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Store Brands and Store Competition
Dr. Sungchul Choi, School of Business, University of Northern British Columbia, Canada
Dr. Karima Fredj, Economics Program, University of Northern British Columbia, Canada
ABSTRACT
Most past studies of store brands ignored store competition and focused on limited interactions among channel
members. This research seeks to extend the literature in this area by considering various channel leadership
structures and retail competition in a channel of a single national brand manufacturer and two competing store brand
retailers that also sell the national brand. Besides the variety in vertical price leadership between the national brand
manufacturer and the store brand retailers, we particularly investigate the role of horizontal price leadership between
two store brand retailers.
We find that the two competing retailers are better-off when they practice price leadership between them.
In addition, consumers are better-off when no leadership exists between the three channel members and worst-off
under the manufacturer’s leadership. Total channel profits are also the highest when no leadership is practiced by
the channel members and larger when the channel leaders are the store brand retailers rather than the national brand
manufacturer.
Keywords: Distribution Channels; Store Brands; Price Competition; Game Theory
INTRODUCTION
Store brands represent more than $40 billion of current retail businesses and are achieving new levels of growth
every year (Private Label Manufacturers Association, 2005 Yearbook). According to the United States Department
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of Agriculture (USDA) 2000's estimates, one out of every five items sold per day in the U.S. supermarkets, drug
chains and mass merchandisers is a store brand product. Because of such success of store brands in several product
categories over the past two decades, competition between national brands and store brands has been extensively
studied.
One research stream focuses on the empirical approach that investigates the effects of some variables such
as advertising, perceived quality, and industry concentration on competition between national brands and store
brands to explain the variation in store brand market share across different product categories (see for example;
Cannor and Peterson 1992, Hoch and Banerji 1993, Hoch 1996, Kim and Parker 1999, Cotterill et al. 2000).
Another research stream introduces theoretical models that describe price competition between national
brands and store brands to study some related issues. For instance, Raju et al. (1995) developed a game-theoretic
model in order to examine the conditions under which it is profitable to introduce store brands; Narasimhan and
Wilcox (1998) examined the incentives for store brand introduction in the loyal/switcher market structure; and more
recently, Sayman et al. (2002), Du et al. (2004), and Choi and Coughlan (2006) investigated the retailer's store brand
positioning issue.
However, the existing literature of price competition in economics-based modeling between national brands
and store brands still has its limitations and our main contribution in this paper is to address some of them.
Firstly, in order to provide maximum brand exposure and more consumer convenience, most consumer
goods are sold intensively through several independent retailers that offer competing brands. Hence, the importance
of inter-store competition between large retailers has been argued as critical for store brand introduction (McMaster
1987). However, most of the previous store brands' studies ignored inter-store competition and accounted only for
product competition between national brands and store brands (e.g. Raju et al. 1995, Narasimhan and Wilcox 1998,
Sayman et al. 2002). On the other hand, the previous models that considered store differentiation effects in a
duopoly common retailers channel did not include store brands in the model (e.g. Choi 1996, Trivedi 1998, Basuroy
et al. 2001). Thus, little is known about the role of store brands in price competition at the retail level.
Our contribution at this level is to have, in the same model, both store competition and product competition
between a national brand and store brands. This is achieved using a model framework where the market structure is
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composed of one national brand manufacturer and two retailers who sell their own store brand in addition to
marketing the manufacturer's national brand.
Secondly, previous studies, related to store brands issues, only investigated the Manufacturer Stackelberg
(MS) channel leadership structure where manufacturers are modeled as Stackelberg leaders and retailers as
followers (see for example; Raju et al. 1995, Narasimhan and Wilcox 1998, Sayman et al. 2002). This excludes
some other possible channel leadership structures that have been proven pertinent by the previous literature that did
not account for store brand competition; such as a Vertical Nash (VN) where manufacturers and retailers are at the
same power level, or Retailer Stackelberg (RS) where, as opposed to the MS, retailers act as price leaders and
manufacturers as price followers. Indeed, as argued in this literature, in certain circumstances retailers may be
"powerful" enough to lead the channel, leaving manufacturers no other choice but to accordingly adjust their
decisions (Lee and Staelin 1997). These retailers are often much larger than most of the manufacturers, and exercise
their power on the flow of products (Choi 1996). This is exemplified in the real world by the dominance of large
retailers such as Wal-Mart (Choi 1991, Lee and Staelin 1997). Henceforth, we believe that considering all the
different leadership structures would particularly reflect the impact of store brands on the strategic role of retailers in
the channel (Trivedi 1998).
Finally, existing studies in this area ignored horizontal price leadership by assuming that channel members
interact in a Bertrand-Nash manner at the horizontal level (two manufacturers or two retailers) (Raju et al. 1995,
Narasimhan and Wilcox 1998, Sayman et al. 2002). Thus, one of our main contributions is to introduce a new
leadership structure where we allow for a sequential interaction à la Stackelberg at the retail level in addition to
considering the Bertrand-Nash interaction. This new assumption of leadership is well justified as most of the
empirical studies show inconsistent results with the Bertrand-Nash manner assumption. For instance, Vilcassim et
al. (1999) analyzed the dynamic price and advertising competition among firms in a personal-care product category
and found evidence rejecting Bertrand-Nash interactions among firms. Dhar and Ray (2004) also found that grocery
supermarkets with strong store brands might show more strategic interaction between retailers in fluid milk product
category (see also Bresnahan 1989 for more related counter-examples). As pointed out by Kadiyali et al. (2000),
“Therefore, a more general model of interactions is needed” and we propose a horizontal Stackelberg pricing game.
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In summary, the primary focus of this paper is to investigate price competition between a manufacturer’s
national brand and retailers’ store brands in the presence of store competition. As indicated above, this paper
extends the previous literature mainly in three directions: (1) considering both product and store differentiation, (2)
applying different vertical price leadership structures (MS, RS and VN), to a store brand model and (3) applying
horizontal price leadership at the retail level.
This paper is organized as follows.
In the next section, we develop a model that examines price
competition between a national brand and store brands in a channel structure with one manufacturer and two
retailers. In the third section, we derive the analytical equilibrium solutions for the prices, margins, quantities
demanded and profits under the different channel leadership structures. In the fourth section, we perform sensitivity
analyses, comparisons and discuss the implications of the channel leadership. Finally, we conclude and delineate
further research directions.
THE MODEL
This section describes the demand and profit functions and provides a description of the channel leadership
structures.
We assume that the manufacturer produces a national brand product that he distributes to two competing
retailers. In addition to the national brand, each retailer offers a store brand. 1 The manufacturer chooses the
wholesale price that maximizes his profits and each retailer determines the optimal retail margins for the national
brand and her store brand that maximize her combined profits from marketing the two products.
The Demand Structure
Following the established literature, we use linear demand functions that capture the main properties; such as the
quantity demanded of a good is decreasing in its price and increasing in the competing product's price and affected
by the degree of product and store differentiation. Accordingly, we extend the demand function used in Raju et al.
(1995) as follows:
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q im 
qi 
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1
(1  p im   ( p jm  pim )   ( p i  p im )
2  2
1
(  pi   ( pim  pi )) ,
2  2
(1)
(2)
where
m : the index for the manufacturer,
i, j  1,2, i  j : indexes for the retailers,
qim : the demand of the manufacturer’s national brand at store i,
qi : the demand of the store i’s brand,
pim : the retail price of the manufacturer’s national brand at store i,
pi : the retail price of the store i’s brand,
 : the cross price sensitivity between the national brand and a store brand at store i,
 : the cross price sensitivity between the two stores for the national brand,
 : the store brand’s base level of demand.
Smaller values of β indicate less product substitutability (or more product differentiation) between the
national brand and a store brand. A small value of the cross-price sensitivity between two products hence implies
that a change in the price of one of the products will have small impact on the demand of the other product and viceversa. By considering the same β between the national brand and each of the store brands, we implicitly assume that
the national brand is symmetrically positioned with respect to the two store brands.
A smaller value of γ, on the other hand, represents less store substitution (or more store differentiation)
implying that price differences for the same national brand between the two stores has less impact on the demand
they will face.
Finally, λ indicates the base level of demand of a store brand. λ=0 represents the case where the store brand
has no base level of demand and λ=1 represents the case where the store brand has exactly the same base level as the
national brand. In general, λ can take any value between 0 and 1, with higher values of λ implying highly
competitive store brands compared to the national brand.
Following Raju et al. (1995), we assume that each retailer procures her store brand from a manufacturing
source. The store brand producers incur a fixed unit cost for a long-term period (Cook and Schutte 1967, Mcmaster
1987). We also assume that the price at which each retailer procures her store brand is equal to the marginal
From now on we shall refer to the manufacturer by “he or him” and to each retailer by “she or her” to avoid the
confusion.
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1
6th Global Conference on Business & Economics
manufacturing cost.
ISBN : 0-9742114-6-X
For mathematical tractability and to separate the effects of different channel leadership
structures from the effects of cost difference, we assume zero marginal costs without loss of generality. The profit
function for a national brand manufacturer can then be written as:
m 
 w
i 1, 2
m
q mi   wm  q mi
(3)
i 1, 2
and the profit function for each retailer is
 Ri  mi qmi  pi qi ,
(4)
where wm is the national brand manufacturer’s wholesale price, mi  pim  wm is the store i’s margin on the
national brand.2
The Channel Leadership Structure
To model variety in price leadership among channel members, we consider both vertical interactions between the
manufacturer and the retailers, and horizontal interactions between the two retailers. In addition, at each interaction
level, we consider both simultaneous and sequential plays, which translate into the following four pricing games:
 The Manufacturer Stackelberg (MS): It refers to a Stackelberg price leadership at the vertical level
(where the manufacturer is the leader and retailers are followers) and a simultaneous Nash game between the two
retailers at the horizontal level. This game is solved backward. Each retailer first chooses her optimal margins for
the national brand and her store brand that maximize her profits conditional on the second retailer's choice.
Afterwards, the manufacturer using this information (i.e., reaction functions of the retailers) chooses the wholesale
price for his national brand that maximizes his own profits.
 The Vertical Nash (VN): It refers to a simultaneous play à la Bertrand-Nash between the manufacturer
and the two retailers. In this game, all channel members maximize their profits conditionally on each other’s
reaction function(s) by choosing the wholesale price for the manufacturer and the different margins for the retailers.
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 The Retailer Stackelberg (RS): It also refers to a Stackelberg price leadership but as opposed to the
MS, the manufacturer is the follower and retailers are the leaders.
Solved backward, this means that the
manufacturer first solves for the wholesale price of the national brand that maximizes his profits. The obtained
reaction function is then used by the retailers while simultaneously maximizing their respective profits.
 The Retailer Double Stackelberg (RDS): This game is similar to the RS in terms of the vertical
interaction between the manufacturer and the retailers. However, it differs at the horizontal level, by considering
sequential interaction à la Stackelberg rather than a simultaneous one à la Bertrand-Nash between the two retailers.
Thus, one retailer (Retailer 2 in our model) has price leadership over the other (Retailer 1). Solved backward, this
means that the manufacturer first chooses his wholesale price. Then the following retailer (Retailer 1) chooses her
margins for the national brand and her store brand before the leading retailer (Retailer 2), using the reaction
functions of the two other channel members, fixes the margins for the national brand and her store brand that
maximize her profits.
Figure 1 illustrates these different configurations of the channel leadership structures. As mentioned in the
introduction section, the different behavioural assumptions for the vertical pricing game were commonly used in the
previous literature (see for example, Choi 1991, Choi 1996, Lee and Staelin 1997, Kadiyali et al. 2000, Tyagi 2005).
Our major contributions are to apply them to a model including store brand products and to consider a sequential
play between the channel members at the horizontal level, building up the last channel leadership structure (RDS).
2
Since we assume that the price at which retailers procure their store brand is equal to the marginal costs (set equal
to zero), the retail prices and the margins for the store brand are equal.
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Figure 1. The Channel Leadership Structure
(a) Manufacturer Stackelberg (MS)
(b) Retailer Stackelberg (RS)
Manufacture
r
Manufacture
r
Retailer 1
Retailer 2
Retailer 2
Retailer 1
(c) Vertical Nash (VN)
(d) Retailer Double Stackelberg (RDS)
Retailer 2
Manufacture
r
Retailer 1
Retailer 1
Retailer 2
Manufacturer
THE EQUILIBRIUM OUTCOMES
In this section, we derive the equilibrium results for the different leadership structures. The optimal results are
superscripted by MS, RS, VN, and RDS for the four leadership assumptions described above.
The MS Leadership
Under the MS leadership, the manufacturer knows up-front the reaction functions of the retailers and takes them into
account when he chooses the wholesale price for the national brand.
These reaction functions are derived as first order conditions of (4) subject to (1) and (2) for each retailer i=1,2:
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miMS 
  1    wmMS (2  1)
, and
4      2
piMS 
2   (2    2)  wmMS
.
2(4      2)
It is interesting to notice from these expressions that as the wholesale price of the national brand goes up,
each retailer decreases her margin on the national brand and increases the price of her store brand. This means that a
high wholesale price of the national brand results in a lower retail margin on the product, for which the retailers can
compensate by choosing higher retail margin on their own store brand.
Substituting these reaction functions into the manufacturer profit function (equation 3) and maximizing it
with respect to the wholesale price gives the following optimal value:
wmMS 
2(2  1   (1   ))  
.
2( (4   2  2)  2(  1)(2  1))
Finally, replacing this value of wmMS in the retailers’ reaction functions yields the optimal control variables’
values for each retailer i=1,2:
miMS 
2(1   )  6  2 (2   )(1   )  2 3 (4   )(1   )   (4  3 )(2   )
2(  3 (4   ) 2  2(2  3   2 )   2 (32  28  5 2 )   (20  24  6 2 ))
and
piMS 
4(2  3   2 )  4 3 (4   )(1   )   2 ( 2 (2  3 )  8(3  5 )  4 (5  7 )  2 (4  16   2 (1  4 )   (5  18 )) .
4(  3 (4   ) 2  2(2  3   2 )   2 (32  28  5 2 )   (20  24  6 2 ))
By replacing the above margins and wholesale price in the demand and profit functions, we can easily get the
equilibrium quantities and profits for each channel member. The full results are available in the appendix.
No Channel Leadership (VN)
Under this scenario, all players optimize their profit functions simultaneously which results in the following reaction
functions:
miVN 
  1    wVN
m ( 2   1)
;
4      2
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piVN 
2   (2    2)  wmVN
;
2(4      2)
wmVN 
2   ( p1VN  p 2VN )  (   1)(m1VN  m2VN )
.
4(   1)
i  1,2 and
The optimal solutions are then obtained from solving the above system:
miVN 
(4   3 2  2)  3(   1) 
;
6(   1)(2   1)   (   2)(3  2)
piVN 
 (3    3)   (   1)(3  2  3)
;
6(   1)(2   1)   (   2)(3  2)
wVN
m 
2(2   1)  (2     2)
.
6(   1)(2   1)   (   2)(3  2)
i  1,2 ,
i  1,2 and
The equilibrium quantities and profits for each channel member can be easily derived by substituting these values in
the right expressions (see the appendix).
The RS Leadership
We first solve for the manufacturer optimization problem to get his reaction function
wmRS 
2   ( p1RS  p2RS )  (   1)(m1RS  m2RS )
.
4(   1)
It is obvious from this reaction function that the wholesale price of the national brand increases as the retail
price of a store brand increases (
wm
w
 0 and m  0 ), which is consistent with the complementarity property of
p1
p2
the two products. Furthermore, the wholesale price of the national brand decreases as the retail margin of the
national brand increases (
wm
wm
 0 and
 0 ) as one can expect, for the national brand to keep competitive
RS
m1
m2RS
prices relative to the store brands.
The retailers maximize their profits given the reaction function of the manufacturer and conditionally on
each other’s reaction functions, yielding the following optimal margins
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miRS 
(8  5 2  4)  5(   1) 
, i  1,2 and
10(   1)( 2  1)  (16  5 2  8)
piRS 
 (5  2  5)   (   1)( 4  5(   1))
, i  1,2 .
10(   1)( 2  1)  (16  5 2  8)
Substituting these values into the manufacturer reaction function gives the optimal wholesale price
wmRS 
6(   1)( 2  1)   (16  7  2  8)  4(   1) 
.
2(   1)(10(   1)( 2  1)  (16  5 2  8) )
It is then straightforward to derive the equilibrium values for the quantities demanded and profits for each channel
members (see the appendix).
The RDS Leadership
Under this channel leadership structure, the two retailers are acting as price leaders and the manufacturer acts as a
price follower in terms of vertical interaction. In addition, Retailer 2 has horizontal price leadership over Retailer 1.
The first maximization problem for the manufacturer gives the same reaction function as in the RS
leadership case. Retailer 1 (follower at the retail level), will then use this information to maximize her profits which
yield the following reaction functions:
m1RDS 
(4  3 2  2)  3(   1)   (3  4  8  2 2  3 2  1)m2RDS  (2  1) p2RDS
,
2(9  4  8  6 2  3 2  3)
p1RDS 
 (3  2  3)  (3  4  3)(  1)   2 p2RDS  2(   1) m2RDS
.
2(9  4  8  6 2  3 2  3)
Finally, Retailer 2 uses the information on the two followers’ reaction functions to maximize her own profits and
obtains the optimal margins for the national brand and her store brand. By substituting these values in the right
expressions, we get the equilibrium retail margin and wholesale price of the national brand, and the retail price of
the store brand. Then, from these values we can derive the equilibrium solutions for the quantities demanded of
each brand and the profits for each channel member. The analytical results for the four channel leadership structures
are summarized in the appendix.
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DISCUSSION
In this section, we conduct sensitivity analyses within each of the channel leadership scenarios to see how the main
variables such as prices, quantities demanded, and profits react to a change in some of the parameters. We then
perform some comparisons within each scenario as well as between the different scenarios with respect to the
equilibrium values of the main variables.3
Sensitivity Analyses
We first conduct sensitivity analyses for each of the four channel leadership scenarios to examine the effects of
product differentiation, store differentiation, and the base level of store brand demand on the equilibrium outcomes.
The results are presented in the three following propositions.
PROPOSITION 1. Every thing else remaining the same, the cross-price sensitivity between the national
brand and store brand i (β) has a positive impact on the level of store brand demand regardless of the channel
leadership structure.
This proposition simply states that the demand for a store brand increases as the degree of product
substitutability between the store brand and the national brand increases. The interpretation is straightforward as
higher cross-price sensitivity means that the two brands are closer substitute. Consequently, small changes in the
price of the national brand will have high impact on the demand of the store brand. The next proposition highlights
the effects of cross price sensitivity between stores.
PROPOSITION 2. Every thing else remaining the same, higher cross-price sensitivity between the stores
(γ) results in a higher wholesale price but lower margins for the retailers. Its impact on the demand of both
products is positive. It results in higher profits for the manufacturer and lower profits for the retailers.
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A straightforward interpretation of this proposition would be that a higher store substitution (γ) implies
more competition between the two stores and consequently lower margins on both the national brand and store
brands resulting in an increase in the demand level of both brands. On the other hand, this competition seems to
favor the manufacturer vis-à-vis the retailers allowing him to raise his wholesale price. This results in more profits
for the manufacturer as both the wholesale price and the quantity demanded of the national brand increase. The
negative impact on the retailers’ profits, however, indicates that the increase in the quantities demand of both the
national brand and store brand are not high enough to compensate for the decrease in the retail margins of these
products.
To resume, higher cross-price sensitivity between stores is good for the manufacturer but not for the
retailers. These results are consistent with the findings of Sayman et al. (2002) as well as Choi (1996) in a duopoly
common retailers channel even if there were no store brand products in the latter models, meaning that the
introduction of store brand does not qualitatively change the results at this level.
PROPOSITION 3. Every thing else remaining the same, a retailer’s base level of demand for her store
brand (λ) has a positive impact on both the wholesale price and the retail margins. It also has a positive effect on
demand for the store brand, but a negative impact on demand for the national brand.
Its impact on the profits is
negative in the case of the manufacturer and undetermined in the retailers’ cases.
On one hand, we can explain the effect on prices by the fact that an increase in the market share of the
retailer’s store brand encourages her to increase the retail prices and margins for the two brands. Accordingly, the
manufacturer charges a higher wholesale price for the national brand. On the other hand, the positive impacts on
demand for the national and store brands are intuitive as higher values of λ mean stronger demand for the store
brand relative to that for the national brand. The negative impact of λ on the manufacturer profits indicates that the
decrease in the demand of the national brand overweighs the increase of the wholesale price and his profits decrease.
For the retailer, the total impact cannot be determined, though it is expected to be positive. These results are
3
Detailed proofs of all propositions in this section are available upon request from the authors.
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consistent with Raju et al. (1995) findings indicating that a retailer is better-off introducing a store brand for which
the base level of demand is high.
The three above propositions resume the effects of store competition, brand competition, and the store
brand’s level of demand. We now move to the effects of the channel leadership structures.
The Channel Leadership Structure Effects
Given the symmetric demand structure in the model, the optimal margins, quantities demanded and profits are the
same for the two retailers except for the RDS case. Hence, we only need to make the distinction between the two
retailers’ behaviour under the RDS scenario.
PROPOSITION 4. The optimal prices of the national brand and store brand compare as follows for the
different scenarios x= VN, MS, RS, and RDS:
i.
pim  pi and pim  wm ;
ii.
 pi x  wmx  pim x if   xp ,
 x
x
x
x
 pi  wm  pim if    p ,
w x  p x  p x if    x ,
i
im
p
 m
x
x
x
x
where the critical values  xp are functions of cross-price sensitivities β and γ and compare as follows:
VN
RS
RDS
RDS
1  MS
p   p   p   p1   p 2  0 .
iii.
p2
RDS
 p1
RDS
, m2
RDS
 m1
RDS
and p2m
RDS
 p1m
RDS
.
The first part of the proposition above indicates that the retail price of the national brand at each store is
always higher than the store brand’s price and the wholesale price of the national brand. This result holds for all
OCTOBER 15-17, 2006
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6th Global Conference on Business & Economics
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channel leadership structures and regardless of the values that the different cross-price sensitivities and base level
demand parameters can take; confirming face validity of the model.
The second part of the proposition shows that the relationship between the national brand's wholesale price
and the store brand i’s retail price, however, depends on the parameters of the demand function and how they relate
to each other. The way we present the results generates critical values of the base level demand of the store brand as
a function of the cross-price sensitivities between stores as well as between products. When λ is greater than the
critical value under each channel leadership structure, the price of a retailer’s store brand is higher than the
wholesale price of the national brand and vise-versa. These findings reinforce the sensitivity analysis results with
respect to λ.
Furthermore, by comparing the different critical values obtained under the different leadership
structures, we find that the highest critical value occurs under the MS leadership case followed consecutively by VN,
RS, and RDS cases. These results seem intuitive and consistent with the rest of our findings as they simply show
that as the retailer gets more power in the channel she needs relatively less base level of store brand demand in order
to start charging higher prices for her store brand compared to the manufacturer’s wholesale price. Finally, it is of
interest to note that the critical value is lower under the RDS compared to the RS structure even for the following
retailer. This implies that both retailers benefit of more strategic power under the RDS scenario regardless of the
roles they play.
However, as shown in the third part of this proposition the leading retailer still has an advantage over her
following competitor as prices and margins under the RDS leadership structure are always higher for the leading
retailer (Retailer 2) than for the follower (Retailer 1).
In sum, the last proposition aiming at comparing the prices within each leadership scenario showed that in
some cases this can be impossible to accomplish without referring to the channel leadership structure effects. We
therefore compare the equilibrium solutions obtained in the four channel leadership structures to have a better idea
of their impact on each channel member’s outcomes. We summarize the results in propositions (5) to (7) stated and
discussed below.
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PROPOSITION 5. Every thing else remaining the same, Stackelberg channel leaders get higher unit
margins on the national brand compared to the VN game. The two competing retailers get even higher unit margins
on the national brand playing a sequential Stackelberg rather than interacting simultaneously à la Bertrand-Nash.
The wholesale price of the national brand is the highest in the MS leadership, consecutively followed by
the VN, RS, and RDS cases ( wm
MS
 wm
VN
 wm
RS
 wm
RDS
). In contrast, the retail margin of the national brand
at each store is the highest in the RDS case followed consecutively by the RS, VN, and MS cases
( m2
RDS
 m1
RDS
 mi
RS
 mi
VN
 mi
MS
i  1,2 ). These results imply that a channel leader can obtain a higher
,
mark-up on the national brand, which provides a direct incentive for each channel member to become the leader. In
addition, even the Stackelberg price follower among the two retailers (Retailer 1) shows higher retail margin for the
national brand under the RDS compared to the RS leadership.
This supports the statement in the previous
proposition that the two retailers benefit by playing a Stackelberg game between them regardless of their roles.
PROPOSITION 6. Every thing else remaining the same, Stackelberg leadership results in higher retail
prices for the national brand compared to the VN game. Due to store competition, both the RS and RDS games
result in lower retail prices for the national brand and the store brand compared to the MS game.
The retail prices of the national brand resulting from the three different Stackelberg leadership are always
higher than those of the VN case ( pm2
MS
 pm2
RDS
 pm2
RS
 pm2
VN
, pm1
MS
 pm1
DRS
, and pm1
RS
 pm1
VN
).
This indicates that consumers are better-off in the absence of channel leadership, which is consistent with previous
studies' findings (Shugan and Jeuland 1988, Choi 1991 and 1996). In addition, the two retailer Stackelberg cases
(RS and RDS) lead to lower retail prices for the national brand compared to the MS case. This result also
corroborates with the previous conclusion that a manufacturer’s leadership results into higher retail prices than a
retailer’s leadership when accounting for store competition (Choi 1996). With respect to two retailer’s Stackelberg
scenarios, the Stackelberg price leader (Retailer 2) benefit from a higher retail price for the national brand under the
OCTOBER 15-17, 2006
GUTMAN CONFERENCE CENTER, USA
6th Global Conference on Business & Economics
ISBN : 0-9742114-6-X
RDS compared to the RS case. The equivalent relationship is, however, undetermined for the Stackelberg follower
(Retailer 1).
The retail prices of the two store brands are also higher under the MS case compared to the VN and under
the RDS compared to the RS case ( pi
MS
 pi
VN
and pi
RDS
 pi
RS
, i  1,2 ). The intuition behind this result is
that each retailer sets a relatively high price for her own store brand under the MS structure because the competing
national brand price is also higher in this case and chooses a high price under the RDS as she has more power under
this scenario compared to the RS. It is not clear though, from these price comparisons, that the store brand provides
the retailers with a concrete mark-up incentive to become leaders. However, we can reach this conclusion by com
paring the profits, which lead us to the last proposition.
PROPOSITION 7. Every thing else remaining the same, each channel member obtains higher profits by
being the Stackelberg leader rather than playing a VN game.
Two competing retailers also benefit from a
Stackelberg leadership at the horizontal level. In contrast, consumers are better-off when there is no channel
leadership and worse-off when the national brand manufacturer leads the channel.
The manufacturer profits are the highest under the MS case followed in order by the VN, RS, and RDS
cases
VN
RS
RDS
(  MS
),
M  M  M  M
whereas
the
retailers
profits
present
the
reverse
order
VN
MS
(  RDS
  RS
Ri
Ri   Ri   Ri , i  1,2 ). These results are expected, as the leader has informational advantage
(knows the followers' reaction functions) and exploits it in his/her pricing strategy. In addition, it is confirmed once
again that the two competing retailers are better-off when there is price leadership between them as they benefit
from higher retail margins for the national brand and store brands compared to the RS case. Thus, horizontal price
leadership at the retail level would be the best pricing strategy not only for the price leader but also for the price
follower when they dominate the national brand manufacturer.
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Globally, and as expected, the total channel profits ( 
x
  mx   Rx1   Rx 2 ) are maximized when there
is no channel leadership. In addition, the two retailer Stackelberg cases (RS and RDS) produce larger channel
profits than the MS case ( VN   RS   RDS   MS ).
CONCLUSION
This paper presents a general analytical framework that helps better understand the nature of price competition
between national and store brands in presence of store competition. In fact, we consider both intra-store competition
between national brand and store brands and inter-store competition between two stores. In addition, we consider
various price leadership structures among the channel members, namely simultaneous interactions à la BertrandNash and sequential à la Stackelberg both at the vertical and horizontal levels of the channel.
Some of the results are intuitively appealing:

A channel member benefits by playing the Stackelberg leader at the expense of the other channel
member(s) who become follower(s) as opposed to consumers who benefit of lower retail prices
when there is no Stackelberg price leader in the market.

Demand levels for store brands increase as the cross price sensitivity between the national brand
and store brands increases.

More competition between retailers’ stores results in lower retail margins for national and store
brands, increasing the demand levels of both products despite a higher wholesale price for national
brands. Accordingly, only the national brand manufacturer benefits from more store competition
by increasing his profits.

The retailers' base level of store brand demand has a positive impact on both the wholesale price
and the retail margins.
Its impacts on the quantities demanded of the store brand at the
equilibrium are positive. On the national brand, demand impacts are negative, resulting in lower
profits for the manufacturer.
Some other results provide new insights:
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6th Global Conference on Business & Economics

ISBN : 0-9742114-6-X
The two competing retailers benefit from price leadership at the retail level regardless of their
roles (leader or follower).

The retail prices of the national brand and store brands under the MS case are always higher than
those of the two retailer Stackelberg cases.

The total channel profits increase as the retailers have more price leadership than the national
brand manufacturer. They are also higher under the RS compared to the RDS leadership.
These findings are insightful for practitioners in many perspectives. First, powerful store brand retailers
need to seek price leadership between them as it would increase their profits in presence of store competition. As
such, a store brand retailer should not fear her competitor (second retailer) as long they dominate over the
manufacturer. Second, each store should develop a unique positioning strategy to differentiate from the competitors
as it helps in increasing the retailer’s profits. Finally, the retailers should offer a store brand that is a close substitute
to the national brand in order to guarantee a high level of demand. This result was also compatible with Sayman et al.
(1995) who found, in a different channel structure, that closer positioning of a store brand to the leading national
brand is the optimal strategy in a different channel structure. Combined, the last two managerial implications
suggest that to be more successful, each retailer needs to differentiate her store more from that of her competitor and
less her store brand from the national brand by providing relatively homogeneous brands in the store.
To conclude, this study can be extended in many directions. For instance, one can consider more than one
manufacturer in the channel; introduce more asymmetry between the retailers (for example, different base levels of
demand); allow for different positioning of the retailers vis-à-vis the manufacturer by using different product
differentiation parameters between the national brands and store brands; consider nonlinear demand functions;
and/or consider more strategic variables other than the price such as advertising, quality and promotions.
REFERENCES
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Choi, S., A. T. Coughlan. 2006. Private label positioning: Quality versus feature differentiation from the national brand. J. Retailing. 82(2) 79-93.
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Connor, J., E. Peterson. 1992. Market structure determinants of national brand-private label price difference of manufactured food products. J.
Industrial Econom. 40 157-171
Cotterill R., B. Putsis, R. Dhar. 2000. Assessing the competitive interaction between private labels and national brands. J. Bus. 73(1) 109-137.
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OCTOBER 15-17, 2006
GUTMAN CONFERENCE CENTER, USA
6th Global Conference on Business & Economics
ISBN : 0-9742114-6-X
APPENDIX
Table 1 Equilibrium Outcomes
(a) The MS case
wm
mi
2 1
4
2
2 2 1
3
4
2
4
2
2
4
2
32
1
2 3 4
4
5 2
28
2
2 2
2
3
4 3 4
3
4
2 1
4
8 2
2
2
4
2
2 2
2
2
4 7
4
2
3
3
2
2
2 1
8 3
2
3
6 2
24
2
5
32
4
5
9
4
7
5 2
28
2
5
6
2
4
20
24
2
16
6 2
1
1
6
2
8 2 1
M
wm q1 m
q2 m
Ri
mi qim pi qi ... i
2
4
4
6
4
8
4
2
3
1
2 1
8
3
4
1, 2
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GUTMAN CONFERENCE CENTER, USA
2
2 2
3
2
4
2
32
28
2
5 2
2
20
24
4
4 6
24
4
2
4
4 1
2
1
3
20
2
1
wm mi
4 2
qi
2 3 4
3
pi
qim
4
1
2 2
2 3
p im
6
6 2 2
2 1
2
2
6 2
1
1
4
5
18
5
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ISBN : 0-9742114-6-X
(b) The VN case
wm
mi
p im
pi
qim
2 1
6
9
4
3
2
9
6
1
2 1
4
4
3 2 4
2
2 6
M
wm q1 m q2 m
Ri
mi qim pi qi ... i
6
6
1
2
9
4
2
4
2
9
4
1
2
3 2 4
3
2
9
2
2
4
8
3
2
2
4
3 2 4
4
3 2 4
4
4
3 2 1
2 2
3 2 1
2
2 6
3
qi
3 2 4
4
6
2
3 2 1
wm mi
3
2
3 2 4
4
2
6
4
1
2
9
1
2 1
4
3 2 4
1, 2
OCTOBER 15-17, 2006
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4
9
4
4
2
1
2
9
4
2
2
1
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ISBN : 0-9742114-6-X
(c) The RS case
wm
mi
p im
pi
qim
6
8
2 1
10
8
2
15
5
5 2 4
8
2
9
4 10
8
5 2 4
4
2
2
2
4 1
M
wm q1 m q2 m
Ri
mi qim pi qi ... i
2
1
15
8
2
10
4 1
10
1, 2
OCTOBER 15-17, 2006
GUTMAN CONFERENCE CENTER, USA
15
20
7
4
8
4
8
5 2 4
8
2
38
1
3
9
2
4
5 2 4
7
8
8
2
2
6
2
5
8
12
15
10
8
21
10
2
6
8
8
4
1
4
15
2 1
8
4
2
10 3 1
8
7
5
5 2 1
10
12
5 2 4
8
14
2
4
5 2 4
8
4
6
2
5 2 1
wm mi
5
9
10
4
2 5
qi
2
2
4
5 2 4
20
3
2
2
2
2 2 6
6
15
12
15
8
7
8
1
2
4
2
1
25
4
11
6th Global Conference on Business & Economics
ISBN : 0-9742114-6-X
(d) The RDS case
wm
2 121
656 2
504
2
2
5
3993
128
8712
8
51
6
8 1
2
2
256 3
3
29
2325
16
1683
2
5
4
3
304
24
2
10
4853
128 3 12
1089
2
3233
2112
3
2
4072
312
13039
2
998
2 51
188
3
912
16 2 287
2
532
11863
3213
4032
4
3
64
8062
3
2
3424
2
208
3
13
5
16
15972
3672
2
5800
7623
3
77
32 3 193
71
2
3389
3
4
22 2 87
1936
288
6680
1088
6
76
20
937
39638
3
424
6732
2
8
439
144
2
10893
2
3800
918
14506
32
3008
2
8831
2
287
166
2411
888
722
29437
2912
3
76
6400
768 3
3
1364
m1
80 2
4 41 120
3
2
5
3728
3760
6
4 51
16
1938
pim
28
4
3264
2
24
2
2 2 1683
m2
51 6 16
10
2
2 34
wm mi ... i
776 463
3
3
188
912 3
1
2
32 2
80
96 2 5
328 51
4
2
3622
4
2550
210
3
2
4 2 1076 357
37
749
572
12 2 99
40
6191 4572
5546 4918
2 51
4072 2
4853
4
7310 4103
1692 1519
17 4 4
48
5 2 1
20
17 4 8
208 2
64 3
5
2 3 3213 8062
70
3389 2
3672 6680
5800 2
1088 3
4
17
4
24
7
2 2 129
2
4
51
100
32 2
4
51 1 8
8
424 3
918
6732
14506
68
2
8831 2
73
2 2 221
2912 2
3008
1364 3
3
42
88 2
354
768 3
214
3
408
170
524
200
163
96 2
1, 2
p1
208 2
4 51 188
2 2 102 7
4
26
204 25
4 3 4
3
41
2
2
64 3
51 6 16
20
80 2 19 74
3
416 996
9
8
5 2 1
16 3 16
2
34 80
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GUTMAN CONFERENCE CENTER, USA
77
7
2
5052 8311
32
2
17
288
4
8
5
1057
4916
8
32 3 1
8703
2
4
82 3 1
2
51
10
3
100
28
2
6
816 4
102 19 44
32
2
2
8
2
8 2 19 156
47
2
5
3
45
221 354
1911 2558
2
142
88
2
5238 6578
2846 7040
3
408
524
4623 10675
96 2
6th Global Conference on Business & Economics
ISBN : 0-9742114-6-X
p2
2 17 40
2
16 2
34 4 9
17 4 4 3
2
4
1
8 23
2
8 2 1 6
17 85
204 451
2 34 80
2
2
32
3
17 80
17
4
14 2 1 2
2
8 8
4
34 5 7
51 100
2
32
187 262
2
2
88 2
221 354
3
408 524
96 2
q1 m
82 240
4
160 2 4
328 8
7
q2 m
123 8 2 20 3
2
55 14
12
16 3
21
2
129 88
4
16 34 80
2
6
3 2 2
4
4 3 246 5
150 7
14
9
2
32
11
8
4
17
2 2 72 35
81 14
2
8 8
4
2 2 533 16 2 29 9
51 100
32
2
2
2
221 354
2
88
2
535 56
3
408 524
96 2
1
4
1
q1
16 2
8 17 40
4
2
8 81 272
16 1
q2
5
4 3
41 2 1 2
8 27 68
208 498
4
34 80
32 2 17 4 8 8
4
3
10
24
226 675
2
7
1
16 1
M
wm q1 m q2 m
Ri
mi qim pi qi ... i
6
8
1
2 1
4
3 2 4
OCTOBER 15-17, 2006
GUTMAN CONFERENCE CENTER, USA
2
27 476
5
32
32 2
51 100
2
3
1, 2
4
2 3 351 1700
30 71
48
4
8
2
2
2
9
4
2
1 10
68 960
2 2 221 354
3 2 2
4
2
4 2 45 142
1
1
6
9
8
2
1
88 2
15
60
4
4
3
2
151 622
81 646
96 2
408 524
2
8
23
4 2 16 77
1
170 1111