Strategic motive of introducing Internet channels in a supply chain

Strategic motive of introducing Internet channels in a supply chain
Lu Hsiao
Department of Business Administration, National Chung Hsing University
Taichung, Taiwan R.O.C.; tel: 886-04-22840571 ext. 613;
fax: 886-4-22858040; e-mail: hsiaolu@dragon.nchu.edu.tw
Ying-Ju Chen
Department of Industrial Engineering & Operations Research, University of California
Berkeley, CA 94720; tel: 510-642-2497; fax: 510-642-1403; e-mail: chen@ieor.berkeley.edu
December 2, 2012
Abstract
Rapid advances of information technology in recent years have enabled both the manufacturers
and the retailers to operate their own Internet channels. In this paper, we investigate
the interaction between the capabilities of introducing the Internet channels, the pricing strategies,
and the channel structure. We classify consumers into two segments: Grocery shoppers
attach a higher utility from purchasing through the physical channel, whereas a priori Internet
shoppers prefer purchasing online. We find that when the Internet shoppers are either highly
profitable or fairly unimportant, the manufacturer prefers to facilitate the channel separation
either through his own Internet channel or the retailer’s. In the intermediate region, however,
the manufacturer encroaches the grocery shoppers and steals the demand from the retailer’s
physical channel. With horizontal competition between retailers, a priori symmetric retailers
may adopt different channel strategies as a stable market equilibrium. The manufacturer may
willingly give up his Internet channel and leverage on the retailer competition. When the manufacturer
sells through an online e-tailer, Internet shoppers may be induced to purchase through
the physical channel. This reverse encroachment strategy emerges because selling through the
e-tailer leads to a more severe double marginalization problem.
Keywords: multi-channel management, retail operations, electronic commerce, game
theory.
History: Received: December 2010; accepted: November 2012 by Vishal Gaur after two revisions.
1

1 Introduction
In recent years, the Internet channel provides a convenient and secure environment for the manufacturer/
retailer and the consumers to make transactions, thereby leading to the “clicks-and-mortar”
phenomenon. A report from the U.S. Census Bureau’s Quarterly Retail E-Commerce Sales shows
that the online quarterly sales has increased to at least $33.6 billions as of second quarter of 2007
(around 28% increase in 7 years). The concurrent increase of the average growth rate for the total
retail sales was only 4.5% (U.S. Census Bureau, 2007). Examples of the manufacturers that adopt
the dual channel structure include, but are not limited to, leading firms in the computer industry
(such as Apple, IBM, and Cisco), cosmetics manufacturers (e.g., Estee Lauder), beverage and food
manufacturers (Budweiser Beer, Coca Cola, and Campbell Soup), sports goods producers (e.g.,
Nike), and electronics suppliers (e.g., PalmOne, Samsung, and Sony). In addition, some leading
U.S. retailers (e.g., Barnes & Noble, Bestbuy, Bloomingdales, Wal-mart, Target, etc.) also have
gone online.
However, in this Internet era, there are still a significant portion of retailers that focus exclusively
on the physical channels, and a number of leading manufacturers insist to sell through the
direct channels. For example, the giant retailers 7-eleven and Carrefour do not provide the online
purchase option for the consumers. Examples that abandon the Internet channels span across various
industries, including consumer electronics (Pricesmart), apparel (Tween Brands, Citi Trends,
Dress Barn, Ross Stores), food (Spartan Stores), fabrics (Duckwall-Alco), home fashion (TJX inc.,
Family Dollar), plastics (Collective Brands), pharmacy (Watsons), and grocery retailers (Pantry,
Retail Enterprises, Ingles Markets, and RT-MART). 1 On the manufacturers’ side, firms that sell
exclusively through independent retailers expand across various product categories such as Acer,
Colgate, Gillette, Heinz, Kellogg’s, and Tylenol.
Given the consistent profitability and large organizations, the aforementioned manufacturers
and retailers are apparently capable of operating their Internet channels; thus, these channel
management decisions seem to be strategic rather than operational. Additionally, there is a large
variation of the online purchasing option across different categories and locations; sometimes the
Internet channel is owned by the manufacturer, whereas in other cases it is the retailer that runs
the Internet channel. Operational concerns such as shipping costs from the manufacturers’ side
and transportation costs from the consumers’ side may not provide a good answer to this variation;
it is hard to explain why consumers can order beers and soups via Budweiser’s and Campbell’s
1 Most of the above retailers are selected as the top/hot retailers by Stores.com based on their dominant performance
and/ or the remarkable growth rates (source: http://www.stores.org/Top 100 new/Top 100 landing page.asp).
2

websites, but are prohibited to purchase laptops or video game consoles directly online.
This paper attempts to provide an answer to when and why the manufacturer and the retailer
should introduce their Internet channels, given that they both are capable of doing so and actively
respond to their channel parties’ channel and pricing decisions. In pursuit of this goal, we construct
a stylized supply chain with a manufacturer, an independent retailer, and a continuum of consumers
with heterogeneous preferences. The retailer operates a physical channel and sells the products for
the manufacturer to the consumers. There are two consumer segments: Grocery shoppers attach a
higher (gross) utility from purchasing the product through the physical (offline) channel, whereas
Internet shoppers obtain a higher utility if purchasing online.
To isolate the strategic concerns of these two channel parties, we start with two benchmark
scenarios with manufacturer-operated or retailer-operated Internet channels. When only the manufacturer
is capable of introducing the Internet channel, we find that two strategies can emerge
as the market equilibrium. If the Internet shoppers are sufficiently profitable, a natural channel
separation arises: Internet shoppers are induced to purchase online, whereas grocery shoppers buy
in the physical channel. On the other hand, when the grocery shoppers become more important,
the manufacturer shall set a low selling price in his Internet channel to attract the low-valuation
consumers from the physical channel. This strategy allows the manufacturer to encroach the grocery
shoppers without creating the channel conflict. When instead only the retailer can introduce
the Internet channel, a similar channel separation strategy arises. Nevertheless, the aforementioned
grocery encroachment strategy is no longer desirable. If the Internet shoppers are relatively important,
a niche targeting strategy is implemented: the retailer abandons the physical channel and
targets only the Internet shoppers through her Internet channel.
We then investigate the market equilibrium when both parties are capable of operating the
Internet channel. When the Internet shoppers are either highly profitable or fairly unimportant,
the manufacturer prefers to facilitate the channel separation. In the intermediate region, however,
the manufacturer intends to encroach the grocery shoppers and steal the demand from the retailer’s
physical channel. To understand this result, observe that when the Internet shoppers are highly
profitable, the manufacturer certainly prefers to go direct to capture this segment. At the other
extreme, when the Internet shoppers are fairly unimportant (compared to the grocery shoppers), it
is in the manufacturer’s best interest to delegate both channels to the retailer. In the intermediate
region, the manufacturer faces two conflicting forces. Facilitating channel separation via his own
Internet channel induces too much competition from the retailer, but completely delegating to the
retailer leaves her a significant portion of revenue. In such a scenario, the manufacturer prices
aggressively in his Internet channel so as to steal some grocery shoppers.
3

Finally, we consider some extended models with retail-level competition. We find that with
retailer competition, in any equilibrium channel structure exactly two supply chain parties introduce
their Internet channels. Even if the retailers are perfectly competitive, the manufacturer intends
to induce them to both introduce the Internet channels, and in equilibrium both retailers willingly
do so. On the other hand, our results also suggest that even if the retailers are a priori symmetric,
asymmetric channel structures may emerge as a stable market equilibrium. When the manufacturer
sells through an online retailer (e.g., Amazon), he may induce Internet shoppers to purchase through
the retailer’s physical channel. This reverse encroachment strategy emerges since all the Internet
channels are “indirect,” i.e., not directly controlled by the manufacturer. The retailer’s physical
channel becomes appealing (from the manufacturer’s viewpoint) because the retailer intends to
set the margin low so as to attract grocery shoppers. Consequently, the double marginalization
problem is less severe.
Since we investigate the strategic choice of channel structure, our work is related to the vast
literature on channel management. Earlier literature focuses on the benefit of adding an Internet
channel when the firm can sell directly to the end consumers (Alba et al. (1997), Balasubramanian
(1998), Bernstein et al. (2008), Kumar and Ruan (2006), Lal and Sarvary (1999), and Peterson et al.
(1997)). In the context of the supply chain, researchers typically focus exclusively on the situations
in which only the manufacturer is able to introduce the Internet channel; see, e.g., Balasubramanian
(1998), Cattani et al. (2006), Chiang et al. (2003), Druehl and Porteus (2005), Hsiao and Chen
(2012), and Tsay and Agrawal (2004). Unlike all the aforementioned papers, we allow both the
manufacturer and the retailer to introduce their own Internet channels. We also highlight the
interactions between the retailer’s and e-tailer’s Internet channels.
Our analysis regarding the horizontal competition is related to Cattani et al. (2007), who
study how competition among the Internet retailers (grocers) influences the channel management
strategies. They document the nuance connection among the product perishability, channel structure,
and competitive nature, and show that the results are robust against the inclusion of capacity
constraint. As a complement of Cattani et al. (2007), we introduce the manufacturer into this competitive
retailer context, and show that this vertical – horizontal supply chain relationship generates
various channel structures in market equilibria.
The rest of this paper is organized as follows. In Section 2, we describe the model. Section
3 derives the equilibrium behavior and compare the manufacturer’s and the retailer’s incentives
of introducing their Internet channels. Section 4 examines different forms of retail competition.
Finally, we draw our conclusions in Section 5. All proofs are in the Appendix.
4

2 Model
We consider a supply chain with a manufacturer, an independent retailer, and a continuum of
consumers with heterogeneous preferences. The manufacturer produces the product at a constant
marginal cost, which is normalized to zero for ease of exposition. The retailer operates a physical
channel and sells the products for the manufacturer to the consumers. As our primary goal is to
evaluate the manufacturer’s and the retailer’s incentives of introducing an Internet channel, we allow
both the manufacturer and the retailer to introduce their own Internet channels. All the supply
chain parties are risk neutral and therefore aim at maximizing their expected profits/utilities. The
bilateral monopoly setting in our basic framework is adopted for ease of exposition. The case with
horizontal competition is investigated in Section 4.
Consumer preferences. Each consumer is willing to purchase at most one unit of product,
and the population of consumer is normalized to 1. We categorize the consumers into two segments
that differ in their preferences towards purchasing online or offline. Consumers in the first segment
attach a higher (gross) utility from purchasing the product through the physical channel, whereas
consumers in the second segment obtain a higher utility if purchasing online. To model this discrepancy,
we assume that a consumer whose valuation from purchasing in the physical channel is
v will obtain a gross utility β i v if purchasing online; the parameters {β i }’s satisfy 0 < β 1 < 1 < β 2
and represent their channel preferences. For ease of presentation, in the sequel we call the first
segment the “grocery shoppers,” and the second segment “Internet shoppers.” These terms indicate
the consumers’ inherent preferences over the physical and Internet channels.
In the majority of the dual channel literature, consumers are assumed to express a lower
willingness to pay while purchasing online due to either the privacy concern or trust issues (see, e.g.,
Chiang et al. (2003), Kacen et al. (2001), and Liang and Huang (1998) for the micro-foundation of
grocery shoppers). Nevertheless, it is possible that some consumers may incur a higher cost upon
visiting the physical channel. This is because all the transactions can be made only when the
consumers actually go to the physical retail store, whereas if purchasing online everything is just
“a click away.” This provides a justification of the Internet shoppers: the effective payoff of a
consumer may be affected by transportation cost, the possibility of seeing a stock-out, the time
spent in figuring out the exact location of the product in the shelf space, and etc.
Grocery versus Internet shoppers. Although we label these two segments as grocery and
Internet shoppers, their actual purchasing behaviors shall depend on the price comparisons, as we
demonstrate in Section 3. We use 1 − α and α to denote the proportions of consumers in the first
and second segments. Thus, α serves as a proxy of how favorable the online channel is a priori
5

from the consumers’ viewpoints. We denote v as the “intrinsic” valuation of a consumer, and
it is assumed to be uniformly distributed over [0, V ]. This distributional assumption is made to
facilitate closed-form expressions of all the equilibrium outcomes.
Manufacturer’s and retailer’s strategies. Given that both the manufacturer and the
retailer can introduce their Internet channels, the relevant pricing decisions are specified as follows.
We use w to denote the wholesale price, p to denote the retail price in the physical channel,
and w d and p d to denote the (retail) price in the manufacturer-owned and retailer-owned Internet
channels, respectively (the subscript d stands for the “direct” channel). Given these prices, if a
consumer with valuation v purchases from the physical channel, her net utility is v − p. On the
other hand, she obtains utility β i v − w d (β i v − p d ) if purchasing from the manufacturer-owned
(retailer-owned) Internet channel. To account for the manufacturer’s additional services or brand
management effort, we use f to denote the manufacturer’s operating cost for the Internet channel.
This cost f is assumed to be reasonably small to avoid trivial results; if the operating cost were
prohibitively high, the manufacturer would have no incentive to introduce his Internet channel
and the problem degenerates. Additionally, we use π M and π R to denote the manufacturer’s and
retailer’s equilibrium payoffs. A graphic illustration of the channel structure is given in Figure 1,
and Table 1 summarizes the notation used in this paper.
Figure 1: Channel structure of the basic framework.
Having described the channel structure and the objectives of these channel parties, we in the
next section derive the equilibrium behaviors in this supply chain.
6

Notation Definition
v consumer valuation from purchasing in the physical channel
β i scaling factor for purchasing online, i = 1, 2
V upper bound of v
α proportion of Internet shoppers
w wholesale price
p retail price in the physical channel
w d
p d
f
3 Equilibrium analysis
retail price in the manufacturer-owned Internet channel
retail price in the retailer-owned Internet channel
manufacturer’s operating cost for the Internet channel
Table 1: Summary of notation.
In this section, we investigate the strategic interactions between the manufacturer and the retailer.
To isolate the strategic concerns of these two channel parties, we start with two benchmark scenarios.
In the first scenario, only the manufacturer is capable of operating the Internet channel,
whereas in the second scenario the retailer is the only party that can introduce her Internet channel;
see the graphic representations of these two scenarios in Figures 2 and 3, respectively. These two
scenarios serve as the benchmark cases that allow us to examine the manufacturer’s (retailer’s)
incentive of introducing the Internet channel. Following these, we then articulate the market equilibrium
when both parties are capable of operating the Internet channel, which provides the full
picture of the general model.
3.1 Manufacturer-owned Internet channel
Let us first consider the case in which only the manufacturer is able to operate the Internet channel.
Our goal is to compare this scenario with the existing literature and use this benchmark to highlight
the strategic role of the Internet channel for both the manufacturer and the retailer.
Timing. The sequence of events is as follows. 1) The manufacturer determines whether
to introduce an Internet channel; 2) The manufacturer offers the wholesale price to the retailer,
and determines the price offered to the consumers in his Internet channel if any; 3) The retailer
7

Figure 2: Manufacturer-operated Internet chan-
Figure 3: Retailer-operated Internet channel.
nel.
responds by determining the appropriate retail margin; and 4) The consumers decide which channel
to purchase the products from. Since the game involves multiple rounds of strategic interactions,
we adopt the subgame perfect Nash equilibrium as our solution concept (Fudenberg and Tirole
(1991)).
Effective demands. By backward induction, we first derive the effective demands in the
physical channel and retailer-owned Internet channel. To this end, we shall discuss the consumers’
purchasing decisions. Note that in equilibrium it must be 0 ≤ p ≤ V and 0 ≤ w d ≤ β 2 V if there
are actual transactions in both channels. First, a type-v Internet shopper buys the product on the
Internet if and only if β 2 v − w d ≥ 0 and β 2 v − w d ≥ v − p. It means that v ≥ max{ w d
β 2
, w d−p
Further, w d
β 2
≥ w d−p
β 2 −1
β 2 −1 }.
if and only if w d ≤ β 2 p. A type-v Internet shopper buys the product in the
physical channel if and only if v − p ≥ 0 and v − p ≥ β 2 v − w d . Thus, p ≤ v ≤ w d−p
β 2 −1
non-empty if and only if w d ≥ β 2 p.
, and the set is
Second, a type-v grocery shopper buys the product on the Internet if and only if β 1 v − w d ≥ 0
and β 1 v − w d ≥ v − p. It means that w d
β 1
≤ v ≤ p−w d
1−β 1
, and the set is non-empty if and only if
w d ≤ β 1 p. On the other hand, a type-v grocery shopper buys the product in the physical channel
if and only if v − p ≥ 0 and v − p ≥ β 1 v − w d . It means that v ≥ max{p, p−w d
1−β 1
}. Further, p ≥ p−w d
1−β 1
if and only if w d ≥ β 1 p.
Therefore, given 0 ≤ p ≤ V and 0 ≤ w d ≤ β 2 V , the demand in the physical channel, denoted
8

as Q, is
⎧
⎪⎨
Q =
⎪⎩
1
V [(1 − α)(V − p−w d
1−β 1
)], if w d ≤ β 1 p
1
V [(1 − α)(V − p)], if β 1p ≤ w d ≤ β 2 p
1
V [α( w d−p
β 2 −1 − p) + (1 − α)(V − p)], if w d ≥ β 2 p
and the demand on the manufacturer-owned Internet channel, denoted as Q M d , is
,
1
⎧⎪ ⎨ V [α(V − w d
β 2
) + (1 − α)( p−w d
1−β 1
− w d
β 1
)], if w d ≤ β 1 p
Q M d = 1
V
⎪ [α(V − w d
β 2
)], if β 1 p ≤ w d ≤ β 2 p
⎩ 1
V [α(V − w d−p
β 2 −1 )], if w d ≥ β 2 p
.
Manufacturer’s channel strategy. These demand functions provide a clear picture of
market segmentation via this supply chain, and suggest that depending on the prices posted,
the retailer may have access to either one consumer segment or both segments. Subsequently,
we characterize the retailer’s optimal pricing decisions using these demand functions as inputs.
Following this, we then investigate the manufacturer’s optimal decisions on the prices and the
channel structure. While we relegate the remaining analysis to the appendix, our first result
identifies the manufacturer’s channel strategy and the corresponding equilibrium outcomes.
Proposition 1. Suppose that only the manufacturer can introduce the Internet channel. There are
two possible equilibrium strategies:
• Channel separation strategies (CS-M and CS’-M): Internet shoppers are induced to purchase
online, whereas grocery shoppers buy in the physical channel (these two strategies differ only
in whether the manufacturer’s pricing decision is the interior or corner solution);
• Grocery encroachment strategy (GE-M): Only the high-valuation grocery shoppers buy in the
physical channel, and others purchase online.
Accordingly, the resulting equilibrium prices are:
Strategy w ∗ w ∗ d
p ∗
GE-M
CS’-M
CS-M
[β 2 −α(1−β 1 )(β 2 −β 1 )]V
2(αβ 1 +β 2 −αβ 2 )
[(2−β 1 )β 2 −α(1−β 1 )(2β1 2+2β 2−β 1 β 2 )]V
2[αβ1 2+(1−α)(2−β 1)β 2 ]
V
2
The corresponding payoffs are:
β 1 β 2 V
2(αβ 1 +β 2 −αβ 2 )
β 1 (1−β 1 )V +β 1 w ∗
2−β 1
β 2 V
2
[(3−β 1 )β 2 −3α(1−β 1 )(β 2 −β 1 )]V
4[αβ 1 +β 2 −αβ 2 ]
wd
∗
β 1
3V
4
9

Strategy π M π R
GE-M
CS’-M
CS-M
[αβ 1 (1−α)(1−β 1 )+β 2 +β 1 β 2 −αβ 2 (2−α)(1−β 1 )]V
8(αβ 1 +β 2 −αβ 2 )
[β 2 +α 2 (1−β 1 )(4β1 2+β 2−5β 1 β 2 )−2α(1−β 1 )(2β1 2+β 2−2β 1 β 2 )]V
4[(2−β 1 )β 2 +α(β1 2−2β 2+β 1 β 2 )]
(1−α+2αβ 2 )V
8
(1−α)(1−β 1 )V
16
(1−α)(1−β 1 )[β 2 +α(2β1 2−β 2−β 1 β 2 )]V
4[(2−β 1 )β 2 +α(β1 2−2β 2+β 1 β 2 )] 2
(1−α)V
16
From Proposition 1, we observe that the benefit of introducing the Internet channel primarily
comes from two sources.
On one hand, including an Internet channel allows the manufacturer
to price discriminate the consumers through their self-selection behaviors.
As some consumers
are willing to pay more in the Internet channel, the manufacturer can set prices appropriately to
induce them to purchase in different channels. Second, the introduction of Internet channel allows
the manufacturer to sell the products directly to the consumers instead of by way of the retailer,
thereby avoiding the double marginalization problem that is present in the physical channel.
Given that grocery shoppers a priori prefer purchasing in the physical channel and Internet
shoppers prefer going online, a natural conjecture is that the manufacturer shall simply induce them
to purchase separately through these two channels. However, Proposition 1 shows that this is true
only when there are sufficiently many Internet shoppers who a priori enjoy buying online (the CS-M
strategy). When a large proportion of consumers a priori prefer to purchase in the physical channel
(α is small), the manufacturer shall set a low selling price in his Internet channel to attract the
low-valuation consumers from the physical channel (the GE-M strategy). We illustrate numerically
the market conditions under which the grocery encroachment strategy emerges as the equilibrium
in Figure 4 (where we fix β 1 = 0.9, V = 8, and f = 1; the same parameters apply to all the
subsequent figures). Notably, we can verify that all the equilibria in different regions are unique
because of the sequential nature of our games. We highlight our finding in the following corollary.
Corollary 1. Suppose that only the manufacturer can introduce the Internet channel. The grocery
encroachment strategy is more likely to be implemented when the Internet shoppers are rather
unimportant (i.e., when α and β 2 are small).
Corollary 1 indicates the precise regime for this grocery encroachment strategy to be profitable.
To understand this result, recall that in the physical channel the retailer demands a markup and
therefore the double marginalization effect gives rise to a relatively high selling price. This high
selling price inevitably forces the manufacturer to exclude some consumers with relatively low
valuations. If the manufacturer is able to retain the selling business through his Internet channel, he
can then set a relatively low price online to recoup these low-valuation consumers. This is precisely
the rationale for the GE-M strategy; thus, occasionally it may dominate the intuitive channel
10

separation strategy. In the extreme case where the Internet shoppers are unimportant, the benefit
from market segmentation cannot justify the hassle of operating the Internet channel. Consequently,
the manufacturer simply abandons it and sells everything through the physical channel.
Note that in order to attract the low-valuation grocery shoppers to purchase online, the manufacturer
necessarily keeps the selling price low in his Internet channel. The downside of this
strategy is to forgo the rent extraction from the Internet shoppers. If instead the Internet shoppers
constitute a highly profitable segment, extracting revenue from the Internet shoppers becomes the
manufacturer’s primary concern. In such a scenario, the manufacturer purposely gives up those
low-valuation consumers and leave all grocery shoppers in the (retailer’s) physical channel. Collectively,
we observe that the manufacturer’s pricing strategies reflect how concerned he is about
different consumer segments.
Figure 4: Equilibrium channel strategies
with manufacturer-owned Internet channel.
Figure 5: Equilibrium channel strategies with
retailer-owned Internet channel.
3.2 Retailer-owned Internet channel
In the second scenario, the Internet channel can only be operated by the retailer. The modified
sequence of events is as follows. 1) The retailer determines whether to introduce an Internet
channel; 2) The manufacturer offers the wholesale price to the retailer; 3) The retailer responds
by determining the retail margin for the physical channel and that for her Internet channel (if
available); and 4) The consumers decide which channel to purchase the products from. Note that
11

in this case, the manufacturer can only indirectly affect the consumers’ purchasing behaviors via
setting a single wholesale price.
By backward induction, the first step is to examine the consumers’ purchasing decisions. As
this step is similar to that in Section 3.1, we omit the details and simply summarize their collective
actions as the following demand functions. The demand in the physical channel Q is
⎧
1
⎪⎨ V [(1 − α)(V − p−p d
1−β 1
)], if p d ≤ β 1 p
Q =
1
V
⎪⎩
[(1 − α)(V − p)], if β 1p ≤ p d ≤ β 2 p ,
1
V [α( p d−p
β 2 −1 − p) + (1 − α)(V − p)], if p d ≥ β 2 p
and the demand on the Internet Q R d
is
1
⎧⎪ ⎨ V [α(V − p d
β 2
) + (1 − α)( p−p d
1−β 1
− p d
β 1
)], if p d ≤ β 1 p
Q R d = 1
V
⎪ [α(V − p d
β 2
)], if β 1 p ≤ p d ≤ β 2 p
⎩ 1
V [α(V − p d−p
β 2 −1 )], if p d ≥ β 2 p
.
Having characterized the effective demands for these channels, we can then return to the
retailer’s and the manufacturer’s strategies in two stages. In the next proposition, we characterize
the equilibrium strategies in this scenario, whose detailed derivations are given in the appendix.
Proposition 2. Suppose that only the retailer may introduce the Internet channel. There are two
possible equilibrium strategies:
• Channel separation strategy (CS-R): Internet shoppers are induced to purchase online, whereas
grocery shoppers buy in the physical channel;
• Exclusive online strategy (EO-R): Internet shoppers are induced to purchase online, and
grocery shoppers and the physical channel are abandoned.
Accordingly, the resulting equilibrium prices are:
Strategy w ∗ p ∗ p ∗ d
CS-R
EO-R
β 2 V
2[α+(1−α)β 2 ]
β 2 V
2
> V
V
2 + β 2 V
4[α+(1−α)β 2 ]
β 2 V β
2
+ 2 V
4[α+(1−α)β 2 ]
3β 2 V
4
The equilibrium payoffs and the feasibility conditions are:
Strategy π M π R Condition
CS-R
EO-R
β 2 V
8[α+(1−α)β 2 ]
αβ 2 V
8
[β 2 +4α(1−α)(β 2 −1) 2 ]V
16[α+(1−α)β 2 ]
α ≤ 1
β 2 −1
αβ 2 V
16
α ≥ 1
β 2 −1
12

Proposition 2 identifies two strategies for the retailer to differentiate the consumers based
on their heterogeneous preferences in the presence of retailer-owned Internet channel. When the
Internet shoppers are not very profitable (i.e., with a small population or when their average
valuation is not very high), the retailer will implement the natural channel separation strategy:
inducing the first consumer segment to purchase in the physical channel and the second consumer
segment to shop online. As aforementioned, this strategy facilitates the price discrimination through
different channels. When the Internet shoppers are relatively important, the retailer now instead
uses a niche targeting strategy. Incidentally, the equilibrium price under this strategy (EO-R)
indicates that the retailer effectively abandons the physical channel: as p ∗ > V , she sets a high
selling price so that only the Internet shoppers purchase in the Internet channel.
It is worth mentioning that unlike the case with the manufacturer-owned Internet channel,
here the retailer has no intention to implicitly split the consumers from the same segment, i.e., the
grocery encroachment strategy is no longer desirable. While the manufacturer intends to use his
Internet channel to subsidize the downside of the double marginalization problem, this initiative is
absent when the retailer coordinates the selling prices over different channels. We hereby highlight
this result as a corollary and provide a numerical illustration in Figure 5.
Corollary 2. Suppose that only the retailer can introduce the Internet channel. The exclusive
online strategy is more likely to be implemented when the Internet shoppers are rather important
(i.e., when α and β 2 are large). In addition, in equilibrium grocery shoppers never purchase online,
whereas Internet shoppers never go to the physical channel.
Incidentally, this niche targeting strategy in Corollary 2 can never emerge as an equilibrium
outcome with only the manufacturer-owned Internet channel. This is because compared with this
targeting strategy, the manufacturer also benefits from inducing some grocery shoppers to purchase
in the physical channel in the first scenario, even if he has to share the revenue with the retailer.
Thus, completely abandoning the physical channel is not preferable from the manufacturer’s perspective.
3.3 Both the manufacturer and the retailer can introduce Internet channels
Having articulated the benefits and consequences of introducing the Internet channel for the manufacturer
and the retailer, we now incorporate the possibility that both parties are able to operate
independent Internet channels. The sequence of events follows the above two subsections except
13

that at the beginning the manufacturer and the retailer determine simultaneously whether to introduce
an Internet channel. The possible equilibrium strategies are characterized in the following
proposition.
Proposition 3. When both the manufacturer and the retailer can sell the products through their
own Internet channels, there are four possible equilibrium strategies:
• Grocery encroachment strategy (GE-M): Only the high-valuation grocery shoppers buy in the
physical channel, and others purchase in the manufacturer-owned Internet channel.
• Channel separation strategy with Retailer’s Internet channel (CS-R): Internet shoppers are
induced to purchase in the retailer-owned Internet channel, whereas grocery shoppers buy in
the physical channel;
• Channel separation strategies (CS-M, CS’-M): Internet shoppers are induced to purchase
online, whereas grocery shoppers buy in the physical channel.
From Proposition 3, we observe that strategy EO-R is no longer sustainable. Recollect that
in the absence of manufacturer-owned Internet channel, the exclusive online (EO-R) strategy indicates
that the retailer may abandon the physical channel and set a high price to serve only those
Internet shoppers. When the manufacturer is also capable of operating his Internet channel, this
niche targeting strategy may ignite the manufacturer’s counteraction. Since the retailer attempts
to give up the physical channel, the manufacturer will certainly undercut the retailer’s price to
capture all the consumers. Pushing this idea further, the manufacturer can raise the wholesale
price to deactivate both the physical channel and the retailer’s Internet channel. To counteract the
retailer’s exclusive online strategy, the manufacturer can meticulously design the wholesale price
and operate his Internet channel to facilitate the maximum benefit of channel separation. This
provides an economic rationale for why the retailer always maintains her physical channel. In addition
to keeping her core competence (as the conventional wisdom), the retailer strategically uses
this physical channel to avoid the vindictive behavior from her supply chain partner.
Notably, Proposition 3 suggests that the manufacturer may willingly give up selling online, but
nevertheless his capability of operating the Internet channel still has a direct impact on the market
equilibrium. Thus, retaining this capability has a strategic value, as it allows the manufacturer to
counterbalance the retailer’s pricing power. This result is somewhat related to a recent industry
report by Brohan (2012), who explicitly mentions that most manufacturers that operate their
14

Internet channels do not really generate additional sales that live up to the market’s expectation.
As Brohan (2012) explains, this phenomenon occurs only to those manufacturers who rely on
their long-term retailer partners; it can therefore be regarded as a consequence of manufacturers’
attempts to avoid the channel conflict.
Figure 6: Equilibrium channel strategies in the full model.
Given the above discussions, a natural question is when these strategies emerge as the market
equilibria in different scenarios. While Proposition 3 lays out the precise conditions that identify
the optimal strategies among the three via routine algebra, we find it more illustrative to show
this graphically in Figure 6. From Figure 6, we observe that when the Internet shoppers are either
highly profitable (when α and β 2 are large) or fairly unimportant (when α and β 2 are small), the
manufacturer prefers to facilitate the channel separation either through his own Internet channel
or the retailer’s. In the intermediate region, however, the manufacturer intends to encroach the
grocery shoppers and steal the demand from the retailer’s physical channel. 2 To understand this
result, observe that when the Internet shoppers are highly profitable, the manufacturer certainly
prefers to go direct to capture this segment. Thus, using his Internet channel is the most effective
way to avoid double marginalization and materialize the benefit. At the other extreme, when the
Internet shoppers are fairly unimportant (compared to the grocery shoppers), the manufacturer’s
primary goal is to avoid channel conflict. In this case, it is in the manufacturer’s best interest
2 We choose to vary β 2 because the conditions that distinguish different regimes (strategies) all depend on β 2 .
Thus, through this one-dimensional change, we can conveniently illustrate all possible strategies in one figure for a
fixed set of other parameters. We have also conducted an alternative numerical experiment where we change β 1 and
β 2 simultaneously. We find that the effect of increasing β 1 is essentially the same as that of decreasing β 2.
15

to delegate both channels to the retailer. In the intermediate region, the manufacturer faces two
conflicting forces. Facilitating channel separation via his own Internet channel induces too much
competition from the retailer, whereas completely delegating to the retailer leaves a significant
portion of revenue to the retailer’s side. In such a scenario, the manufacturer sets a low price in his
Internet channel so as to attract some low-valuation grocery shoppers to purchase online (strategy
GE-M). This low-price strategy allows the manufacturer to steal the obscure market of grocery
shoppers at no cost of channel conflict.
4 Discussions
In this section, we consider some variants of our model characteristics. 3 To avoid repetition, we
will only highlight the primary differences and focus on the new implications that are absent in the
basic framework.
4.1 Retailer competition
In our basic model, we assume away the horizontal competition and study the bilateral monopoly
setting. However, in reality, the manufacturer typically sells through multiple retailers that compete
against each other. In such a scenario, there are multiple physical channels, and each retailer can
determine whether to introduce her own Internet channel. A natural question is therefore how the
equilibrium channel structure is influenced by the horizontal competition.
To address this question, we consider an extended model in which the manufacturer sells
through two independent retailers, indexed as 1 and 2. We allow both retailer (as well as the
manufacturer) to introduce their own Internet channels. The sequence of events proceeds as follows.
1) The manufacturer and the retailers simultaneously determine whether to introduce an Internet
channel; 2) The manufacturer offers the wholesale price to the retailers; 3) The manufacturer and
the retailers simultaneously determine the selling prices of their own channels (if available); and 4)
The consumers decide which channel to purchase the products from. Figure 7 presents a graphic
illustration of the possible channel structure.
As in Section 3, we can also examine the consumers’ purchasing decisions and express them in
the form of effective demands for different channels. Afterwards, we then use backward induction
to characterize the equilibrium strategies of the manufacturer and the retailers. These detailed
3 We thank an anonymous reviewer for suggesting these extensions.
16

Figure 7: Channel structure under retailer competition.
derivations are given in the appendix, and we summarize the main findings below.
Proposition 4. With retailer competition, in any equilibrium channel structure, exactly two supply
chain parties introduce their Internet channels. Moreover, given any primitive parameter combination,
it is always an equilibrium that the manufacturer abandons his Internet channel and both
retailers introduce their own.
Figure 8: Equilibrium channel strategies with retailer competition.
Proposition 4 shows that retailer competition can significantly influence the equilibrium channel
structure, and it gives rise to various kinds of channel structures we observe in practice. A
notable observation is that even if the retailers are perfectly competitive, the manufacturer intends
to induce them to both introduce the Internet channels, and in equilibrium both retailers will-
17

ingly do so. To elaborate the intuition behind this, recollect that the economic rationale for the
manufacturer to introduce his own Internet channel is to fight against the double marginalization
problem. Thus, this direct channel allows the manufacturer to bypass the retailer’s mark-up and
at the same time induces the retailer to reduce the selling price in the physical channel. In the
presence of retailer competition, however, this direct channel is no longer required. Specifically, the
intense competition between the retailers effectively eliminates the double marginalization problem
and the price competition automatically drives down the selling prices in the physical channels. In
light of this, the manufacturer does not need to go through the hassle of opening his own Internet
channel. This might explain why in reality some leading manufacturers (such as Acer, Colgate,
Gillette, Heinz, Kellogg’s, and Tylenol) do not offer their Internet channels.
On the other hand, our results also suggest that even if the retailers are a priori symmetric,
asymmetric channel structures may emerge as a stable market equilibrium. This possibility prevails
even if these retailers are selling the same products and compete head-to-head for the end consumers.
The primary reason is that when the opponent has already opened the Internet channel, introducing
another one does not mitigate the competition and therefore is not beneficial for the retailer. Thus,
we document the possibility of asymmetric equilibrium channel structure. Our analysis provides a
partial answer to the prevalent phenomenon that a significant portion of retailers focus exclusively
on the physical channels in this Internet era. As aforementioned in the introduction, this applies
to the following retailers: 7-eleven, Carrefour, Pricesmart, Tween Brands, Citi Trends, Dress Barn,
Ross Stores, Spartan Stores, Duckwall-Alco, TJX inc., Family Dollar, Collective Brands, Watsons,
Pantry, Retail Enterprises, Ingles Markets, and RT-MART.
Finally, we offer a graphic illustration of when these channel structures may emerge as the
market equilibrium in Figure 8. From Figure 8, we observe that the manufacturer is willing to give
up his Internet channel only when the Internet shoppers are relatively less important (when α and
β 2 are both small). On the other hand, the aforementioned asymmetric channel structures appear
in various scenarios. The economic forces have been elaborated in Section 3.3, as the manufacturer’s
concern about the consequence of retailers’ counteractions is more pronounced with a less important
segment of Internet shoppers. Notably, even if the double marginalization problem in the physical
channels is largely eliminated by the horizontal competition, the channel conflict concern remains
salient.
18

4.2 Selling through an e-tailer
Figure 9: Channel structure with an e-tailer.
We now consider the scenario wherein the manufacturer sells through an online retailer (e.g., Amazon).
In this scenario, the modified sequence of events becomes the following. 1) The manufacturer
determines the wholesale prices w and w d for the physical and Internet channels, respectively. 2)
The retailer and e-tailer determine their selling prices p and p d simultaneously. 3) Consumers make
their purchasing decisions. When both the manufacturer and the retailer can introduce Internet
channels, in stage 2) the retailer also determines her online selling price.
The primary departure from our basic framework is that both online channels are in a sense
“indirect:” one operated by the retailer, whereas the other operated by the e-tailer. Figure 9
presents a graphic illustration of the channel structure in this modified setting. As we verify in the
appendix, most of the equilibrium properties in the basic framework are preserved. Nonetheless, a
new equilibrium channel strategy may arise, as highlighted in the following proposition.
Proposition 5. Suppose that the manufacturer sells through an e-tailer and a dual-channel retailer.
In equilibrium, the manufacturer may induce Internet shoppers to purchase through the retailer’s
physical channel.
Proposition 5 suggests that the manufacturer now has a stronger incentive to sell through the
physical channel. In our basic framework, the manufacturer may encroach the grocery shoppers
via his own Internet channel (the GE-M strategy). This is because the direct channel effectively
bypasses the retailer’s mark-up. Nevertheless, when the Internet channel is facilitated by the e-
19

tailer, selling online does not allow the manufacturer to escape from the double marginalization
problem. This substantially changes the manufacturer’s channel management strategy, as now the
manufacturer captures some Internet shoppers via the physical channel. The retailer’s physical
channel becomes appealing (from the manufacturer’s viewpoint) because the retailer intends to
set the margin low so as to attract grocery shoppers. Consequently, the double marginalization
problem is less severe. In contrast, the e-tailer targets Internet shoppers who have high valuations
upon online shopping. Thus, the e-tailer is more inclined to set a high margin. We have also
verified via numerical experiments that such a new strategy indeed emerges as an equilibrium in
some situations. We omit the details here to avoid repetition.
5 Conclusions
In this paper, we examine the rationale for introducing the Internet channels of the manufacturer
and the retailer. We identify three equilibrium strategies that feature channel separation, consumer
encroachment, and exclusive selling. When the Internet shoppers are either highly profitable or
fairly unimportant, the manufacturer prefers to facilitate the channel separation either through
his own Internet channel or the retailer’s. In the intermediate region, however, the manufacturer
intends to encroach the grocery shoppers and steal the demand from the retailer’s physical channel.
With horizontal competition between the retailers, a priori symmetric retailers may adopt different
channel strategies as a stable market equilibrium. Furthermore, the manufacturer may willingly
give up his Internet channel and leverage on the retailer competition. When the manufacturer
sells through an online retailer, he may induce Internet shoppers to purchase through the retailer’s
physical channel. Our results provide an economic rationale for the apparent discrepancy among
various market phenomena in the Internet channel adoptions.
Our analysis reveals several economic rationales for introducing/abandoning the Internet channels.
Naturally, there are other reasons why the retailers’ Internet channels exist, such as one-stop
shopping of multiple products, loyalty programs, and etc. While these issues have their own merits
and perhaps warrant a separate analysis, it seems rather difficult to incorporate all the possible
ingredients in a single model. Nevertheless, one-stop shopping and loyalty programs are two crucial
components for the success of prevalent retailer-owned Internet channels, and they remain research
priority. In addition, while our model excludes all the possible restrictions on the pricing strategies,
there are situations in which the manufacturer may be forced to use the same (retail) price in the
Internet channel as the wholesale/retail price in the physical channel. As aforementioned, the retail
20

price in the manufacturer’s Internet channel may be necessarily higher than the wholesale price
in the physical channel in order to eliminate the retailer’s arbitrage opportunity (Chiang et al.
(2003)). The (retail) prices in different channels may be set equal to alleviate the channel conflict
(Cattani et al. (2006)). These restrictions on the pricing strategy in the Internet channel definitely
affect the manufacturer’s/ retailer’s incentive to introduce the Internet channel.
Acknowledgement
We thank Vishal Gaur (the department editor) and the review team for the detailed comments
and many valuable suggestions that have significantly improved the quality of the paper. We have
also benefited from the discussions with Gangshu Cai, Jane Gu, Daniel Lin, Olga Perdikaki, Jiong
Sun, Chi-Cheng Wu, Wenqiang Xiao, and Xuying Zhao. Hsiao acknowledges the financial support
by the National Science Council in Taiwan (NSC 98-2410-H-005-005). All remaining errors are our
own.
References
Alba, J., J. Lynch, B. Weitz, C. Janiszewski, R. Lutz, A. Sawyer, and S. Wood (1997). Interactive
home shopping: Consumer, retailer, and manufacturer incentives to participate in electronic
marketplaces. Journal of Marketing 61 (3), 38–53.
Balasubramanian, S. (1998). Mail versus mall: A strategic analysis of competition between direct
marketers and conventional retailers. Marketing Science 17 (3), 181–195.
Bernstein, F., J. Song, and X. Zheng (2008). Bricks-and-mortar vs.clicks-and-mortar: An equilibrium
analysis. European Journal of Operational Research 187 (3), 671–690.
Brohan, M. (2012). Top 500 manufacturers can do more to run at full capacity
online: Channel conflict remains an issue. May 11, 2012, InterentRetailer.com;
http://www.internetretailer.com/2012/05/11/top-500-brand-manufacturers-can-domore-online
(retrived 12/02/2012).
Cattani, K., H. Heese, W. Gilland, and J. Swaminathan (2006). Boiling frogs: Pricing strategies for
a manufacturer adding a direct channel that competes with the traditional channel. Production
and Operations Management 15 (1), 40–56.
21

Cattani, K., O. Perdikaki, and A. Marucheck (2007). The perishability of online grocers. Decision
Sciences 38 (2), 329–355.
Chiang, W., D. Chhajed, and J. Hess (2003). Direct marketing, indirect profits: A strategic analysis
of dual-channel supply-chain design. Management Science 49 (1), 1–20.
Druehl, C. and E. Porteus (2005). Online versus offline price competition: Market outcomes and
the effect of internet shopping penetration. Working Paper. University of Maryland.
Fudenberg, D. and J. Tirole (1991). Game Theory. Cambridge, Massachussetts: The MIT Press.
Hsiao, L. and Y.-J. Chen (2012). The perils of selling online: Manufacturer competition, channel
conflict, and consumer preferences. Marketing Letters. Forthcoming.
Kacen, J., J. Hess, and W. Chiang (2001). Shoppers attitudes toward online and traditional grocery
stores. Working paper, University of Illinois, Champaign, IL.
Kumar, N. and R. Ruan (2006). On manufacturers complementing the traditional retail channel
with a direct online channel. Quantitative Marketing and Economics 4 (3), 289–323.
Lal, R. and M. Sarvary (1999). When and how is the internet likely to decrease price competition?
Marketing Science 18 (4), 485–503.
Liang, T. and J. Huang (1998). An empirical study on consumer acceptance of products in electronic
markets: A transaction cost model. Decision Support Systems 24 (1), 29–43.
Peterson, R., S. Balasubramanian, and B. Bronnenberg (1997). Exploring the implications of the
internet for consumer marketing. Journal of the Academy of Marketing Science 25 (4), 329–346.
Tsay, A. and N. Agrawal (2004). Channel conflict and coordination in the e-commerce age. Production
and Operations Management 13 (1), 93–110.
22

Technical appendix for “Strategic motive of introducing Internet channels in
a supply chain”
In this appendix, we provide the detailed derivations of the equilibrium analysis. We find
it convenient to organize the appendix based on the scenarios rather than the propositions and
corollaries. Thus, in the sequel we shall start with our basic framework with bilateral monopolies,
and then examine the cases with retailer competition and e-tailer. In what follows, we will apply the
first-order conditions to obtain the interior solutions in various scenarios, and then verify whether
these interior solutions are indeed feasible. We will also investigate all the possible corner solutions.
Regarding the interior solutions, the second-order conditions all hold automatically as (most of) the
expected profit expressions are quadratically concave. For brevity we omit the detailed verifications
of the second-order conditions.
A
Basic framework: bilateral monopolies
In our basic framework, we divide our analysis into the following four subgames: (I) Neither party
can introduce the Internet channel; (II) Only the manufacturer can introduce the Internet channel;
(III) Only the retailer can introduce the Internet channel; and (IV) Both parties can introduce the
Internet channels.
A.1 Neither party can introduce the Internet channel
In this case, the only transactions take place in the physical channel. By backward induction, we
first start with the consumers’ choices, and then return to the retailer’s pricing decision. Finally,
we examine the manufacturer’s optimal wholesale price. Given the selling price p, a consumer buys
the product if and only if v − p ≥ 0. Thus, the retailer’s profit is π R = (p − w) 1 V
(V − p). From
the first-order conditions, we have p ∗ = V +w
2
and Q ∗ = V −w
2V
. This gives rise to the manufacturer’s
profit: π M = w V −w
2V . The first-order condition then leads to the optimal wholesale price w∗ = V 2 .
In sum, when neither party introduces the Internet channel,
w ∗ = V 2 , p∗ = 3V 4 , Q∗ = 1 4 , π M = V 8 , and π R = V 16 .
23

A.2 Only the manufacturer can introduce the Internet channel
As the consumers’ purchasing decisions have been discussed in the main text (via the demand
functions Q and Q M d
), below we characterize the retailer’s optimal pricing decisions. Following this,
we then investigate the manufacturer’s optimal decisions on the prices and the channel structure.
A.2.1
Retailer’s optimal strategy
Because the retailer does not introduce the Internet channel, her profit is π R = (p−w)Q. If w > V ,
it is obvious that the retailer does not sell any products; thus, π R = 0. Therefore, the following
discussions focus on the case in which 0 ≤ w ≤ V and 0 ≤ w d ≤ β 2 V .
Given w and w d , the
retailer has three pricing strategies, depending on how her selling price compares with that in the
manufacturer-owned Internet channel: (i) w d ≤ β 1 p, (ii) β 1 p ≤ w d ≤ β 2 p, and (iii) w d ≥ β 2 p.
First, consider the case (i) w d ≤ β 1 p. Under this strategy,
π R = (p − w) 1 V [(1 − α)(V − p − w d
1 − β 1
)].
From the first-order condition, we have p ∗ = (1−β 1)V +w+w d
2
. Note that w d ≤ β 1 p ∗ if and only if
w d ≤ β 1(1−β 1 )V +β 1 w
2−β 1
. Under this condition, p ∗ ≤ V also holds. Second, in the case (ii) β 1 p ≤ w d ≤
β 2 p,
π R = (p − w) 1 [(1 − α)(V − p)].
V
From the first-order condition, we have p ∗ = V + w . β 1 p ∗ ≤ w d ≤ β 2 p ∗ if and only if β 1(V + w)
≤
2
2
w d ≤ β 2(V + w)
.
2
Third, in the case (iii) w d ≥ β 2 p,
π R = (p − w) 1 V [α(w d − p
β 2 − 1
− p) + (1 − α)(V − p)].
It is verifiable that this strategy is dominated from the manufacturer’s perspective. Thus, while
analyzing the equilibrium strategies, it suffices to focus on cases (i) and (ii).
A.2.2
Manufacturer’s optimal strategy
Next, we return to the manufacturer’s decision making in the first stage.
We shall discuss the
optimal pricing strategies case by case, depending on how the wholesale price w and the selling
24

price w d in the Internet channel fare. Note that
β 1 (1 − β 1 )V + β 1 w
≤ β 1(V + w)
2 − β 1 2
≤ β 2(V + w)
.
2
Therefore, the manufacturer has three strategies: 1) GE-M: w d ≤ β 1(1−β 1 )V +β 1 w
; 2) CS’-M:
β 1 (1−β 1 )V +β 1 w
2−β 1
≤ w d ≤ β 1(V +w)
2
; 3) CS-M: β 1(V +w)
2
≤ w d ≤ β 2(V +w)
2
.
First, under GE-M, p ∗ = (1−β 1)V +w+w d
2
and
2−β 1
π M = w 1 V [(1 − α)(V − p∗ − w d
1 − β 1
)] + w d
1
V [α(V − w d
β 2
) + (1 − α)( p∗ − w d
1 − β 1
− w d
β 1
)].
From the first-order conditions, we have w ∗ = [β 2 − α(1 − β 1 )(β 2 − β 1 )]V
and wd ∗ 2(αβ 1 + β 2 − αβ 2 )
= β 1 β 2 V
2(αβ 1 + β 2 − αβ 2 ) .
Note that wd ∗ ≤ β 1(1 − β 1 )V + β 1 w ∗
β 2
if and only if α ≤
2 − β 1 3(β 2 − β 1 ) . In addition, w∗ ≤ V if and only
β 2
if α ≤
(1 + β 1 )(β 2 − β 1 ) . Thus, w∗ d ≤ β 1(1 − β 1 )V + β 1 w ∗
implies w ∗ ≤ V . Under this strategy,
2 − β 1
p = [(3 − β 1)β 2 − 3α(1 − β 1 )(β 2 − β 1 )]V
4[αβ 1 + β 2 − αβ 2 ]
, Q = 1 − α
4
, Q M d = 1 + α ,
4
π M = [αβ 1(1 − α)(1 − β 1 ) + β 2 + β 1 β 2 − αβ 2 (2 − α)(1 − β 1 )]V
8(αβ 1 + β 2 − αβ 2 )
Second, under CS’-M, p ∗ = w d
β 1
and
π M = w 1 V [(1 − α)(V − w d
β 1
)] + w d
1
V [α(V − w d
β 2
)].
, π R = (1 − α)(1 − β 1)V
16
The above formula suggests that the manufacturer would like to make w as large as possible. Thus,
at optimality w ∗ satisfies w d = β 1(1 − β 1 )V + β 1 w ∗
. This implies that as long as Strategy GE-M is
2 − β 1
a feasible (interior) solution, Strategy CS’-M is dominated. Substituting w d = β 1(1−β 1 )V +β 1 w
2−β 1
in π M ,
we obtain from the first-order condition that w ∗ = [(2 − β 1)β 2 − α(1 − β 1 )(2β1 2 + 2β 2 − β 1 β 2 )]V
2[αβ1 2 + (1 − α)(2 − β ;
1)β 2 ]
accordingly,
π M = [β 2 + α 2 (1 − β 1 )(4β 2 1 + β 2 − 5β 1 β 2 ) − 2α(1 − β 1 )(2β 2 1 + β 2 − 2β 1 β 2 )]V
4[(2 − β 1 )β 2 + α(β 2 1 − 2β 2 + β 1 β 2 )]
Third, under CS-M, p ∗ = V +w
2
and
π M = w 1 V [(1 − α)(V − p∗ )] + w d
1
V [α(V − w d
β 2
)].
From the first-order conditions, we have w ∗ = V 2
and w∗ d = β 2V
2 . Obviously, w∗ < wd ∗ < β 2(V +w ∗ )
2
.
Note that β 1(V +w ∗ )
2
≤ wd ∗ if and only if β 2 ≥ 3 2 β 1. Accordingly, p = 3V 4 , Q = 1−α
4 , QM d
= α 2 ,
25
.
.

π M = (1−α+2αβ 2)V
8
, and π R = (1−α)V
16
. Finally, if w > V , π M = w d
1
V [α(V − w d
β 2
)].
optimality w ∗ d = β 2V
2 , and π M = αβ 2V
4
< (1 − α + 2αβ 2)V
8
Thus, at
. It is therefore a dominated strategy.
We can then compare the manufacturer’s payoffs under three strategies and determine the
optimal strategy. The algebra is tedious and the table in the proposition summarizes the equilibrium
outcomes in this scenario.
A.3 Only the retailer can introduce the Internet channel
In the main text, we have discussed the consumers’ purchasing decisions. Below, we characterize
the equilibrium behaviors in two stages.
A.3.1
Retailer’s optimal strategy
When 0 ≤ w ≤ V , the retailer’s profit is π R = (p − w)Q + (p d − w)Q R d ; when V ≤ w ≤ β 2V ,
π R = (p d − w) 1 V [α(V − p d
β 2
)]. We first discuss the case 0 ≤ w ≤ V , and then consider the case
V ≤ w ≤ β 2 V .
Suppose that 0 ≤ w ≤ V . First, when p d ≤ β 1 p,
π R = (p − w) 1 V [(1 − α)(V − p − p d
1 − β 1
)] + (p d − w) 1 V [α(V − p d
β 2
) + (1 − α)( p − p d
1 − β 1
− p d
β 1
)].
From the first-order conditions, we have p ∗ = (1 − β 1){αβ 1 (β 2 − β 1 )V + [αβ 1 + (1 − α)β 2 ]w}
and
2[αβ 1 + (1 − α)β 2 ]
p ∗ d = β 1β 2 V + [αβ 1 + (1 − α)β 2 ]w
. Note that p ∗ d
2[αβ 1 + (1 − α)β 2 ]
≥ β 1p ∗ , and thus p d ≤ β 1 p is not an optimal
strategy. Second, when β 1 p ≤ p d ≤ β 2 p,
π R = (p − w) 1 V [(1 − α)(V − p)] + (p d − w) 1 V [α(V − p d
β 2
)].
From the first-order conditions, we have p ∗ = V +w
2
and p ∗ d = β 2V +w
2
. Note that β 1 p ∗ ≤ p ∗ d ≤ β 2p ∗ .
Given p ∗ and p ∗ d , we have Q = 1 V −w
V
[(1 − α)
2
] and Q R d = 1 V [α β 2V −w
2β 2
]. Third, when p d ≥ β 2 p,
π R = (p − w) 1 V [α( p d − p
β 2 − 1 − p) + (1 − α)(V − p)] + (p d − w) 1 V [α(V − p d − p
β 2 − 1 )].
From the first-order conditions, we have p ∗ = V +w
2
and p ∗ d = β 2V +w
2
. Note that p ∗ d ≤ β 2p ∗ , and
thus p d ≥ β 2 p is not the optimal strategy.
On the other hand, when V ≤ w ≤ β 2 V , the retailer’s profit is π R = (p d − w) 1 V [α(V − p d
β 2
)].
From the first-order condition, we have p ∗ d = β 2V +w
2
and thus Q R d = 1 V [α β 2V −w
2β 2
].
26

A.3.2
Manufacturer’s optimal strategy
The manufacturer has two strategies: 1) CS-R: 0 ≤ w ≤ V ; 2) EO: V ≤ w ≤ β 2 V . Next, we
analyze the manufacturer’s optimal w. Under CS-R, the manufacturer’s profit is
π M = w(Q + Q R d ) = w V
From the first-order condition, we have w ∗ =
[(1 − α)V
− w
2
+ α β 2V − w
2β 2
].
β 2 V
2[α + (1 − α)β 2 ] and thus π M =
β 2 V
8[α+(1−α)β 2 ] .
Under EO-R, the manufacturer’s profit is π M = w V [α β 2V −w
2β 2
]. From the first-order condition,
we have w ∗ = β 2V
2
and thus π M = αβ 2V
β 2 V
8
. Note that
2[α + (1 − α)β 2 ] < β 2V
. Therefore, when
2
β 2 V
2
≤ V (i.e. β 2 ≤ 2), w ∗ =
w ∗ = β 2V
2 . When β 2 V
β 2 V
If
≥ αβ 2V
8[α + (1 − α)β 2 ] 8
β 2 V
2[α + (1 − α)β 2 ] . When β 2 V
2[α+(1−α)β 2 ]
≥ V (i.e. α ≥
2[α+(1−α)β 2 ]
≤ V ≤ β 2V
2
(i.e. β 2 ≥ 2 and α ≤ β 2
(i.e. α ≤ 1
β 2 −1 ), then w∗ =
2(β 2 −1)
β 2
2(β 2 −1) ),
), there are two cases.
β 2 V
2[α+(1−α)β 2 ]; on the other hand, if
αβ 2 V β 2 V
≥
(i.e. α ≥ 1
8 8[α + (1 − α)β 2 ]
β 2 −1
), then w∗ = β 2V
2
. We can then compare the two
strategies and the equilibrium outcomes are summarized in the table in the proposition.
A.4 Both parties can introduce the Internet channels
Finally, we consider the scenario in which both parties have the capabilities of operating their
Internet channels. As the derivations are complicated, we first start with some separate cases and
examine the manufacturer’s optimal strategies in these four different regions. Following this, we
then compare the manufacturer’s payoffs across four regions to characterize the equilibrium channel
structure in every instance.
A.4.1
Manufacturer’s optimal pricing and channel strategies
Given the manufacturer’s strategies w and w d , we can divide our analysis into the following four
cases: 1.1) 0 ≤ w ≤ V and w d ≥ β 2V +w
2
; 1.2) 0 ≤ w ≤ V and w ≤ w d ≤ β 2V +w
2
; 1.3) 0 ≤ w ≤ V
and w d ≤ w, and 1.4) w > V and 0 ≤ w d ≤ β 2 V .
1) 0 ≤ w ≤ V and w d ≥ β 2V +w
2
:
When the price w d is sufficiently large (w d > β 2V +w
2
), the game is equivalent to the case
without the manufacturer’s Internet channel from the retailer’s viewpoint as the manufacturer’s
27

Internet channel is not competitive. Thus, p ∗ = V +w
2
, p ∗ d = β 2V +w
2
, Q = 1 V −w
V
[(1 − α)
2
], and
Q R d = 1 V [α β 2V −w
2β 2
]. Accordingly, π M = w(Q + Q R d ) = w V −w
V
[(1 − α)
2
+ α β 2V −w
2β 2
].
2) 0 ≤ w ≤ V and w ≤ w d ≤ β 2V +w
2
:
From the above discussions, in this case the manufacturer’s selling price w d sets a limit on the
retailer’s selling price p d . In equilibrium, p ∗ d = w d, and all the Internet shoppers purchase from
the retailer’s Internet channel (if this were not the case, the retailer could simply lower the price
p d to attract all the Internet shoppers). Since p ∗ d = w d, the reduction of w d mitigates the double
marginalization problem in the physical channel as well. In the sequel, w ∗ d
detailed proof.
3) 0 ≤ w ≤ V and w d ≤ w :
In this case, p d
= w. We omit the
< w is an obviously dominated strategy for the retailer, because all the
Internet shoppers will purchase in the manufacturer’s Internet channel. In addition, p < w is also
a dominated strategy. Thus, it is impossible to see w d ≥ β 2 p. The demand in the physical channel
Q is
Q =
and the demand on the Internet Q M d
{ 1
V [(1 − α)(V − p−w d
1−β 1
)], if w d ≤ β 1 p
1
V [(1 − α)(V − p)], if β 1p ≤ w d ≤ w ,
is
Q M d
{ 1 = V [α(V − w d
β 2
) + (1 − α)( p−w d
1−β 1
− w d
β 1
)], if w d ≤ β 1 p
1
V [α(V − w d
β 2
)], if β 1 p ≤ w d ≤ w
.
We can then examine possible equilibria in two cases. From the above demand functions,
we shall divide our analysis into two cases: 1) w d ≤ β 1 w and 2) β 1 w ≤ w d ≤ w because the
manufacturer’s pricing strategy will influence the retailer’s counteraction. The algebra is tedious;
by and large, we compare across different scenarios to determine their optimal strategies. The table
below summarizes π M , π R and feasibility conditions of the three strategies when β 1 w ≤ w d ≤ w; a
similar table can be constructed for w d ≤ β 1 w.
28

Strategy π M and π R Feasibility Conditions
GE-M
CS’-M π M =
CS”-M
π M = [αβ 1(1−α)(1−β 1 )+β 2 +β 1 β 2 −αβ 2 (2−α)(1−β 1 )]V
8(αβ 1 +β 2 −αβ 2 )
π R = (1−α)(1−β 1)V
⎧
⎪⎨
⎪⎩
16
[β 2 + α 2 (1 − β 1 )(4β 2 1 + β 2 − 5β 1 β 2 )
−2α(1 − β 1 )(2β 2 1 + β 2 − 2β 1 β 2 )]V
4[(2−β 1 )β 2 +α(β 2 1 −2β 2+β 1 β 2 )]
π R = (1−α)(1−β 1)[β 2 +α(2β 2 1 −β 2−β 1 β 2 )]V
4[(2−β 1 )β 2 +α(β 2 1 −2β 2+β 1 β 2 )] 2
π M =
(1+α)2 β 2 V
8(2α+β 2 −αβ 2 ) − f
π R = (1−α)(4α+β 2−3αβ 2 ) 2 V
16(2α+β 2 −αβ 2 )
− f
⎫
⎪⎬
⎪⎭
− f
α ≤
α ≥
β 2
3(β 2 −β 1 )
β 2
3(β 2 −β 1 )
(β 2 + β 1 β 2 − 2β 2 1 )α ≤ β 2
(2β 2 + β 1 β 2 − 4β 1 )α ≥
(3β 1 − 2)β 2
(3β 2 − 4)α ≤ β 2
4) w > V and 0 ≤ w d ≤ β 2 V
If w > V , π M = w d
1
V [α(V − w d
β 2
)]. Thus, w ∗ d = β 2V
2 , and then π M = αβ 2V
4
. It is the strategy
EO-M.
5) Comparison across the first four regions:
From the above analysis, we find that when α ≤
is GE-M, CS”-M, or EO-M. When α ≥
β 2
3(β 2 −β 1 )
β 2
3(β 2 −β 1 ), the manufacturer’s optimal strategy
, his optimal strategy lies between CS’-M, CS”-M,
or EO-M. Thus, we can simply compare the payoffs across the regions to obtain the manufacturer’s
optimal strategy. We omit the tedious calculations here.
A.4.2
Equilibrium channel structure
We now consider the equilibrium channel structure.
For ease of exposition, we use N and I to
represent their channel choices, where N corresponds to “no Internet channel,” and I corresponds
to “introduce the Internet channel.” We further use (I,N) to represent the subgame in which the
manufacturer introduces his Internet channel (the first argument), and the retailer decides not to
do so (the second argument). Likewise, we use (I,I), (N,I), and (N,N) to indicate other channel
structures. Recall that f denotes the manufacturer’s operating cost for the Internet channel, where
0 < f < αβ 2V
8
. The retailer’s operating cost is normalized to zero.
We first show that (N,N) is not an equilibrium. Given that the manufacturer does not introduce
the Internet channel, if the retailer also abandons the Internet channel, she obtains the profit
π R = V 16 . If she introduces her Internet channel, π R = [β 2 + 4α(1 − α)(β 2 − 1) 2 ]V
if α ≤ 1
16[α + (1 − α)β 2 ]
β 2 −1 , and
π R = αβ 2V
16
if α ≥ 1
β 2 −1 . Comparing the profits, we obtain that [β 2+4α(1−α)(β 2 −1) 2 ]V
16[α+(1−α)β 2 ]
≥ V 16 implies
29

β 2 +4(1−α)(β 2 −1) 2 ≥ 1, which always holds after routine algebra. In addition, αβ 2V
16
≥ V 16 implies
αβ 2 ≥ 1, which is satisfied when α ≥ 1
β 2 −1
. Thus, (N,N) is never an equilibrium.
Next, we prove that (I,I) is not an equilibrium either. Given that the manufacturer introduces
the Internet channel, if the retailer also does so, the possible equilibrium is GE-M, CS”-
M, CS”-M or EO-M. First, if GE-M is the equilibrium strategy, then the retailer obtains the
payoff π R = (1−α)(1−β 1)V
16
. Nevertheless, if she abandons her Internet channel, her payoff becomes
either π R = (1−α)(1−β 1)V
16
(GE-M) or π R = (1−α)V
16
(CS-M). In both cases, the retailer has
an incentive to deviate. Second, if the equilibrium strategy is CS’-M, then the retailer obtains
π R = (1 − α)(1 − β 1)[β 2 + α(2β1 2 − β 2 − β 1 β 2 )]V
4[(2 − β 1 )β 2 + α(β1 2 − 2β 2 + β 1 β 2 )] 2 . Abandoning the Internet channel, she obtains
either π R = (1 − α)(1 − β 1)[β 2 + α(2β1 2 − β 2 − β 1 β 2 )]V
4[(2 − β 1 )β 2 + α(β1 2 − 2β 2 + β 1 β 2 )] 2 (CS’-M) or π R = (1−α)V
16
(CS-M), which
dominates CS’-M.
Third, if the equilibrium strategy is CS”-M (a necessary condition is α(2β 2 − 3) ≤ 1), then
the retailer’s payoff is π R = (1 − α)(4α + β 2 − 3αβ 2 ) 2 V
. If instead the retailer abandons the
16(2α + β 2 − αβ 2 )
Internet channel, the equilibrium must be CS-M (because the manufacturer obtains a strictly
higher payoff under CS-M than under CS”-M). In such a scenario, the retailer’s payoff is π R =
(1−α)V (1 − α)V
16
. Since − (1 − α)(4α + β 2 − 3αβ 2 ) 2 V
= α(1 − α)(β 2 − 1)(3α + β 2 − 2αβ 2 )V
16 16(2α + β 2 − αβ 2 )
4(2α + β 2 − αβ 2 ) 2 > 0
(as α(2β 2 − 3) ≤ 1 implies α(2β 2 − 3) ≤ β 2 ), we identify a profitable deviation for the retailer.
Finally, if EO-M is the equilibrium, the retailer obtains a null payoff π R = 0. This is certainly
suboptimal because by abandoning the Internet channel she obtains at least some positive payoff.
In sum, (I,I) can never be sustained as an equilibrium. The table in the proposition summarizes
the equilibrium channel structures in different scenarios.
B
Retailer competition
Since each supply chain party can decide whether to introduce the Internet channel, there are
eight possible subgames. In the first stage, we examine the equilibrium pricing strategies in each
subgame. In the second stage, we then examine the equilibrium channel structure.
B.1 Equilibrium pricing strategies
We again adopt the same notation N and I to represent their channel choices. We further use
(I,N,I) to represent the subgame in which the manufacturer introduces his Internet channel (the
30

first argument), retailer 1 decides not to do so (N), and retailer 2 introduces her Internet channel
as well (the last argument). Likewise, we use the triples to indicate other channel structures. It is
readily observable that (N,I,N) and (N,N,I) are symmetric, and (I,I,N) and (I,N,I) are symmetric.
Thus, in the sequel we only discuss the former two cases, which leaves us with six subgames in
total. Note that in evaluating the equilibrium pricing strategies, the manufacturer’s operating cost
has been sunk and thus does not factor into these subgame derivations.
B.1.1
Scenario (N,N,N)
In the absence of Internet channels, the retailers compete head-to-head in their physical channels.
Thus, given the manufacturer’s wholesale price w, the equilibrium selling prices are p 1 = p 2 = w.
In accordance, a consumer buys the product if and only if v − w ≥ 0.
This gives rise to the
manufacturer’s expected profit π M = w 1 V (V −w). From the first-order conditions, we have w∗ = V 2
and Q ∗ = 1 2 . Therefore, π M = V 4 . To summarize, in this subgame, w∗ = p ∗ 1 = p∗ 2 = V 2 , Q∗ = 1 2 ,
π M = V 4 and π R1 = π R2 = 0.
B.1.2
Scenario (N,I,N)
Now suppose that only retailer 1 introduces her Internet channel. We again obtain that in the
physical channels the equilibrium selling prices are p 1 = p 2 = w. To examine the manufacturer’s
optimal wholesale price, we divide our analysis into two cases: 1) 0 ≤ w ≤ V and 2) V < w ≤ β 2 V .
Case A. 0 ≤ w ≤ V :
Obviously, p 1d < w is a dominated strategy for retailer 1 as it generates no sales. Thus, we
ignore the case p 1d ≤ β 1 w. The demand in the physical channel Q is
{ 1
V
Q =
[(1 − α)(V − w)], if w ≤ p 1d ≤ β 2 w
1
V [α( p 1d−w
β 2 −1 − w) + (1 − α)(V − w)], if β 2w ≤ p 1d ≤ β 2 V ,
and the demand on the Internet Q d is
{ 1
V
Q d =
[α(V − p 1d
β 2
)], if w ≤ p 1d ≤ β 2 w
1
V [α(V − p 1d−w
β 2 −1 )], if β 2w ≤ p 1d ≤ β 2 V .
Based on the above demands, let us consider the optimal pricing strategy p ∗ 1d
First, when w ≤ p 1d ≤ β 2 w,
for retailer 1.
π R1 = (p 1d − w)Q d = (p 1d − w) 1 V [α(V − p 1d
β 2
)].
31

Applying the first-order conditions, we have p ∗ 1d = β 2V + w
. Note that p ∗ 1d
≥ w always holds, and
2
p ∗ 1d ≤ β 2w if and only if w ≥ . Thus, we obtain the equilibrium payoffs:
β 2V
2β 2 −1
π R1 = α(β 2V − w) 2
, and π M = w 1 4β 2 V
V [(1 − α)(V − w) + α(V − β 2V + w
)].
2β 2
We can do similar calculations for the case p 1d ≥ β 2 w.
Finally, we can characterize the manufacturer’s
optimal wholesale price w ∗ based on the above derivations.
here.
Case B. V < w ≤ β 2 V
The algebra is omitted
In this case no consumer prefers to purchase in the physical channel because the wholesale price
and subsequently the selling prices are too high. Thus, π R1 = (p 1d −w)Q d = (p 1d −w) 1 V [α(V − p 1d
β 2
)].
Following the first-order conditions, we have p ∗ 1d = β 2V +w
2
. Thus, π M = w 1 V [α(V − β 2V +w
2β 2
)]. This
gives rise to w ∗ = β 2V
2 . Note that w∗ > V if and only if β 2 > 2, in which case π M = αβ 2V
8
.
We can then determine the manufacturer’s optimal wholesale price strategy by comparing the
two cases.
B.1.3
Other scenarios and summary
Following the same procedure, we can find the equilibria in the other four subgames (N,I,I), (I,N,N),
(I,I,N) and (I,I,I). We summarize the manufacturer, retailer 1 and retailer 2’s equilibrium profits
in the table below.
Subgame π M π R1 π R2
(N,I,I)
(I,N,N)
(I,I,N)
(I,I,I)
αβ 2 V
4
0 0
(1−α+αβ 2 )V
αβ 2 V
4
0 0
4
− f 0 0
β 2 V
4(α+β 2 −αβ 2 ) − f 0 0
B.2 Equilibrium channel structures
We have paved the way to characterize all the equilibria in every subgame. Now we can examine the
channel strategies of the manufacturer and the retailers. First, neither of (N,N,N) and (I,N,N) will
be an equilibrium. This is because given the strategies of the manufacturer and retailer 2, retailer
1 obtains a null payoff. However, she always benefits from introducing her Internet channel and
32

claims a strictly positive payoff. Second, (I,I,I) is never an equilibrium. To see this, let us take the
retailers’ strategies as given. When α ≤ 1
he obtains the profit
β 2 V
4(α+β 2 −αβ 2 )
β 2 V
4(α+β 2 −αβ 2 )
β 2 −1
, if the manufacturer introduces his Internet channel,
− f. On the other hand, if he abandons it, his profit becomes
as he saves the operating cost but obtains the same gross revenue. When α ≥
1
β 2 −1 ,
if the manufacturer introduces the Internet channel, his profit is αβ 2V
4
− f; again, he can save his
cost by abandoning the Internet channel (the profit is then αβ 2V
4
).
Third, (N,I,I) is always an equilibrium. To verify this, first observe that given the retailers’
strategies, the manufacturer has no incentive to introduce his own Internet channel because he
obtains exactly the same gross revenue. Given that the manufacturer does not introduce his Internet
channel but retailer 2 does, retailer 1’s profit is zero regardless of whether he introduces his Internet
channel. Thus, he has no incentive to deviate. Likewise, retailer 2 does not want to deviate by
symmetry.
The last two cases are possible equilibria but also require some feasibility conditions.
consider first (N,I,N). Given the equilibrium strategies of the manufacturer and retailer 2, if retailer
1 abandons her Internet channel, she obtains a null payoff. Thus, she has no incentive to deviate.
Given the equilibrium strategies of the manufacturer and retailer 1, retailer 2 cannot obtain a
positive payoff regardless of whether she introduces her Internet channel.
We
This eliminates any
profitable deviation as well. Finally, given the retailers’ equilibrium strategies, the manufacturer’s
payoff depends on the consumer composition.
In the last scenario, (I,I,N) can be sustained as an equilibrium under some conditions characterized
below. Given the equilibrium strategies of the manufacturer and retailer 2, if retailer
1 abandons her Internet channel, she obtains a null payoff and thus it is not a profitable deviation.
Given the equilibrium strategies of the manufacturer and retailer 1, retailer 2 is indifferent
between introducing her Internet channel or not. To eliminate any possible profitable deviation
for the manufacturer, we need the following conditions: (1) when α ≤ 1
β 2 −1 , f ≤ α(β 2−1)V
4(α+β 2 −αβ 2 ) ; (2)
1
when
β 2 −1 ≤ a ≤ 2 β 2
, f ≤ (αβ 2−1)V
4
; (3) when 2 β 2
≤ α ≤ 2β 2
3β 2 −2 , f ≤ [4(1−α)(αβ 2−1)+α 2 ]V
8(α+2β 2 −2αβ 2 )
; (4) when
α ≥ 2β 2
3β 2 −2 , f ≤ αβ 2V
8
.
C
Selling through an e-tailer
In this section, we consider the scenario wherein the manufacturer sells through an online retailer
(e-tailer). We shall discuss two possible cases, depending on whether the retailer can introduce her
own Internet channel.
33

C.1 The retailer can only sell through the physical channel
Given 0 ≤ p ≤ V and 0 ≤ p d ≤ β 2 V , the demand in the physical channel Q is
⎧
1
⎪⎨ V [(1 − α)(V − p−p d
1−β 1
)], if p d ≤ β 1 p
Q =
1
V
⎪⎩
[(1 − α)(V − p)], if β 1p ≤ p d ≤ β 2 p ,
1
V [α( p d−p
β 2 −1 − p) + (1 − α)(V − p)], if p d ≥ β 2 p
and the demand on the Internet Q d is
⎧
1
⎪⎨ V [α(V − p d
β 2
) + (1 − α)( p−p d
1−β 1
− p d
β 1
)], if p d ≤ β 1 p
Q d =
1
V
⎪⎩
[α(V − p d
β 2
)], if β 1 p ≤ p d ≤ β 2 p
1
V [α(V − p d−p
β 2 −1 )], if p d ≥ β 2 p
By backward induction, we shall start with the subgame in which the retailer and e-tailer compete
in prices; afterwards, we return to the manufacturer’s pricing decisions.
.
C.1.1
Retailer’s and e-tailer’s strategies
Now we consider the e-tailer’s strategy. Let p ∗ and p ∗ d
denote the equilibrium selling prices. There
are five possible cases: i) p ∗ d < β 1p ∗ , ii) β 1 p ∗ < p ∗ d < β 2p ∗ , iii) p ∗ d > β 2p ∗ , iv) p ∗ d = β 1p ∗ , and v)
p ∗ d = β 2p ∗ .
In case i) p ∗ d < β 1p ∗ , π R = (p − w) 1 V [(1 − α)(V − p−p d
1−β 1
)]. Following the first-order condition, we
obtain the optimal price p ∗ = (1−β 1)V +w+p d
2
. In addition, π A = (p d −w d ) 1 V [α(V − p d
β 2
)+(1−α)( p−p d
1−β 1
−
p d
β 1
)]. The first-order condition suggests that p ∗ d = αβ 1β 2 (1−β 1 )V +[αβ 1 (1−β 1 )+(1−α)β 2 ]w d +(1−α)β 1 β 2 p
2[αβ 1 (1−β 1 )+(1−α)β 2 ]
.
Solving these equations jointly, we find that
p ∗ = (1 − β 1)V + w
2
+ (1 + α)(1 − β 1)β 1 β 2 V + (1 − α)β 1 β 2 w + 2[αβ 1 (1 − β 1 ) + (1 − α)β 2 ]w d
(1) ,
8αβ 1 (1 − β 1 ) + 2(1 − α)(4 − β 1 )β 2
p ∗ d = (1 + α)(1 − β 1)β 1 β 2 V + (1 − α)β 1 β 2 w + 2[αβ 1 (1 − β 1 ) + (1 − α)β 2 ]w d
4αβ 1 (1 − β 1 ) + (1 − α)(4 − β 1 )β 2
.
p ∗ d < β 1p ∗ implies w > β 1(1−β 1 )[αβ 2 (3−β 1 )−2αβ 1 (1−β 1 )−β 2 ]V +[αβ 1 (1−β 1 )(2−β 1 )+(1−α)(2−β 1 )β 2 ]w d
2αβ 2 1 (1−β 1)+(1−α)β 1 β 2
. Likewise,
we can also work out the other four cases. The details are omitted since they follow from
straightforward algebra.
C.1.2
Manufacturer’s strategies
Now we proceed to examine the manufacturer’s strategies. The five cases lead to different optimal
selling prices and subsequently different expressions of the manufacturer’s payoffs. For example,
34

when p ∗ d < β 1p ∗ ,
π M = w 1 V [(1 − α)(V − p∗ − p ∗ d
1 − β 1
)] + w d
1
V [α(V − p∗ d
β 2
) + (1 − α)( p∗ − p ∗ d
1 − β 1
− p∗ d
β 1
)],
where p ∗ and p ∗ d are given in (1). We then apply the first-order condition and obtain w∗ =
[β 2 −α(1−β 1 )(β 2 −β 1 )]V
2(αβ 1 +β 2 −αβ 2 )
and wd ∗ = β 1 β 2 V
2(αβ 1 +β 2 −αβ 2 ). In this case, the manufacturer’s profit is πIE
M
(Internet
encroachment). The other cases are analyzed similarly.
C.2 Both the manufacturer and the retailer can introduce Internet channels
We again use backward induction to characterize the equilibrium. We shall distinguish between
the online selling prices between the retailer (p R d ) and the e-tailer (pE d ). When pR d < pE d
, the e-tailer
has no sales; when p E d
< pR d
, the retailer earns nothing from her Internet channel. Therefore, if
w < w d , in equilibrium pd
R∗ ≤ p E∗
d
= w d , and the e-tailer gets no sales. This is equivalent to the
case when the manufacturer owns his Internet channel in our basic framework. Recall that we have
shown that when w < w d , the manufacturer’s payoff is decreasing in w d . Thus, in what follows, we
can simply focus on the case w d ≤ w.
Moreover, when w d ≤ w, in equilibrium the retailer gets no sales in her Internet channel, and
p E∗
d
≤ w. If this is violated (i.e., p E∗
d
consumers that purchase from the e-tailer.
> w), the retailer can always decrease p d to capture the
Note that p E∗
d
< w is satisfied only under strategy
GE-M in equilibrium. Therefore, if other equilibria can be sustained, it must be that p E∗
d
= w, in
which case the value of w d does not influence the e-tailer’s sales. Accordingly, the manufacturer
will increase the wholesale price w d as much as possible, leading to wd ∗ = w in equilibrium.
We can then examine the manufacturer’s payoff given that w = w d .
For example, when
w ≥ V , the induced selling prices are p R d = pE d
= w. The corresponding manufacturer’s payoff is
π M = w[ 1 V α(V − w β 2
)]. Applying the first-order condition, we have w ∗ = β 2V
2
and thus π M = αβ 2V
4
.
Note that w ∗ > V if and only β 2 > 2. This strategy is labeled as strategy EO. When w ≤ V , the
induced selling prices become p R d = pE d
= w, and there are several subcases to discuss. We can then
derive the optimal wholesale prices in each subcase and then compare the manufacturer’s payoffs
across scenarios. The calculations are routine and tedious; thus, we omit the details and simply
summarize the results in the proposition.
35