Advertising Assignment I

Received: 1 March 2018 Revised: 22 October 2018 Accepted: 24 November 2018

DOI: 10.1002/ mde.2994

R E S E A R C H A R T I C L E

The strategic effect of retailers' in-store advertising services under product variety competition

Haruki Kobayashi1 Nobuo Matsubayashi2

1 DENTSU INC., Higashi Shinbashi, Minato,

Tokyo, Japan 2 Department of Administration Engineering,

Faculty of Science and Technology, Keio

University, Yokohama, Japan

Correspondence

Nobuo Matsubayashi, Department of

Administration Engineering, Faculty of Science

and Technology, Keio University, 3-14-1

Hiyoshi, Kohoku-ku, Yokohama 223-8522,

Japan.

Email: [email protected]

Funding information

Grants-in-Aid for Scientific Research (C),

Grant/ Award Number: 15K01202 ; Ministry of

Education, Culture, Sports, Science and

Technology of Japan

We study a retailer service model of in-store advertising, in which a neutral retailer provides

product information to consumers for free but charges manufacturers. Our results show that the

retailer's optimal pricing induces the manufacturers to decrease the number of items they offer.

Nevertheless, this relaxes the competition between the manufacturers so that they benefit

from using the in-store service, unless the cost of communicating with consumers about the

between-firm products is lower. Furthermore, the service can be made socially beneficial by

reducing the inefficiency resulting from an excessive number of items when manufacturers are

not well differentiated.

1 I N T R O D U C T I O N

Today's information and communication tools, such as social network-

ing sites, enable consumers to communicate with each other about

products, as well as with the firms that provide them. As a result, firms

can effectively understand the diverse needs of consumers and utilize

them in their product development. However, this also gives firms an

incentive to increase the number of products they provide, causing

intense competition on variety. Unfortunately, this intense competi-

tion might hurt not only firms' welfare but also consumer satisfaction,

because an excessive variety of products may confuse consumers.

As the variety increases, the possibility that consumers can find the

ideal product for their needs increases. However, at the same time,

consumers incur temporal or psychological costs in identifying these

products from among the wide variety available. 1

When consumers need to compare several items offered by dif-

ferent manufacturers, they typically use online marketplaces (e.g.,

Amazon and eBay) or physical retailers (e.g., Walmart), because these

sellers provide neutral product information to customers. As a result,

these platforms try to decrease the costs incurred by consumers when

comparing items from different manufacturers. For example, Amazon,

which declares that it sells the highest number of products worldwide

(about 50 million items), provides a useful search system to help con-

sumers find their ideal products as easily as possible. Furthermore,

it offers a recommendation system to guide customers in their pur-

chases across numerous products from different sellers. Some physical

retailers, including Macy's, BestBuy, and SportsAuthority, are known

for their neutral in-store guides provided by well-trained staff. In this

study, we refer to a service offered by a retailer to help consumers

understand product information as an ‘‘in-store advertising service.’’

When a retailer offers an in-store advertising service to its cus-

tomers, it must incur some positive cost for developing search systems,

encouraging consumers to make recommendations, hiring and train-

ing staff, and so on. 2

Clearly, as the number of products the retailer

stocks increases, this cost can become significant. Therefore, the

retailer should consider how it can profitably offer its in-store adver-

tising service by taking into account the responses of manufacturers

who have their own advertising options. On the basis of this moti-

vation, we explored a service model in which the retailer charges

manufacturers for an in-store advertising service but offers the same

service to consumers for free. Our primary interest is to investi-

gate whether introducing this service can contribute to a win-win

232 © 2019 John Wiley & Sons, Ltd. wileyonlinelibrary.com/ journal/ mde Manage Decis Econ. 2019;40:232–242.

KOBAYASHI AND MATSUBAYASHI 233

partnership between the retailer and the manufacturers in the pres-

ence of variety competition. In other words, under what conditions

can the service be used to coordinate the parties in the supply chain?

Specifically, we consider a fee structure that is proportional to the

number of products that each manufacturer provides. In fact, Ama-

zon employs a tariff structure, charging a $0.99 ‘‘per-item fee’’ to

individual sellers (see the Amazon website at https:/ / www.amazon.

com/ gp/ help/ customer/ display.html?nodeId=1161240). In addition,

eBay charges a per-item ‘‘insertion fee’’ to sellers who sell more than 50

items (with free listings for up to 50 items; see ‘‘Standard selling fees’’

at http:/ / pages.ebay.com/ help/ sell/ fees.html). Furthermore, several

online marketplaces, including ArtFire and Etsy, charge a fee per item

listing (see ‘‘Where to Sell Online’’ at http:/ / www.wheretosellonline.

com/ marketplace- comparisons/ compare- fees- pricing/ ). These pric-

ing schemes seem similar to our proposed scheme in the

sense that retailers have an economic incentive to effi-

ciently offer a greater variety of products. However, note that

many other marketplaces do not charge a per-item fee (see

‘‘Where to Sell Online’’ at http:/ / www.wheretosellonline.com/

marketplace- comparisons/ compare- fees- pricing/ ). Therefore, the

economic rationale for retailers' in-store advertising services with a

per-item fee should be investigated.

Furthermore, from a social viewpoint, we investigate whether the

retailer's in-store service appropriately resolves the inefficiency of

offering too many items, which results from intense variety com-

petition between manufacturers. In the real world, some retailers

intentionally attempt to decrease the number of products they sell.

For example, Apple's App Store implements a rigid policy of rejecting

undifferentiated goods in an attempt to prevent consumer confusion

(see ‘‘App Store Review Guidelines’’ at https:/ / developer.apple.com/

app- store/ review/ guidelines/ ). In addition, T-mall, the biggest Inter-

net mall in China, contracts exclusively with certain luxury brand

manufacturers in order to eliminate the possibility of displaying undif-

ferentiated goods; see Chiu and Chu (2014) and Chu and Chiu (2014).

Rather than considering these contract schemes, we analyze the effect

of the pricing scheme on coordinating the product assortment, that is,

on controlling the number of products.

We formally employ a game-theoretic model to explore the strategic

interaction between one monopolistic retailer and two compet-

ing manufacturers associated with the retailer's in-store advertising

service. Both manufacturers can potentially develop numerous hori-

zontally differentiated items and, thus, can choose the sizes of their

product lines endogenously. However, we assume that when manu-

facturers provide multiple items, they must incur two types of positive

costs, both of which are convexly proportional to the number of items

they offer. Specifically, there is an operation cost owing to the neg-

ative effects arising from operating multiple items, including effects

such as congestion and complexity. The second cost, which plays a

key role in this study, is the cost of explaining the product differences

to consumers in order to lead them to comfortable purchasing deci-

sions. Following previous studies, this differentiation cost is assumed

to be classified into two types: the cost of communicating the differ-

ences between products offered by the same manufacturer and the

cost of communicating the differences between products offered by

different manufacturers. In the presence of these costs, we consider a

two-stage game. First, the retailer sets the unit fee for its in-store ser-

vice. Then, both manufacturers simultaneously determine the number

of items they wish to sell. Although we focus on a game with a linear

fee structure as a base model, we also examine two types of quadratic

fee structures as extensions to this model.

By analyzing the equilibrium of the base model, we first show

that the monopolistic retailer can benefit from offering an in-store

advertising service by setting the unit fee for the service at an inter-

mediate level. This implies that, by doing so, the retailer optimally

resolves the trade-off between obtaining a higher profit margin by set-

ting a higher unit fee and giving manufacturers an incentive to increase

the number of items they sell by reducing the unit fee. This result,

in turn, implies that manufacturers are compelled to decrease the

number of items they offer. Nevertheless, this retailer's pricing policy

successfully reduces the intense competition between manufacturers.

As a result, the manufacturers are better off using the in-store ser-

vice than advertising their items directly to consumers, unless they

are sufficiently horizontally differentiated and the cost of explaining

the between-firm product differences is very low. Furthermore, our

comparison between the equilibrium outcome and the socially opti-

mal level proves that this service can effectively resolve the social

inefficiency caused by an excessive number of items. Therefore, it

improves the social welfare in a market where manufacturers are not

well differentiated. Finally, we find that the simple linear fee is supe-

rior to a quadratic fee structure for the retailer, even though the costs

are assumed to be quadratic. Although this result might seem coun-

terintuitive, it reflects the efficiency of manufacturers: A quadratic fee

significantly decreases the manufacturers' motivation to increase the

number of varieties in competition with each other.

The rest of the paper is organized as follows. In Section 2, we review

the literature related to our study. In Section 3, we formulate the

game-theoretic model for our in-store advertising service. In Section 4,

we analyze the equilibrium outcome and discuss the strategic impact

of the in-store advertising service. Several fee structures are compared

in Section 5. Finally, Section 6 concludes the paper. The proofs of all

propositions are provided in Appendix A.

2 R E L A T E D L I T E R A T U R E

In this section, we review the literature related to this study. As men-

tioned in Section 1, this study is strongly motivated by the negative

impact of product variety on consumer satisfaction. In this respect,

we first note that many empirical works, such as those of Jacoby,

Speller, and Berning (1974), Bettman and Zins (1979), and Malhotra

(1982), indicate the presence of a consumer cost for selection. In addi-

tion, Huffman and Kahn (1998) empirically examine how to reduce

consumers' confusion in their purchasing processes. In contrast, many

studies have addressed a firm's decision problems across the mar-

keting mix. Kuksov and Villas-Boas (2010) rigidly model a consumer's

product-choice process by incorporating an evaluation cost propor-

tional to the number of alternatives. They find that a monopoly should

provide a finite and optimal number of products that maximizes

the firm's profit. L. Liu and Dukes (2013) examine variety compe-

tition between multiproduct firms in the presence of consumers'

consideration sets that arise as a result of their evaluation costs

234 KOBAYASHI AND MATSUBAYASHI

(Hauser & Wernerfelt, 1990). Here, consumers must incur differ-

ent evaluation costs when comparing products offered by the same

manufacturer and when comparing products offered by different man-

ufacturers. Our work is related to theirs in the sense that we also

consider this difference in evaluation costs, which plays a key role in

our analysis. Finally, in the context of advertising, Van Zandt (2004)

and Anderson and de Palma (2009) refer to a negative externality

arising from information overload and discuss how message senders

should interact strategically with each other.

However, all of the aforementioned works assume that the disutility

due to confusion must be incurred by consumers directly, which indi-

rectly hurts firms' profits. In this regard, the study by J. M. Villas-Boas

(2004) is more closely related to ours, because, as we do, he considers

the possibility that a firm eliminates a consumer's confusion and cor-

rectly indicates product information by incurring the associated cost

itself. Specifically, in the absence of a firm's ability to target advertis-

ing, he explicitly models the cost of communicating with consumers

about different products using a function that is convexly propor-

tional to the number of products offered to the market. Applying this

model, he investigates a monopoly's optimal strategy with regard to

the product line selection, as well as the advertising level for each

product being sold. However, although a manufacturer directly incurs

the costs in his study, we consider the cost of variety as a cost to the

retailer for its in-store advertising service.

Our study is also related to the literature on product line selection.

Although this covers many research topics, several works that exam-

ine strategic interactions between retailers and manufacturers with

regard to product assortment decisions are of particular import. For

example, Dukes, Geylani, and Srinivasan (2009) compare cases where

a manufacturer or a retailer decides on assortments. They demonstrate

the possibility of an assortment reduction by a prominent retailer.

Y. Liu and Cui (2010) investigate the product line decision of a

monopolistic manufacturer under decentralization and show that

the equilibrium number of products can be socially optimal. Xiao,

Choi, and Cheng (2014) explore a dual-channel setting (online and

bricks-and-mortar stores), in which a retailer can choose the number

of products it sells, whereas a customized product is sold directly by

a manufacturer. As in our study, these works focus on the effect of

channel coordination through product line selections. However, none

of them explore coordination in the context of an in-store advertising

service, in which a retailer charges a service fee to manufacturers, while

incurring an advertising cost when communicating with consumers

about different products.

Note too that our study is similar in spirit to several other works (e.g.,

Armstrong, 2006; Choi, 2010; Hagiu, 2009; Li, Liu, & Bandyopadhyay,

2010; Maruyama & Zennyo, 2015; Rochet & Tirole, 2006) in the

economics, marketing, and information system literature on platform

firms, because these studies also consider the situation in which a

retailer can offer numerous products to the market as a marketplace

operator. These works focus on pricing in a two-sided market and,

thus, assume that retailers charge appropriate fees to price-taking

agents in each market. In contrast, the present study explores the

strategic interaction between a retailer and competing manufacturers,

specifically, by providing an in-store advertising service. Bakos (1997)

and Hagiu and Wright (2015) highlight an important function of the

online marketplace as reducing the search and transaction costs of

both sellers and buyers through its marketing activities. Among such

provisions by retailers, we reveal how a retailer's in-store advertising

service helps buyers select their desired items.

Finally, we mention several studies that discuss the effect of in-store

advertising. Many empirical works investigate the effectiveness of

in-store displays as a tool of promotion and advertising (e.g., Bemmaor

& Mouchoux, 1991; Breugelmans & Campo, 2011; Chevalier, 1975).

In contrast, Dukes and Liu (2010) conduct a theoretical study on

the effect of in-store media services offered by retailers on the

channel coordination between manufacturers, which has a similar

motivation to the present study. However, although Dukes and Liu

(2010) consider a retailer's in-store service that provides information

on a single product to consumers, we focus on a retailer's service that

helps shoppers compare multiple products in order to find the best fit.

Therefore, unlike Dukes and Liu (2010), we explicitly incorporate in our

model the cost of evaluating multiple products, which is proportional

to the number of products on sale. In addition, we investigate the

effectiveness of this type of in-store service on variety competition

between multiproduct manufacturers. This differs from the work

of Dukes and Liu, which mainly analyzes the strategic interaction

between monopolistic manufacturers and retailers. Furthermore, they

only consider a quadratic-type fee for the in-store service. Here, we

also discuss other types of fee structures and show that a simple linear

fee structure outperforms quadratic fee structures.

3 M O D E L

We consider a supply chain that consists of two manufacturers,

labeled 1 and 2, and one retailer R. It does not matter whether the

retailer is an online retailer or a physical store. Both manufacturers sell

multiple products through this retailer. Here, we implicitly consider

the situation in which the manufacturers are not well differentiated.

Thus, to help consumers choose an ideal product from among the

numerous products on offer, the retailer offers an in-store advertising

service, such as a search system and a recommendation system,

through which it can communicate product information to consumers

in a neutral manner. We assume that without this in-store service,

consumers cannot find any products for sale; for example, it is easy

to see that an online marketplace with no search system is almost

an ‘‘empty system.’’ This service is offered for free to consumers,

but the retailer charges manufacturers for the same service. Each

manufacturer can potentially develop numerous horizontally (though

slightly) differentiated products or items and, thus, can choose the

size of its product line endogenously. Let n1 and n2 be the numbers of

items offered by Firms 1 and 2, respectively. 3

Note that, throughout

this paper, the integer constraint on n1 and n2 is ignored and, thus,

they are assumed to be continuous variables. This can be justified

in a situation of primary interest to us, where there are potentially

numerous products that can be offered to the market; Hagiu (2009)

also mentions this case.

3.1 The demand structure

We employ the well-known linear (aggregate) demand system,

as introduced in the economics and management literature (e.g.,

KOBAYASHI AND MATSUBAYASHI 235

Balasubramanian & Bhardwaj, 2004; Karaer & Erhun, 2015; Sayman,

Hoch, & Raju, 2002), as follows:{ D1(n1, n2) = 1 − p1 + 𝛽(p2 − p1) + vn1 + 𝛽v(n1 − n2) D2(n1, n2) = 1 − p2 + 𝛽(p1 − p2) + vn2 + 𝛽v(n2 − n1).

Note that this system is derived by maximizing the following

representative consumer's utility function:

U(q1, q2) = − 1 4 (q1 + q2)2 −

1 2(1 + 2𝛽)

( q2

1 + q2

2 −

(q1 + q2)2

2

) + (1 + vn1)q1

+ (1 + vn2)q2 − p1 q1 − p2 q2,

(1)

which is based on the utility function known to represent the typical

quadratic utility with a limited market size (see Vives, 2001, and Shubik

and Levitan, 1971, for further detail). Note that this utility function

assumes that although both manufacturers offer multiple products,

consumers do not choose a specific item. Instead, they choose the

consumption level for each manufacturer, where the utility increases

linearly with the number of items that each manufacturer sells through

the retailer. In other words, consumers evaluate the number of items

that a manufacturer offers as the manufacturer's ‘‘quality.’’ 4

The

parameter v( > 0) represents the sensitivity to the number of items. The utility function (1) is justified by considering the situation where

consumers optimize their utility by selecting the firm that is likely to

offer the items they want, prior to deciding on the item that is actually

purchased (Anderson & de Palma, 1992; Draganska & Jain, 2005; L. Liu

& Dukes, 2013). For example, imagine a situation in which you choose

a restaurant to visit. To determine which restaurant is most likely

to offer dishes you prefer, you might compare their menus provided

on the Internet or in guidebooks. Nevertheless, you are selecting a

restaurant, not a dish. Only after taking a seat in the restaurant would

you decide on a dish to order. As such, a greater variety of products

increases the possibility of a consumer finding a better fit, which

improves her utility.

To ensure that all channel members earn positive profits in equilib-

rium, we assume that v is relatively small. The parameter 𝛽( > 0) is the degree of substitutability (horizontal differentiation) between the two

manufacturers, which implies the intensity of competition between

them. As mentioned above, we assume that the two manufacturers

are relatively undifferentiated. Thus, 𝛽 is implicitly assumed to be high.

Finally, pi is the retail price of the products made by manufacturer

i and is identical for all of its products. Furthermore, we assume that

price competition between products can be ignored, as in Dukes and

Liu (2010). Specifically, we consider a simple setting where all prices

of items are identical and normalized to p1 = p2 = p(0 < p < 1). This assumption enables us to focus on the strategic interaction

between the manufacturers and the retailer with regard to the in-store

advertising service under variety competition. In practice, we often

observe that firms sell many less differentiated products, such as those

offered via mass customization, with identical wholesale and retail

prices (Alptekinoglu & Corbett, 2008; Chen & Cui, 2013; Draganska &

Jain, 2006). In addition, there are many instances where manufacturers

do not practice price discrimination for chain retailers (S. B. Villas-Boas,

2009; Vakharia & Wang, 2014) or where chain retailers adopt uniform

pricing across their stores (Dobson & Waterson, 2005; Peng & Tabuchi,

2007; Takaki & Matsubayashi, 2013). These facts imply that such firms

do not tend to engage in price competition in a focal market, at least

as an issue of first-order importance, but instead engage in variety

competition. 5

Thus, we can rewrite the demand system as{ D1(n1, n2) = 1 − p + vn1 + 𝛽v(n1 − n2) D2(n1, n2) = 1 − p + vn2 + 𝛽v(n2 − n1).

(2)

3.2 The cost structure

We assume that there are two types of costs when attempting to

provide consumers with product information so that they can perfectly

resolve any confusion arising from a comparison between products.

Note that unless they incur these costs, consumers cannot find some

of the ni products on offer, which means that strictly fewer than

ni products are available. The first cost is that of explaining the

differences between products made by a single manufacturer. We

denote this cost as C1(ni), where the functional form is identical for both manufacturers. In this study, we specifically assume that C1 is

quadratic on ni :

C1(ni) = c1 n2i (i = 1, 2), (3)

where c1 is a positive coefficient. The quadratic form is appropriate

because, without any guidance, the comparison between ni items takes

time proportional to ni(ni−1)

2 , which is approximately

n2 i

2 when ni is large.

Thus, any effort to reduce the time spent would be of the same order.

The second cost is that of explaining the differences between prod-

ucts made by different manufacturers. We denote this cost by C2(ni, nj), where the functional form is also identical for both manufacturers. We

again assume a quadratic form for C2 :

C2(ni, nj) = 2c2 ni nj (i ≠ j), (4)

where c2 is a positive coefficient. As in the case of C1 , this functional

form is justified by the fact that the comparison between ni and nj items takes time proportional to ni × nj .

Hereafter, we assume 0 < c1 < c2 . As in L. Liu and Dukes

(2013), the cost that consumers must incur to compare and evaluate

products is different for within-firm products and for between-firm

products, and, in general, the latter is higher than the former. In line

with this observation, we assume that the unit cost of communicat-

ing about between-firm product differences is higher than that of

communicating about within-firm product differences.

3.3 The retailer's profit function

We assume that in order to offer the in-store advertising service, the

retailer must incur both types of costs introduced above. However, a

fee for this service can be charged to both manufacturers. Given ni , let

T(ni) be the tariff for this service. Specifically, following the examples of actual online marketplaces shown in Section 1, we assume a linear

form for this tariff:

T(𝜙; ni) = 𝜙ni, (5)

where 𝜙 is a price per item (unit price). In addition, we assume that

manufacturers have full powers for wholesale price negotiations with

the retailer; that is, the retailer's revenue obtained from consumers

is fully transferred to the manufacturers. Clearly, as the retailer has

relatively strong negotiation powers, it extracts almost all of the

revenue, and the manufacturers would prefer to sell their products via

236 KOBAYASHI AND MATSUBAYASHI

their direct channels, instead of using the retailer's marketplace service.

On the contrary, even if the manufacturers have strong negotiation

powers, they do not necessarily benefit from using the retailer's service

because they pay the retailer for the in-store advertising service.

Therefore, our interest is to analyze the case when the manufactures

are in a powerful position for wholesale price negotiations with the

retailer. The assumption of manufacturers' full powers is simply for

ease of exposition because setting the rate of transfer at any particular

level to some extent does not qualitatively change any our results. 6

Therefore, we can describe the profit function of the retailer as

𝜋R(𝜙; n1, n2) = 𝜙(n1 + n2) − c1(n21 + n 2 2 ) − 2c2 n1 n2. (6)

3.4 The manufacturers' profit function

With regard to the manufacturers' cost structures, we assume two

types of costs: the fee for the in-store advertising service charged

by the retailer, denoted by T(𝜙; ni), and the cost that is quadratically proportional to the number of items ni . This second cost can be

regarded as an operation cost rather than a production cost that

must be incurred by manufacturer i when offering its items to the

retailer; this is reasonable because an increase in the number of items

has significant negative operational effects, such as congestion and

complexity.

Formally, the manufacturers' cost functions are defined as follows:{ CM1(n1; 𝜙) = 𝜙n1 + sn21 CM2(n2; 𝜙) = 𝜙n2 + sn22,

(7)

where s( > 0) is the coefficient of the operation cost, which is assumed to be identical for both manufacturers for simplicity.

Thus, we have the following profit functions for the manufacturers:{ 𝜋1(n1, n2; 𝜙) = p(1 − p + vn1 + 𝛽v(n1 − n2)) − 𝜙n1 − sn21 𝜋2(n1, n2; 𝜙) = p(1 − p + vn2 + 𝛽v(n2 − n1)) − 𝜙n2 − sn22.

(8)

3.5 Game setup

The decision sequence of our game is as follows. In the first stage, the

retailer R decides the unit fee of the in-store service, 𝜙. Then, in the

second stage, the two manufacturers simultaneously determine the

number of items (n1 and n2 , respectively) they will offer to the retailer's

service. Then, we determine the subgame perfect Nash equilibrium

(hereafter, the equilibrium) of the game.

4 A N A L Y S I S

4.1 Equilibrium outcome of the game

Using backward induction, the outcome in the equilibrium of our game

follows immediately.

Proposition 1. There exists a unique equilibrium, where the

equilibrium outcome is given as follows:

𝜙 ∗ =

pv(1 + 𝛽)(c1 + c2 + s) c1 + c2 + 2s

, 𝜋 ∗ R =

p2 v2(1 + 𝛽)2

2(c1 + c2 + 2s) , n∗(= n∗

1 = n∗

2 )

= pv(1 + 𝛽)

2(c1 + c2 + 2s) ,

𝜋 ∗(= 𝜋∗

1 = 𝜋∗

2 ) = p(1 − p) +

(1 + 𝛽)p2 v2

4(c1 + c2 + 2s)2 (s − (2c1 + 2c2 + 3s)𝛽).

Proposition 1 first shows that the optimal 𝜙 is determined as an

interior solution. In other words, the retailer benefits from offering its

in-store advertising service by charging a fee at an intermediate level.

Indeed, the retailer faces a trade-off: A higher profit margin, obtained

by charging a higher unit fee, is desirable but so is providing an

incentive to manufacturers to increase the number of items they sell,

which is achieved by reducing the unit fee. Therefore, the retailer's

optimal pricing strategy is to set the fee at an intermediate level.

As the degree of substitutability, 𝛽, increases, the optimal 𝜙

increases. Nevertheless, the equilibrium number of items n∗ also

increases and, as a result, the retailer's equilibrium profit 𝜋∗ R

increases

whereas the manufacturers' 𝜋∗ decreases. In other words, because

the manufacturers are less differentiated, the retailer has an incentive

to charge a higher unit fee for its in-store service. If it does not do

so, their intense variety competition erodes the retailer's profit, owing

to the cost increases. However, because the intensity of competition

increases, the number of items being offered increases, which benefits

the retailer. In contrast, the manufacturers are compelled to decrease

their profits.

4.2 Effectiveness of the in-store advertising service

for manufacturers

In the previous subsection, we showed the profitability of the in-store

advertising service for the retailer. However, note that the above set-

ting assumes that the manufacturers do not have outside options. To

ensure the effectiveness of the service model, we must investigate

whether manufacturers benefit from the use of the in-store advertis-

ing service. To see this, we consider a benchmark case in which both

manufacturers advertise their items directly to consumers. By compar-

ing the equilibrium outcomes in the presence of the in-store service

with those in this benchmark case, we attempt to show the strategic

effect of the in-store service under variety competition.

Formally, we consider a game in which both manufacturers have to

incur the costs of explaining the differences between their products to

consumers. Thus, the profit functions of manufacturers are formulated

as follows:{ 𝜋′

1 (n1, n2) = p(1 − p + vn1 + 𝛽v(n1 − n2)) − (c1 n21 + 2c2 n1 n2 + sn

2 1 )

𝜋′ 2 (n1, n2) = p(1 − p + vn2 + 𝛽v(n2 − n1)) − (c1 n22 + 2c2 n1 n2 + sn

2 2 ). (9)

Both manufacturers simultaneously determine the number of items

they sell, n1 and n2 , to maximize their profits 𝜋 ′ 1

and 𝜋′ 2

, respectively.

Here, we focus on the case where both manufactures can earn positive

profits in equilibrium. Then, we immediately derive the equilibrium

outcome given in the following lemma.

Lemma 1. Suppose that Manufacturers 1 and 2 advertise their items

directly to consumers. Let n̄1 and n̄2 be the number of items offered

by the two manufacturers in equilibrium, and let �̄�1 and �̄�2 be their

equilibrium profits, respectively. If s > c2 − c1 , then both n̄1 and n̄2 are determined uniquely at positive levels, and the specific outcomes

are given as follows:

n̄(= n̄1 = n̄2) = pv(1 + 𝛽)

2(c1 + c2 + s) , �̄�(= �̄�1 = �̄�2) = p(1 − p)

+ (1 + 𝛽)p2 v2

4(c1 + c2 + s)2 (c1 + s − (c1 + 2c2 + s)𝛽).

KOBAYASHI AND MATSUBAYASHI 237

We first note that some amount of operation cost is needed

to ensure that both manufacturers are active in the equilibrium,

particularly when the unit cost c2 is relatively high. This is because

if the operation cost is extremely small, then one manufacturer, say

Manufacturer 1, can offer too many items. However, in that case,

the best response by Manufacturer 2 is to completely withdraw its

items, even when costs are symmetric. If it does not do so, it must

incur the significant cost C2(n1, n2) to explain the difference between its own products and those made by the other manufacturer. As a

result, only Manufacturer 1 is active in the equilibrium. Because a

higher operation cost restricts a manufacturer's ability to significantly

increase the number of items it offers, both manufacturers can earn

positive profits in equilibrium in the presence of such high costs.

We are now ready to state our main proposition, which ensures the

effectiveness of using the retailer's in-store advertising service.

Proposition 2. Provided that s > c2 − c1 , we always have n∗ < n̄. In addition, if c2 is sufficiently higher than c1 and 𝛽 is sufficiently

higher, then �̄� < 𝜋∗ holds.

Proposition 2 first shows that n∗ is necessarily lower than n̄, which

implies that the retailer's service decreases the number of items

offered to the market compared with the case where the manufactur-

ers advertise their items directly. Proposition 2 also shows that if the

unit cost of explaining the differences between the products made by

different manufacturers is sufficiently higher than that of explaining

the differences between their own products, and if both manufactur-

ers are considerably less differentiated, then this equilibrium outcome

indeed leads to the retailer's service benefiting the manufacturers.

In other words, in this case, manufacturers benefit more from using

the retailer's advertising service, despite the fact that the retailer

charges them a service fee as a monopoly. The key to understanding

this somewhat unintuitive result is the change of the manufacturer's

advertising cost with c2 . As c2 increases, although the manufacturers

are charged a higher unit fee, 𝜙, for the retailer's service, they can

instead benefit by decreasing the number of items they sell as a result

of decreasing the intensity of the variety competition. Indeed, com-

pared with direct advertising, the latter benefit is important at higher

c2 and higher 𝛽. When communicating between-firm product differ-

ences, the retailer must incur a cost of 2c2 n1 n2 to provide its service

to both manufacturers. In contrast, when the manufacturers advertise

directly, they must each incur the same cost, as in (9). Because the man-

ufacturers are less differentiated, this inefficiency has a substantial

impact on their advertising costs resulting from their intense variety

competition. In fact, in equilibrium, each manufacturer must incur a

communication cost of (c1 n̄ + 2c2 n̄)n̄ = c1+2c2

2(c1+c2+s) n̄ when advertising

directly but incur a cost of 𝜙∗n∗ = c1+c2+s c1+c2+2s

n∗ when using the retailer's

service. Then, the difference between both costs per item is given as

(c1 n̄ + 2c2 n̄) − 𝜙∗ = −c1(c1+c2+2s)−2s2

2(c1+c2+s)(c1+c2+2s) . Although this is always negative,

we can easily see that this difference in unit costs is likely to increase

for higher c1 rather than higher c2 . In other words, the optimal unit

fee for the retailer's service is less affected by higher c2 , relative to c1 .

However, the equilibrium number of items when using the retailer's

service is n∗, which is much less than n̄ as 𝛽 becomes higher. There-

fore, the manufacturers' advertising cost through using the retailer's

service can become lower than that through direct advertising.

4.3 Social efficiency of the in-store advertising

service

From the discussion in the previous section, we explicitly find that the

retailer's in-store service controls the variety competition between the

manufacturers. Then, our interest is whether this control can actually

improve the social efficiency. To investigate this, we compare the

equilibrium number of items in the presence of the in-store service,

the equilibrium number in the absence of the in-store service, and the

socially optimal number of items as a benchmark. To begin with, we

formulate the social planner's optimization problem. Specifically, the

social planner maximizes social welfare W with respect to the number

of items n1 and n2 , where W is given by

W = U(q1, q2) + 𝜋R + 𝜋1 + 𝜋2

= 1 − p2 + (1 + 𝛽)v2

2 (n2

1 + n2

2 ) − 𝛽v2 n1 n2 + v(n1 + n2)

− (c1 + s)(n21 + n 2 2 ) − 2c2 n1 n2,

where the second equality is derived by substituting the relation (2)

into (1), (6), and (8). Then, we immediately obtain the following lemma.

Lemma 2. Suppose s > c2 − c1 and v2 < 2(c1−c2+s)

1+2𝛽 . Then, the

socially optimal values of n1 and n2 that maximize W are identical

and positive:

n̂ = v 2(c1 + c2 + s) − v2

.

By comparing the number of items shown in Proposition 1 and in

Lemmas 1 and 2, we derive the following proposition.

Proposition 3. Suppose s > c2 − c1 and v2 < 2(c1−c2+s)

1+2𝛽 . Then, for

a higher 𝛽, we have n̂ < n∗ < n̄, which implies that W(n̂) > W(n∗) > W(n̄).

Indeed, Proposition 3 shows that when manufacturers are poorly

differentiated, the retailer's control of variety competition between

manufacturers certainly improves social welfare. Therefore, the retail-

er's in-store service can be socially beneficial in a market where

manufacturers lack differentiation.

5 E X T E N S I O N O F T H E M O D E L : O T H E R F E E S T R U C T U R E S

In this section, to examine the robustness of the simple linear fee as an

effective fee structure for the in-store advertising service, we consider

two additional types of fee structure and compare the retailer's profits

in each case with that under the linear fee model. One of the fee

structures we consider is a quadratic fee, where the retailer charges

manufacturers a fee that is quadratically proportional to the number

of items they sell:

Fee Structure 2: T2(𝜙; ni) = 𝜙n2i . (10)

The second fee structure is a fee that is proportional not only to

the number of items a manufacturer sells but also to that of its rival.

Similarly to a congestion fee, this can be interpreted as a kind of tax,

in the sense that one must incur the cost of negative externalities.

Formally, we define this fee structure as follows.

238 KOBAYASHI AND MATSUBAYASHI

Fee Structure 3: T3(𝜙; ni, nj) = 𝜙(n2i + ni nj). (11)

As in the case of the linear fee, we formulate a two-stage game. In the

first stage, the retailer sets the unit fee 𝜙 to maximize its profit.

Fee Structure 2: 𝜋R(2)(𝜙; n1, n2) = 𝜙(n21 + n 2 2 ) − c1(n21 + n

2 2 ) − 2c2 n1 n2.

(12)

Fee Structure 3: 𝜋R(3)(𝜙; n1, n2) = 𝜙(n21 + n 2 2 + 2n1 n2)

− c1(n21 + n 2 2 ) − 2c2 n1 n2.

(13)

Then, in the second stage, given the value of 𝜙 determined by the

retailer, both manufacturers simultaneously determine the number of

items they offer to the market to maximize their profits:

Fee Structure 2:

{ 𝜋1(2)(n1, n2; 𝜙) = p(1 − p + vn1 + 𝛽v(n1 − n2)) − (𝜙n21 + sn

2 1 )

𝜋2(2)(n1, n2; 𝜙) = p(1 − p + vn2 + 𝛽v(n2 − n1)) − (𝜙n22 + sn 2 2 ).

(14)

Fee Structure 3:

{ 𝜋1(3)(n1, n2; 𝜙) = p(1 − p + vn1 + 𝛽v(n1 − n2)) − 𝜙(n21 + n1 n2) − sn

2 1

𝜋2(3)(n1, n2; 𝜙) = p(1 − p + vn2 + 𝛽v(n2 − n1)) − 𝜙(n22 + n1 n2) − sn 2 2 .

(15)

Then, by analyzing the subgame perfect Nash equilibrium of this game,

the equilibrium outcome under each fee structure is summarized in

the following lemmas.

Lemma 3. The outcomes in the equilibrium under Fee Structure 2 are

𝜙 ∗ (2) = 2c1 + 2c2 + s, 𝜋

∗ R(2) =

p2 v2(1 + 𝛽)2

8(c1 + c2 + s) ,

n∗(2) = pv(1 + 𝛽)

4(c1 + c2 + s) , 𝜋

∗ (2) = p(1 − p) +

p2 v2(1 − 𝛽2) 8(c1 + c2 + s)

.

Lemma 4. The outcomes in the equilibrium under Fee Structure 3 are

𝜙 ∗ (3) =

3c1 + 3c2 + 2s 3

, 𝜋 ∗ R(3) =

2p2 v2(1 + 𝛽)2

3(3c1 + 3c2 + 4s) ,

n∗(3) = pv(1 + 𝛽)

3c1 + 3c2 + 4s , 𝜋

∗ (3) = p(1 − p)

+ p2 v2(1 + 𝛽){(3 − 6𝛽)c1 + (3 − 6𝛽)c2 + (5 − 7𝛽)s}

3(3c1 + 3c2 + 4s)2 .

Comparing the equilibrium number of items shown in Proposition

1 and Lemmas 3 and 4, we find the relation n∗(2) < n ∗ (3) < n

∗. There-

fore, it follows that, relative to the linear fee, the quadratic-type fee

structures further relax the intensity of variety competition between

manufacturers. This is intuitive because a quadratic fee is very inef-

ficient for manufacturers, because it decreases their motivation to

enhance their varieties in competition with each other. However, note

that the equilibrium number of items under Fee Structure 2 is less

than that under Fee Structure 3. This might seem unintuitive because

under Fee Structure 3, manufacturers must pay the retailer an addi-

tional fee that is proportional to the rival's number of items. The key

to understanding this is the retailer's pricing. Indeed, Fee Structure

3 is the better fee structure for the retailer, because it can compen-

sate for the cost C2(n1, n2) (for communicating between-firm product differences) by charging manufacturers a fee that is proportional to

the rival's number of items. This efficiency enables the retailer to set

the unit fee 𝜙(3) at a lower level. Therefore, manufacturers can effi-

ciently increase the number of items they sell. In contrast, under Fee

Structure 2, the retailer chooses a higher unit fee owing to its inef-

ficiency, which, in turn, compels the manufacturers to be inefficient.

Thus, the number of items offered to the market is suppressed.

As can be easily inferred from the above discussion, the efficiency

of the fee structure for the retailer directly determines its profitability.

In the following proposition, we formally state the relations between

the profits earned by the retailer in equilibrium under the three fee

structures examined.

Proposition 4. We necessarily have 𝜋∗ R > 𝜋∗

R(3) > 𝜋 ∗ R(2). Therefore,

the simple linear fee is the most profitable for the retailer of the three

fee structures examined.

Finally, note that, apart from its profitability, Fee Structure 3 might

be impractical because manufacturers incur a cost arising from the

rival's variety, as if being forced to pay a tax. However, we need not

concern ourselves with this matter. Proposition 4 shows that although

this structure is seemingly efficient, the retailer's best option is actually

to use the simple linear fee.

6 C O N C L U S I O N

In this study, we explored the strategic effect of an in-store advertis-

ing service provided by a retailer in the presence of product variety

competition between manufacturers. Although the recent progress of

information and communication technology has increased the abili-

ties of manufacturers to enhance their product varieties, this causes

intense variety competition between them. In addition, consumers face

an excessive variety of products, which confuses them when trying to

choose those that best fit their needs. Thus, they must incur tempo-

ral or psychological costs when comparing and evaluating products,

particularly those provided by different manufacturers. In such circum-

stances, retailers are expected to help shoppers select their desired

products by utilizing their neutral position. Thus, if a retailer provides

an in-store advertising service that adequately explains to shoppers

the differences between products on sale, this can not only benefit the

retailer but can also improve the relation between the parties in the

supply chain. On the basis of this motivation, we constructed a simple

game-theoretic model to investigate the effectiveness of an in-store

advertising service provided by a monopolistic retailer. In this model,

the retailer charges manufacturers a fee proportional to the number

of items they introduce, while offering the service to consumers for

free. This model is evident in several real-world online marketplaces.

Our equilibrium analysis showed that the retailer's in-store adver-

tising service contributes to forming mutually beneficial relations

between all of the channel members. The retailer can benefit from

setting the unit fee for the service at an intermediate level. This, in

turn, relaxes the intense competition between manufacturers, which

means they earn higher profits than when they advertise their items

KOBAYASHI AND MATSUBAYASHI 239

to consumers directly, unless they are sufficiently differentiated and

the cost of explaining the between-firm product differences is very

low. We also show that the retailer's service can reduce the social

inefficiency caused by an excessive number of items and that this

reduction can be socially beneficial. We further find that a simple lin-

ear fee structure (such as those of Amazon and eBay) outperforms

quadratic fee structures, even though the latter seem to represent

efficient pricing in that they reflect the fact that the cost of explaining

the differences between products increases convexly with the number

of items offered to the market.

These results offer several new managerial insights. First, a retailer

should establish an in-store service to help shoppers compare multiple

products, particularly when dealing with products in a highly compet-

itive and, thus, less differentiated category (e.g., consumer electronics

or beverages). Within such categories, although highly symmetric man-

ufacturers must engage in intense competition, consumers experience

confusion when comparing many similar products, which implies a

higher cost for explaining between-firm product differences. How-

ever, by implementing the type of in-store advertising service modeled

here, the retailer can profitably resolve both problems. In addition, our

result that the simple linear fee is superior has practical implications,

as several retailers such as Amazon and eBay have already found.

Fortunately, the number of products in a market can be socially opti-

mized, as shown in our proposition that for a market with an excessive

number of items on offer, the in-store service can reduce the resulting

inefficiency.

We should mention several further implications of our results. First,

we considered a monopolistic retailer that can offer an in-store adver-

tising service. Although competition between retailers is realistic, we

expect that as retailers become more competitive, the coordination

effect of an in-store service vanishes because the unit fee is likely to be

zero in equilibrium. In this sense, a monopolistic retailer is preferred,

which implies that an in-store service should be highly differentiated

from rivals' services. Furthermore, in practice, manufacturers might

be unaware of or pay little attention to the costs of eliminating con-

sumers' confusion. However, our result suggests that in such cases,

particularly if this leads to intense variety competition between man-

ufacturers, a retailer should consult manufacturers about eliminating

their inefficiencies due to this cost by introducing an in-store advertis-

ing service. In these normative senses, our results could have practical

implications.

However, much of the previous literature on consumers' purchasing

behavior considers the purchase-decision process in more detail than is

modeled in our study. We assume that the in-store advertising service

can completely explain the differences between all of the products

on offer by incurring convex costs and, as a result, consumers' utility

increases linearly with the number of items on sale. However, for

example, if we assume that consumers always have consideration sets,

as discussed in Section 2 and that the retailer's in-store service can only

eliminate the consumers' confusion to a certain extent, then the utility,

demand, and cost functions might all change. Although we believe that

our basic analysis of a simple model provides relevant insights about

the strategic implications of retailers' in-store advertising services,

further refinements to the model and the analysis pose challenges for

future research.

E N D N O T E S 1 The well-known experimental study conducted by Iyengar and Lepper

(2000) shows that ‘‘[p]eople are more likely to purchase gourmet jams or chocolates or to undertake optional class essay assignments when offered a limited array of 6 choices rather than a more extensive array of 24 or 30 choices.’’

2 In this sense, the costs discussed here can also be interpreted as those incurred for sales efforts beyond those of advertising. However, throughout this paper, we describe these costs in the context of an advertising effort to avoid confusion. We thank the anonymous referee for suggesting this viewpoint.

3 We use the terms ‘‘item’’ and ‘‘product’’ interchangeably throughout this paper.

4 Many existing studies on platform markets, including Armstrong (2006), Hagiu (2009), Choi (2010), Li et al. (2010), and Maruyama and Zennyo (2015), employ similar settings, where the consumer's utility increases with the number of contents.

5 Even if we consider firm-level price competition, our results do not change qualitatively. The details are available from the authors upon request.

6 Specifically, for i = 1, 2, when only the fraction r ∈ (0, 1) of the unit retail price is transferred to the manufacturers, then the equilibrium numbers of items are rn∗

i , where n∗

i are the equilibrium numbers

obtained in Proposition 1. The complete analysis is available from the authors upon request.

A C K N O W L E D G E M E N T S

We thank the editor and anonymous referees for helpful comments.

O R C I D

Nobuo Matsubayashi https:/ / orcid.org/ 0000- 0001- 7743- 362X

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S U P P O R T I N G I N F O R M A T I O N

Additional supporting information may be found online in the

Supporting Information section at the end of the article.

How to cite this article: Kobayashi H, Matsubayashi N.

The strategic effect of retailers' in-store advertising ser-

vices under product variety competition. Manage Decis Econ.

2019;40:232–242. https:/ / doi.org/ 10.1002/ mde.2994

A P P E N D I X A

A.1 Proof of Proposition 1

For Equation 8, we have 𝜕2𝜋1

𝜕n2 1

= 𝜕 2𝜋2

𝜕n2 2

= −2s < 0. As a result, the profit function 𝜋i(i = 1, 2) is strictly concave in ni . Therefore, for any given 𝜙 > 0, the best response of firm i is derived by solving 𝜕𝜋i

𝜕ni = 0 for ni ,

which is independent of the rival's decision:

n1 = max {

pv(1 + 𝛽) − 𝜙 2s

, 0

} , n2 = max

{ pv(1 + 𝛽) − 𝜙

2s , 0

} .

When 𝜙 > pv(1 + 𝛽), both n1 and n2 are zero. However, the retailer then does not gain a positive profit, which implies that we must have

𝜙 ≤ pv(1 + 𝛽) in equilibrium. Therefore, we may assume the interior solution

n1 = n2 = pv(1 + 𝛽) − 𝜙

2s . (A1)

By substituting these into (6), we can rewrite the retailer's profit

function as

𝜋R(𝜙) = (pv(1 + 𝛽) − 𝜙){2s𝜙 − (c1 + c2)(pv(1 + 𝛽) − 𝜙)}

2s2 .

The second derivative of 𝜋R with respect to 𝜙 is

𝜕2𝜋R

𝜕𝜙2 = −

c1 + c2 + 2s s2

< 0,

which implies that 𝜋R is strictly concave in 𝜙. Therefore, by solving 𝜕𝜋R

𝜕𝜙 = 0 for 𝜙, we have

𝜙 ∗ =

pv(1 + 𝛽)(c1 + c2 + s) c1 + c2 + 2s

.

Because it clearly follows that 𝜙∗ ≤ pv(1 + 𝛽), this 𝜙∗ is optimal. Then, we can obtain the equilibrium outcomes by substituting 𝜙∗ into (A1) to

obtain the equilibrium numbers of items and then substituting these

values into (6) and (8).

A.2 Proof of Lemma 1

For Equation 9, we have 𝜕2𝜋′

1

𝜕n2 1

= 𝜕2𝜋′

2

𝜕n2 2

= −2c1 − 2s < 0. Thus, the profit function 𝜋′

i (i = 1, 2) is strictly concave in ni . Therefore, the best

response function of firm i is derived by solving 𝜕𝜋′

i

𝜕ni = 0 for ni :

KOBAYASHI AND MATSUBAYASHI 241

R1(n2) = max {

pv(1 + 𝛽) − 2c2 n2) 2(c1 + s)

, 0

} ,

R2(n1) = max {

pv(1 + 𝛽) − 2c2 n1) 2(c1 + s)

, 0

} .

Therefore, it can be easily verified that for s > c2 − c1, R1 and R2 intersect only once, at (n1, n2) =

( pv(1+𝛽)

2(c1+c2+s) ,

pv(1+𝛽) 2(c1+c2+s)

) . In addition,

these values of n1 and n2 are positive. The equilibrium profit follows

after substituting these values into (9).

A.3 Proof of Proposition 2

By Proposition 1 and Lemma 1, the difference between 𝜋∗ and �̄� is

𝜋 ∗ − �̄� =

p2 v2(1 + 𝛽){(c1 + c2 + s)2(s − (2c1 + 2c2 + 3s)𝛽) − (c1 + c2 + 2s)2(c1 + s − (c1 + 2c2 + s)𝛽)} 4(c1 + c2 + 2s)2(c1 + c2 + s)2

. (A2)

We can see that the denominator is positive. Thus, let S(s) ≡ (c1 + c2 + s)2(s − (2c1 + 2c2 + 3s)𝛽) − (c1 + c2 + 2s)2(c1 + s − (c1 + 2c2 + s)𝛽) in the numerator of (A2). Then, we have 𝜕S

𝜕s = 3(𝛽 − 3)s2 + (−12c1 +

4(2𝛽 − 1)c2)s − 4(c1 + c2) + 2𝛽(c22 − c 2 1 ), and for higher c2 (relative

to c1 ) and 𝛽, this is positive. This implies that S is increasing on s

and, thus, S is minimized at s = c2 − c1 . Then, we directly have S(s = c2 − c1) = c2((3𝛽 − 1)c21 − 2(7𝛽 − 1)c1 c2 + (7𝛽 − 5)c

2 2 ), which is

also positive for higher c2 (relative to c1 ) and 𝛽. Therefore, when c2 is sufficiently higher relative to c1 , and 𝛽 is sufficiently higher, S is

positive for any s > c2 − c1 . This ensures 𝜋∗ > �̄�.

A.4 Proof of Lemma 2

We first verify the strict concavity of W. The Hessian matrix of W is

⎛⎜⎜⎝ 𝜕2 W 𝜕n2

1

𝜕2 W 𝜕n1𝜕n2

𝜕2 W 𝜕n2𝜕n1

𝜕2 W 𝜕n2

2

⎞⎟⎟⎠ = (

v2(1 + 𝛽) − 2(c1 + s) −v2𝛽 − 2c2 −v2𝛽 − 2c2 v2(1 + 𝛽) − 2(c1 + s)

) .

To see the strict concavity, it suffices to check the following conditions: 𝜕2 W 𝜕n2

1

< 0, 𝜕 2 W 𝜕n2

2

< 0, and 𝜕 2 W 𝜕n2

1

𝜕2 W 𝜕n2

2

− 𝜕 2 W

𝜕n1𝜕n2

𝜕2 W 𝜕n2𝜕n1

> 0. Using simple algebra,

it can be directly obtained that all of the conditions are satisfied under

the assumption that v2 < 2(c2−c1+s) 1+2𝛽

.

Thus, we next consider the first-order condition. By solving the

equation system 𝜕W 𝜕n1

= 0 and 𝜕W 𝜕n2

= 0, for n1 and n2 , we have

n̂(= n̂1 = n̂2) = v

2(c1 + c2 + s) − v2 .

Clearly, under the assumption of v2 < 2(c2−c1+s) 1+2𝛽

, n̂ is positive.

A.5 Proof of Proposition 3

By Proposition 1 and Lemmas 1 and 2, we obtain

n∗ = pv(1 + 𝛽)

2(c1 + c2 + 2s) , n̄ =

pv(1 + 𝛽) 2(c1 + c2 + s)

,

n̂ = v 2(c1 + c2 + s) − v2

.

Therefore, we clearly have n∗ < n̄. In contrast, we can derive

n∗ − n̂ = v{p(1 + 𝛽)(2(c1 + c2 + s) − v2) − 2(c1 + c2 + 2s)}

2(c1 + c2 + 2s)(2(c1 + c2 + s) − v2) ,

which is clearly positive for higher 𝛽. Finally, because W is strictly

concave, as shown in the proof of Lemma 2, the relation of n̂ < n∗ < n̄

implies W(n̂) > W(n∗) > W(n̄).

A.6 The proof of Lemma 3

As in the case of a linear fee (Structure 1), we can easily see that

an interior solution is ensured for the second-stage game. Therefore,

by solving 𝜕𝜋1

𝜕n1 = 0 and 𝜕𝜋2

𝜕n2 = 0 for n1 and n2 , we have a symmetric

equilibrium in terms of the numbers of items:

n(2) = pv(1 + 𝛽) 2(𝜙 + s)

. (A3)

By substituting this into (12), we can rewrite the retailer's profit

function as

𝜋R(2)(𝜙) = p2 v2(1 + 𝛽)2(𝜙 − c1 − c2)

2(𝜙 + s)2 .

It is straightforward to see that this 𝜋R is strictly concave in 𝜙.

Therefore, by solving 𝜕𝜋R

𝜕𝜙 = 0, we have the optimal level

𝜙 ∗ (2) = 2c1 + 2c2 + s.

Then, we can obtain the equilibrium outcomes by substituting 𝜙∗(2) into

(A3) to obtain the equilibrium number of items and then substituting

this value into (12) and (14).

A.7 Proof of Lemma 4

As in the previous cases (Structures 1 and 2), we can easily see that

an interior solution is ensured for the second-stage game. Therefore,

by solving 𝜕𝜋1

𝜕n1 = 0 and 𝜕𝜋2

𝜕n2 = 0 for n1 and n2 , we have a symmetric

equilibrium in terms of the numbers of items:

n(3) = pv(1 + 𝛽) 3𝜙 + 2s

. (A4)

By substituting this into (13), we can rewrite the retailer's profit

function as

𝜋R(3)(𝜙) = 2p2 v2(1 + 𝛽)2(2𝜙 − c1 − c2)v2

(3𝜙 + 2s)2 .

It is straightforward to see that this 𝜋R is strictly concave in 𝜙.

Therefore, by solving 𝜕𝜋R

𝜕𝜙 = 0, we have the optimal level

𝜙 ∗ (3) =

3c1 + 3c2 + 2s 3

.

Then, we can obtain the equilibrium outcomes by substituting 𝜙∗(3) into

(A4) to obtain the equilibrium number of items and then substituting

this value into (13) and (15).

A.8 Proof of Proposition 4

By Proposition 1 and Lemma 4, the difference between the retailer's

equilibrium profits for Structures 1 and 3 is

242 KOBAYASHI AND MATSUBAYASHI

𝜋 ∗ R − 𝜋∗

R(3) = p2 v2(1 + 𝛽)2

2(c1 + c2 + 2s) −

2p2 v2(1 + 𝛽)2

3(3c1 + 3c2 + 4s)

= p2 v2(1 + 𝛽)2(5c1 + 5c2 + 4s)

6(c1 + c2 + 2s)(3c1 + 3c2 + 4s) > 0.

Thus, 𝜋∗ R > 𝜋∗

R(3) always holds. In addition, by Lemmas 3 and 4, the

difference between the equilibrium retailer's profits for Structures 2

and 3 is

𝜋 ∗ R(2) − 𝜋

∗ R(3) =

p2 v2(1 + 𝛽)2

8(c1 + c2 + s) −

2p2 v2(1 + 𝛽)2

3(3c1 + 3c2 + 4s)

= − p2 v2(1 + 𝛽)2(7c1 + 7c2 + 4s)

24(c1 + c2 + s)(3c1 + 3c2 + 4s) < 0,

which implies that 𝜋∗ R(3) > 𝜋

∗ R(2) always holds. Therefore, we necessarily

have 𝜋∗ R > 𝜋∗

R(3) > 𝜋 ∗ R(2).

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