given w and 1, the optimal pric-
ing strategy of altruistic retailer is given by:

1
1
A
rr
pwv
21
2
ppvw

 
2
A
p
w1
p
 .
Substituting into (16), then taking the first order
condition with respect to and and setting them
to zero, we get the manufacturer’s best response:


12
Acv
p



 
,
 
2
12222
21 2
rm rmrmr
A
rm rm
cvv
w

 
 


 



A
w2
A
p
Then substituting and into , we get the retailer’s best response:
1
A
p









2
222 12
42
rm rmrmrm
A
mrm
vc vv
p


6 2
r r
  






From Proposition 4, we know that the altruistic re-
tailer’s traditional price and the altruistic manufacturer’s
wholesale price both decrease with increasing θ in supply
chain (a), while the retailer’s retail price decreases with
increasing θ. That means, the more compatible with
online market the product is, the more profitable for the
manufacturer and less profitable for the retailer. In addi-
tion, both the manufacturer’s optimal wholesale price
and the retailer’s retail price are affected by the altruism
coefficient, but the manufacturer’s direct price is inde-
pendent of the altruism magnitude.
4.2. Manufacturer-Dual Channel
Retailer-Supply Chain
Substituting (11) and (12) into (13) and (14), we obtain:
 
2121 11
21
11
r r
Bpp pppp
pww wcUv pv 

 

 
 
 

 
 (17)


  
121211
21
11
B
mm
pppppp
wc vpwvpwU 

 
 

  

 

(18)
Proposition 5. For given w, the optimal pricing stra-
tegy of altruistic retailer is given by

1
1
2
B
rr
pwcwv

  ,

2
1
2
B
rr
pwcwv   .
Substituting 1
B
p and 2
B
p
 
into (18) and taking the first
order condition with respect to w, letting it to zero, we have:
2
2
12
Brrm m
rmrm
cc cvv
w



 
,
which is the altruistic manufacturer’s best response. Then
substituting
B
w1
into
B
p2
and
B
p, we get the altruistic
retailer’s best response:





1
3
22
mmrmr mrmB
mrm
vcvc c
prm




 







2
2
22
mmrmr mrmB
mrm
vcvvc c
prm




 


From Proposition 5, we know that the optimal whole-
sale price, traditional price and online price all increase
with increasing

in altruism scenario. Compared with
supply chain (a), in supply chain (b), the retailer, who
adopted dual channel, owns more power to control the
traditional and online prices, which leads to the positive
correlation between her profit and the product web-fit. In
addition, the wholesale price, online price and traditional

K. R. SHI ET AL. 408
price are all influenced by the altruism coefficient.
120
5. Numerical Examples
The purpose of our numerical examples is to explore the
effect of product web-fit and altruism magnitude on each
player’s strategies in dual-supply chain. The numerical
examples will complement our analytical results and
provide us with more managerial insights. The values we
used for the various parameters in our numerical exam-
ples are shown in Tabl e 2. We vary some of the parame-
ters in Table 2 to find their effects on the optimum
strategies.
5.1. Effect of Product Web-Fit,

The impacts of the product web-fit on each supply chain
player’s strategies under the various scenarios are shown
in Figures 2 and 3.
In Figure 2, we observe that the traditional and online
price in supply chain (b) both increase with increasing θ,
while in supply chain (a), the online price increases with
increasing θ, but the traditional price decreases when the
product web-fit increases. This is to be expected be-
cause the retailer in supply chain (b) decides both the
online and the traditional price, when the product is more
Table 2. Parameters values and range of values used in the
numerical examples.
Parameters Base values of values
c 20
v 100

0.5 (0 - 1)
r

0.5 (0 - 1)
m

0.5 (0 - 1)
00.2 0.4 0.6 0.81
0
20
40
60
80
100
120
140
θ
p
1
c
,p
1
dA
,w
dB
p
2
dA
p
1
dB
p
2
dB
Figure 2. Impact of the product web-fit on each player’s
pricing strategy without altruism.
00.1 0.20.3 0.4 0.5 0.6 0.70.8 0.9 1
0
20
40
60
80
100
θ
pc
1
wA
pA
2
wB
pB
1
pB
2
Figure 3. Impact of the product web-fit on each player’s
pricing strategy in altruistic scenario.
compatible with the online channel, the retailer benefits
more from higher price. However, in supply chain (a),
the retailer sets the retail price while the manufacturer
decides the direct price for the same product, which
brings competitive to the retailer and forces the retailer to
reduce the retail price, and the more compatible with the
online channel the product is, the lower the retail price is
set. From Figure 2, we also know that the online price is
always lower than the traditional price in both supply
chain (a) and (b), which is intuitively because customers’
evaluation for a product online is always lower than that
in physical stores (see [28]).
Figure 3 illustrates the effect of the product web-fit on
the altruistic retailer’s and altruistic manufacturer’s pric-
ing strategies. We see some interesting changes com-
pared with Figure 2. In supply chain (a), the retailer’s
traditional price and the manufacturer’s wholesale price
both decrease with increasing

, but the manufacturer’s
direct price increases with increasing

.hat means, the
more compatible with online market the product is, the
more the manufacturer obtains but the less the retailer
obtains. So the altruistic manufacturer will transfer some
part of his profit to the retailer by reducing wholesale
price when he considers the other player’s welfare. In
supply chain (b), wholesale price, traditional price and
online price all increase with increasing
T

, and the manu-
facturer’s wholesale price is so close to the retailer’s
online price, which makes the retailer obtain little profit
from online channel, and the retailer would sale the pro-
duct only through traditional channel in the long run. We
also see that the online price is also lower than traditional
price in both supply chains (a) and (b), just as in F ig ure 2.
5.2. Effect of Altruistic Preference, r

, m

Figures 4 and 5 summarize the impacts of the altruistic

K. R. SHI ET AL. 409
00.1 0.20.3 0.40.5 0.6 0.70.8 0.91
0
200
400
600
800
1000
1200
η
r
w
A
p
A
2
w
B
p
B
1
p
B
2
Figure 4. Impact of the retailer’s altruistic preference on
the player’s pricing strategy.
00.1 0.20.3 0.40.5 0.6 0.70.8 0.91
0
50
100
150
200
250
300
η
m
w
A
p
A
2
w
B
p
B
1
p
B
2
Figure 5. Impact of the manufacturer’s altruistic preference
on each player’s pricing strategy.
preference on each player’s pricing strategies.
In Figure 4, all the price increase with increasing r

,
in which the effect of retailer’s altruistic preference on
wholesale price is much more obvious, and the effect on
the other prices is less observable. That means, the more
altruistic the retailer is, the higher wholesale price the
manufacturer set. The manufacturer benefits from the
retailer’s increasing altruistic preference or say the
manufacturer use the retailer’s altruistic preference to
obtain more profit by increasing wholesale price. In ad-
dition, the effect of retailer’s altruistic preference on
wholesale price in supply chain (a) is greater than that in
supply chain (b). It’s because the manufacturer in supply
chain (a) is more powerful as he controls both wholesale
price and direct price while he is less powerful in supply
chain (b) where he only control the wholesale price,
which also explains why wholesale price in supply chain
B is lower than that in supply chain (a).
From Figure 5, we clearly see that wholesale prices in
both supply chains (a) and (b) are decreasing with in-
creasing m

, while the online price and traditional price
are increasing. The more altruistic the manufacturer is,
the lower the wholesale price is set. That means, altruis-
tic manufacturer transfers some part of his profit to re-
tailer by reducing wholesale price as he shows concerns
about the retailer’s well-being (note that wholesale price
in supply chain B is also lower than that in supply chain
(a), just as in Figure 4). The retailer benefits from the
manufacturer’s increasing altruistic preference or say the
retailer use the manufacturer’s altruistic preference to
obtain more profit by increasing traditional and online
price. Comparing Figures 4 and 5, we see that the effect
of the manufacturer’s altruistic preference on the two dual-
channel supply chains is more obvious than that of the
retailer’s altruistic preference. Moreover, the optimal
prices in supply chain (a) are higher than those in supply
chain (b).
In this paper, we develop a framework to study the ef-
fect of altruistic preference in two classic dual-channel
supply chains. The results show that altruism strongly
influences the retailer’s and manufacturer’s pricing
strategies. Numerical studies reveal that the product web-
fit also has great effect on optimal pricing strategies.
We obtain some new results differing from those in
previous literature. Study shows that altruism greatly
affects each player’s pricing strategies. The more altruis-
tic a player is, the more profitable the other player is.
Specifically, one player benefits from the other player’s
altruistic preference. In addition, we found that the ma-
nufacturer’s altruistic preference influences each player’s
pricing strategies more greatly than the retailer’s altruis-
tic preference. In a dual-channel supply chain, online
price is always lower than traditional price, which also
holds true when the retailer and the manufacturer are
altruistic according to our study. Analysis reveals that
product web-fit affects each player’s pricing strategies.
The more compatible with the online channel the product
is, the lower the retail price is set, the more profitable for
the manufacturer and less profitable for the retailer. From
numerical examples, we see that the optimal prices in
supply chain (a) are set higher than the corresponding
prices in supply chain (b).
There are several directions for future research that
will achieve a better understanding of dual channel sup-
ply chain. For instance, it is assumed that all information
is known to the retailer and the manufacturer, and thus, it
is insightful to consider asymmetric information, which
may change the interaction between the players. In addi-
tion, it would be interesting to examine conditions under
which it would be more profitable when two channels
compete with each other.
6. Acknowledgements
This research was supported in part by: 1) the National

K. R. SHI ET AL. 410
Natural Science Foundation of China under Grant
71071075 and 71173103; 2) the Major Program of Na-
tional Social Science Foundation of China under Grant
12&ZD204; and 3) the Humanities and Social Science
Foundation (10YJA790183, 12YJC630180) of the Min-
istry of Education, China.
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Appendix
Proof of Proposition 1
Taking the second-order partial derivatives of c

with
respect to and , we have the Hessian matrix
1
p2 p
1
2
22
2
12
22
2
21
2
cc
cc
ppp
H
pp p

11 2
11
22
11







 






 











 

.
Since
1
2
20
c
p
 

,
and
11
2





2
11
0
22
11






c
,

is strictly jointly concave in and . So the
optimal solution exists. Then let the first-order condition
equal to zero, we derive Proposition 1.
1
p2 p
A
r
Proof of Proposition 2
Taking the second-order partial derivatives of

with
respect to , we have
2
p
2
2
2
r
p
 20
1 
 

A
r
.
Then let the first-order partial derivative of

with
respect to be zero, we have
2
p

1
2
vp w
 
A
2
1
p,
then substitute it into (10), and m

becomes a joint
function of and . We can easily obtain the opti-
mal solution by analyzing Hessian matrix and the first-
order condition.
1
pw
Proof of Proposition 3
Taking the second-order partial derivatives of
B
r

with
respect to and , we have the Hessian matrix
1
p2 p
1
2
22
2
12
22
2
21
11 2
211
22
11
BB
rr
BB
rr
ppp
H
pp p







 















.

 


Since
1
2
20
c
p
 
,
and
11 2
211
0
22
11
 








c
,

is strictly jointly concave in and . So the
optimal solution exists. Then let the first-order condi-
tions equal to zero, we derive
1
p2 p
12
wv
p


,
22
wv
p 
w
.
Substituting them into (12), and letting the first-order
condition of be zero, we have
2
cv
w 

,
and then Proposition 3 is proved.
Proof of Proposition 4
The proof of Proposition 4 is similar to Proposition 2, so
we omit it.
Proof of proposition 5
The proof of Proposition 5 is similar toProposition 3, so
we omit it.