ISSN (Print) 0473-453X

Discussion Paper No. 1123

ISSN (Online) 2435-0982

COMPETITIONBETWEENPHYSICAL AND ELECTRONICCONTENT RETAILERS
Yuta Kittaka
Noriaki Matsushima
Fuyuki Saruta

March 2021

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan

Competition between physical and electronic content retailers∗
Yuta Kittaka†

Noriaki Matsushima‡

Fuyuki Saruta§

March 11, 2021

Abstract
We investigate a model in which a monopoly supplier distributes two types of its
product through a traditional retailer with a wholesale price contract and an online
retailer with an agency contract. Because such an agency contract eliminates the
double marginalization problem, the online retailer has a cost advantage over the traditional retailer. Given the advantage of the online retailer, we also consider a possible
request by the traditional retailer: the retail price of the online retailer is not smaller
than the wholesale price for the traditional retailer. We obtain the following results.
An increase in the online retailer’s bargaining power over the supplier benefits the tworetailers but harms the supplier. Under the request to protect the traditional retailer,
the wholesale price is strictly higher than that in the baseline model. The retailers’ equilibrium prices are also strictly higher than those in the baseline model. The
request benefits the supplier and the online retailer, but harms the traditional retailer.
Keywords: Agency contract, Price–quantity competition, Dual-channel supply chain,
Royalty rate.
JEL Classification: L22, L13, C72, C78.

∗

We thank Masayoshi Maruyama and Yusuke Zennyo, as well as the seminar participants at Nanzan University. We gratefully acknowledge the financial support from JSPS KAKENHI grant numbers JP15H05728, JP17H00984, JP18H00847, JP18K01593, JP19H01483, JP19J10596, JP20H05631, andJP20J11411. The usual disclaimer applies.
†
Yuta Kittaka, Graduate School of Economics, Osaka University, 1-7 Machikaneyama-cho, Toyonakashi, Osaka, 560-0043. E-mail: kittaka@econ-io.jp.
‡
Noriaki Matsushima, Institute of Social and Economic Research, Osaka University, 6-1 Mihogaoka,
Ibaraki, Osaka 567-0047, Japan. E-mail: nmatsush@iser.osaka-u.ac.jp, ORCID: 0000-0002-7865-3875.
§
Corresponding author: Fuyuki Saruta, Graduate School of Economics, Osaka University, 1-7
Machikaneyama-cho, Toyonaka-shi, Osaka, 560-0043. E-mail: saruta@iser.osaka-u.ac.jp.

11Introduction

The recent advancement of online platforms facilitates selling digital content, including
books, games, movies, and music, and purchasing such content without leaving home. The
facilitation of selling and buying digital content is a competitive threat to the traditional
brick-and-mortar retailers handling physical content. For instance, in the US book industry, the sales share of e-books was about 20% in 2015 (Gilbert, 2015), and in 2018, 34% ofyounger consumers, aged 18 to 29, had read e-books in the previous 12 months (Pew Research Center, 2019). The penetration of devices for reading e-books, including e-readers
and tablet PCs, is increasing constantly (Deloitte, 2018). Therefore, we easily imagine
that the e-books market has a substantial market share. The flipside of the previous argument is that some consumers still prefer traditional paper books to e-books. Even forthe younger generation, at least half of consumers had not read e-books. Thus, consumers
still purchase both traditional paper books and e-books, depending on preferences, situations, and places (see, for instance, Bergström and Höglund (2020) for the recent trend in
e-books in Sweden). We can see such co-existence of physical and digital content in thegames, movies, and music industries.1 Therefore, it is reasonable to investigate a market
in which consumers can purchase both physical and digital content.
One advantage of distributing digital content over physical content is lower production costs. In addition to the cost advantage, the different contract types applied to online
and brick-and-mortar retailers can create advantages for online retailers. In the US bookindustry, brick-and-mortar book retailers employ standard wholesale price contracts, although some online retailers (e.g., Apple) use agency contracts. The latter form eliminates
the double-marginalization problem and allows the trading pair to be a quasi-integrated
firm. Those two advantages of online retailers cause the following additional threat to
traditional brick-and-mortar book retailers: online retailers’ prices for consumers can belower than the wholesale prices offered to those brick-and-mortar retailers.
The disadvantages mentioned above are reminiscent of the concern about price/marginsqueezes in a competitive market with a dominant vertically integrated firm (see, e.g.,
Bouckaert and Verboven, 2004) because nonintegrated firms cannot earn positive profits
if their retail prices are the same as that of integrated firms. Given the disadvantage ofbrick-and-mortar retailers over online retailers (quasi-integrated firms), brick-and-mortar
1

For example, see Capcom Co., Ltd. (2020), page 69, for recent trends and forecasts for the games

industry.

2

retailers may request that their upstream content providers avoid imposing wholesale
prices that are higher than the providers’ retail prices. The request is similar to theremedy in the context of price/margin squeezes. Following such requests, the content
providers may impose self-regulation such that the retail prices of the online retailer are
not lower than the wholesale prices for the brick-and-mortar retailers.
We investigate a model in which a monopoly supplier distributes two types of its
product through a traditional retailer with a wholesale price contract and an online retailer
with an agency contract. We also consider the impact of the self-regulation mentioned in
the previous paragraph on the three players and the consumer and total surpluses. In thebaseline model, we consider the following stage game. First, the supplier and the online
retailer negotiate the royalty rate through Nash bargaining, which is a key element in ourmodel. Second, the supplier unilaterally determines the wholesale price for the traditional
retailer. Third, observing the trading terms determined before, the traditional retailer
and the supplier simultaneously set their own strategic variables. By taking into accountthe nature of physical and digital content, we assume that the traditional retailer and the
supplier via the online retailer compete in quantity and price, respectively (e.g., a subgame
in Singh and Vives (1984)). In the self-regulation case, the supplier cannot set a retailprice that is lower than the wholesale price for the traditional retailer in the third stage.
The assumption of price–quantity competition is consistent with the standard view onwhen price and quantity are strategic variables of firms (e.g., the textbook by Belleflamme
and Peitz (2015), Section 3.3.3 on page 67). Belleflamme and Peitz (2015) mention thatwhen capacity is unlimited, assuming a firm is a price setter is appropriate; when capacity
is limited, assuming a firm is a quantity setter is appropriate. Case 3.4 on page 68 in
Belleflamme and Peitz (2015) explains the product characteristics change in the publishing industry: “it seems that the quantity competition model fits better with the batch
printing technology (because prices will adjust to sell the existing capacity) and the pricecompetition model with the POD technology (because quantity can be adjusted immediately at the announced prices)” (POD in the quotation is ‘publish on demand’). Thus,
we think that the market structure discussed in our paper properly captures the natureof product characteristics in real-world industries, including books, games, movies, andmusic.
We obtain the following results in the baseline model. The equilibrium royalty rate
has a positive correlation to the online retailer’s bargaining power over the supplier. An

3increase in the online retailer’s bargaining power over the supplier benefits the two retailers
but harms the supplier. The wholesale price for the traditional retailer can be higher thanthe online retailer’s retail price in equilibrium. We also obtain the following results in the
self-regulation case. The wholesale price is strictly higher than that in the baseline model.
The retail prices are also strictly higher than those in the baseline model. The retailprice of the online retailer is always binding by the constraint. Self-regulation benefits the
supplier and the online retailer but harms the traditional retailer. That is, the attempt toprotect the traditional retailer fails. The consumer and total surpluses are smaller thanthose in the baseline model. Therefore, we should regard suspiciously content suppliers(e.g., publishers, game producers) who employ the remedy discussed here using the excuse
that they attempted to protect traditional retailers using “fair trading terms.”
To understand the importance of assuming price–quantity competition in the selfregulation case, we consider a modified model in which the two retailers compete in priceinstead of through price–quantity competition. The price competition model differs fromthe main model as follows. The supplier can indirectly control the traditional retailer’squantity through its price, inducing the supplier to consider the wholesale revenue in theretail pricing stage. The supplier credibly sets the online retail price that is strictly higher
than the wholesale price under any degrees of bargaining power and product differentiation.
However, in the price–quantity competition, such a consideration for the wholesale revenue
in the retail pricing stage does not exist, and the supplier ignores the wholesale revenue
when it sets its retail price. In the modified model, self-regulation does not work becauseof the supplier’s less aggressive pricing policy in the downstream market. We can conclude
that price–quantity competition is crucial to obtaining the anti-competitive effect of selfregulation.
The remainder of this paper is organized as follows. Section 2 surveys the related
papers. Section 3 constructs the model. Section 4 analyzes the game and shows theresults. Section 5 analyzes the effect of self-regulation on retail prices. Section 6 discusses
the case in which two retailers compete in price and how contract forms influence firms’
profits. Section 7 offers concluding remarks.

4

2

Related Literature

There are a few papers discussing price–quantity competition with vertical relations (e.g.,Manasakis and Vlassis, 2014; Yang et al., 2015; Basak and Wang, 2016; Fanti and Scrimitore, 2019). We discuss two categories of papers whose market structure is the same asours: (i) endogenous choices of price and quantity in asymmetric downstream duopoly
models, (ii) optimal channel structures. The purposes of those papers, however, differ
from ours.
Fanti and Scrimitore (2019) extend Arya et al. (2008) to investigate price versus quantity competition in market structures similar to ours: a vertically integrated firm supplies
upstream inputs to an independent downstream firm, which is its downstream competitor,and each of them chooses price or quantity as its strategic variable before they compete in
the downstream market, as in Singh and Vives (1984) (see also Bylka and Komar (1976);
Reisinger and Ressner (2009), and the comprehensive survey of Tremblay and Tremblay(2019)). Their main themes are the endogenous choices of those strategic variables andthe implications of the results. The royalty rate and the self-regulation discussed in ourmodel are beyond the scope of their papers.
The model in the supplementary appendix in Lei (2019) is the closest to ours. The
market structures in her model and ours use price–quantity competition, as in Fanti and
Scrimitore (2019). The difference between her model and ours is threefold. First, the main
focuses of the two models are different. She investigates the optimal channel structure for amonopoly manufacturer, as in Chiang et al. (2003) and Arya et al. (2007). We investigate
the equilibrium royalty rate and the impact of self-regulation by an upstream firm, but
fix the dual-channel supply chain. Second, the properties of the realized royalty rates inthe two models differ from each other. The endogenous royalty rate in her model binds
at the exogenous upper bound because the retailer unilaterally sets the royalty rate. The
endogenous royalty rate in our model can range from 0 to 1 because we consider Nashbargaining. Third, self-regulation by the supplier is only discussed in our model. In thissense, we should regard our model as an extension of price–quantity competition in a
direction different from her extension.
Similar to the discussion of price/margin squeezes (see, for instance, the recent survey
by Jullien et al. (2014)), we also consider (self-)regulation in which the supplier’s retailprice is not lower than the wholesale price for the traditional retailer. An interesting5

feature of the regulation is the following: self-regulation increases the wholesale price forthe traditional retailer as well as the supplier’s retail price. This feature has a detrimental
effect on the profit of the (nonintegrated) traditional retailer. The detrimental effect differsfrom the standard result in the literature regarding price/margin squeezes, which showsthat a ban on price squeezes is always preferable for downstream competitors throughlower wholesale prices or higher retail prices (Sidak, 2008; Choné et al., 2010; Petulowa
and Saavedra, 2014). Our contrasting result stems from the price–quantity competition.
When the supplier sets the retail price, it does not consider the wholesale revenue throughthe traditional retailer, the quantity setter. The lack of concern about the wholesalerevenue in the price-setting stage accelerates downstream competition. The self-regulation
mentioned above induces the supplier to set a higher wholesale price in order to commit
to setting a higher retail price in the downstream competition, mitigating the downstream
competition. Therefore, an increase in the wholesale price through the self-regulation does
not occur in the standard price competition because of indirect control.
Because online retailers with agency contracts are similar to store-within-store retail
formats, our paper complements the literature of store-within-store formats in traditional
retailers (Jerath and Zhang, 2010; Netemeyer et al., 2012). Our additional contribution
to the literature is twofold: (1) the endogenous choice of the royalty rate between the
supplier and the online retailer under Nash bargaining, which differs from Abhishek et al.
(2016), Tian et al. (2018), and Zennyo (2019, 2020), also considering endogenous choicesof royalty rates; (2) self-regulation restricting the pricing policy of the supplier. Those
two discussions also contribute to the literature on agency contracts (e.g., Foros et al.,2017; Johnson, 2017; Tan and Carrillo, 2017; Maruyama and Zennyo, 2020). Although thethemes of those papers differ from ours, the market structure of Zennyo (2019) partiallyoverlaps with that of ours. We discuss the difference between Zennyo (2019) and our paper
in Section 6.

3

The Model

A monopolistic supplier produces a good and distributes it through two retailers: (i)a traditional retailer who resells a physical version of the good and (ii) an e-commerce
retailer who handles a digital version of the good. For the sake of clarity, we focus ona book market where a monopolistic publisher publishes a book and sells it through a6

traditional bookstore (henceforth referred to as T -retailer) and an e-commerce platform(E-retailer). T -retailer sells a traditional paper version of the book (hereafter, we refer toit as paper book), and E-retailer sells an electronic version of the book (e-book).
First, we assume that the distribution processes of the paper book and the e-book are
different. For the paper book, T -retailer determines its sales quantity, qt , because it must
consider the stock of the book. By contrast, for the e-book, the monopolistic supplierand E-retailer sign an agency contract that allows the supplier to set its retail price, pe ,directly without worrying about stock of the book. This assumption is consistent with thestandard view on when price and quantity are strategic variables of firms (e.g., Belleflamme
and Peitz (2015), Section 3.3.3 on page 67 and the discussion in Section 1). To describe
the price–quantity competition in the retail market, we use the demand system in Singhand Vives (1984) and Fanti and Scrimitore (2019). The inverse demand functions for thepaper book and the e-book are:pt = α − qt − γqe ,(1)pe = α − qe − γqt ,(2)where α(> 0) is a positive constant and γ ∈ [0, 1) is the degree of product substitutability
between the two products. Hereafter, the subscripts t and e denote the T -retailer and Eretailer, respectively. Note that the demand system means that the product characteristicsof the paper book and the e-book generate horizontal product differentiation.
The monopolistic supplier transacts with T -retailer and E-retailer with a wholesale
contract and an agency contract, respectively. With a wholesale contract, the supplierdetermines its wholesale price before T -retailer sets its sales quantity, qt . With an agency
contract, the supplier sets the retail price of the e-book, pe , directly, and the supplier andE-retailer split sales revenues according to a royalty rate, r, that is determined before thesupplier determines pe . Concretely, the supplier pays r times its revenue earned via the Eretailer’s channel to the E-retailer. We believe that this assumption fits the reality wheremost publishers adopt wholesale contracts with brick-and-mortar bookstores, and thosepublishers adopt agency contracts with online retailers to sell e-books. Dantas et al. (2014)
and Gilbert (2015) describe the pricing arrangements between publishers and retailers inbook industries.
For notational simplicity, we assume that their marginal costs of producing or selling7the books are zero. If the marginal cost of producing one unit of the paper book is positive,
an equilibrium wholesale price is more likely to be higher than an equilibrium supplier’s
retail price. Therefore, the assumption on the marginal costs is not restrictive in our case.
The profits of the supplier and the retailers are:πs = wt qt + (1 − r)pe qe = wt qt + (1 − r)pe (α − γqt − pe ),πt = (pt − wt )qt = ((1 − γ)α + γpe − (1 − γ 2 )qt − wt )qt ,(3)πe = r pe qe = r pe (α − γqt − pe ),where the subscript s represents the supplier. For the royalty rate, r, we assume that
it is determined by bargaining between the supplier and E-retailer in advance, given the
E-retailer’s bargaining power over the supplier is β ∈ (0, 1).
In sum, the timing of the game is as follows.
Stage 1. The supplier and E-retailer determine the royalty rate, r, through bargaining.
Stage 2. The supplier sets a wholesale price, wt , for T -retailer.
Stage 3. T -retailer and the supplier choose its sales quantity, qt , and the price of the ebook, pe , simultaneously.
We solve by backward induction.

4

Analysis

In this section, we analyze the baseline model.

4.1

Stage 3To begin with, we derive the results of Stage 3. In this stage, T -retailer sets qt and the
supplier sets pe simultaneously. They maximize their profits expressed in (3) given thewholesale price, wt , and the royalty rate, r. The first-order conditions of T -retailer andthe supplier are:∂πt
= (1 − γ)α + γpe − 2(1 − γ 2 )qt − wt = 0,∂qt

∂πs
= (1 − r)(α − γqt − 2pe ) = 0. (4)∂pe∂πs /∂pe in (4) gives us two remarks on the pricing of the supplier. First, it does notinternalize the profit through the wholesale price wt , leading to fiercer competition in the8downstream market. The discrepancy between the internalization and the maximization
stems from the price–quantity competition discussed here. If the strategic variable of T retailer is also price (say pt ), T -retailer’s quantity is a function of pt and pe (say qt (pt , pe ))and then the supplier indirectly takes into account the wholesale profit, wt qt (pt , pe ), mitigating the discrepancy. Second, the supplier does not care about the royalty rate, r. As
the royalty rate increases, the discrepancy mentioned above becomes serious.
From (4), we obtain the optimal quantity and price:α(2 − γ) − 2wt
qt (wt ) =,4 − 3γ 2()
α 2 − γ − γ 2 + γwt
pe (wt ) =.
4 − 3γ 2(5)We can check that ∂qt (wt )/∂wt < 0 and ∂pe (wt )/∂wt > 0; that is, T -retailer reduces its
sales quantity of the paper book and the supplier raises its retail price for the e-book when
the wholesale price of the paper book increases. Therefore, the supplier can intensify or
weaken the retail competition by adjusting the wholesale price.

4.2

Stage 2

In Stage 2, given the quantity and price in (5), the supplier chooses the optimal wt thatmaximizes its profit. The supplier tries to balance the wholesale revenue of the paper bookand the sales revenue of the e-book.2 The optimal wholesale price is:{}α 8 − 4 rγ − 2(4 − r)γ 2 + (1 + 2 r)γ 3
wt (r) =.
2 {8 − γ 2 (7 − r)}(6)

From (6), it is straightforward that ∂wt (r)/∂r < 0. If, for example, the supplier’s shareof the e-book’s revenue decreases, the supplier places weight on the wholesale revenue ofthe paper book and lowers the wholesale price to intensify the downstream competition.

4.3

Stage 1

At last, in Stage 1, expecting the results that we have seen so far, the supplier and Eretailer negotiate over the royalty rate, r. For simplicity, we assume that E-retailer’s
outside option is zero. However, we assume, if the negotiation breaks down, the suppliersells the paper book only through T -retailer. At that time, the supplier sets wto ≡ α/22This trade-off between the two sources of revenue is similar to that of vertically integrated producers(VIP) who consider both wholesale revenue from independent retailers and sales revenue of their integrated
retailers (see, e.g., Arya et al. (2008) and Arya and Mittendorf (2018)).

9and T -retailer chooses qto = α/4, where the superscript o indicates the case in which the
supplier executes its outside option. Therefore, the outside option of the supplier is:
Os =

α2
.
8

(7)

The equilibrium royalty rate, r∗ , solves the following problem,max [πs (r) − Os ]1−β [πe (r)]β ,

(8)

{
(
) }
α2 12 − 8γ − 3γ 2 − 4 2 − γ − γ 2 r
πs (r) =,4 {8 − (7 − r)γ 2 }

(9)

r

where

and
πe (r) =()2
α2 8 − 2γ − 5γ 2 r
4 {8 − (7 − r)γ 2 }2

.

(10)

We represent the equilibrium royalty rate in the following proposition.
Proposition 1 In equilibrium, as a result of their Nash bargaining, the supplier andE-retailer set the royalty rate as:
r∗ =

{
1
−(8 − 2γ − 5γ 2 )2 + βγ 2 (16 − 16γ + γ 2 )βγ 2 (16 − 8γ − 7γ 2 )} (11)√
22
2
2
2+ (8 − 2γ − 5γ ) (8 − 2γ − 5γ ) − 2(1 − β)βγ (16 − 16γ + γ ) .

Hereafter, the superscript ‘∗’ represents the equilibrium outcome in the baseline model.
We obtain the equilibrium profit of the supplier, that of T -retailer, and that of E-retailer,
πs∗ , πt∗ and πe∗ , respectively. The other variables such as qi∗ , p∗i for i = t, e, and wt∗ are also
derived and shown in the Appendix.
The simple but tedious partial derivatives of r∗ with respect to β and γ respectively
lead to ∂r∗ /∂β > 0 for any β and γ and ∂r∗ /∂γ < 0 if β < 1/4 or if γ < 4/5 (sufficient conditions). The former outcome is intuitive in that the stronger bargaining powerof E-retailer leads to its higher profit share. We explain the latter complex outcome.
The royalty rate r is based on the additional contribution of E-retailer, which is related
to the two channels’ relative profitabilities. An increase in γ has two contrasting effects: (i) accelerating retail competition, which diminishes E-retailer’s profitability, and(ii) enhancing the direct channel advantage of E-retailer because of the nonexistence of10

double-marginalization. The mixture of the two effects causes the nonmonotonicity of∂r∗ /∂γ. Similarly, the signs of ∂pe∗ /∂γ and ∂wt∗ /∂γ are not uniquely determined.
Comparing the equilibrium outcomes, we obtain the following proposition.
Proposition 2 In the equilibrium of the baseline model, the supplier may set the retailprice of the e-book below the wholesale price of the paper book depending on β and γ, thatis,wt∗ > p∗e120 < β ≤and 0 < γ < 1, or
47
√
if
1
4 4 − 9β + 6β 2 − 8β12
 < β < and 0 < γ <
.
47
2
4−β

(12)

The supplier may implement below-wholesale-price retail pricing when E-retailer’s bargaining power, β, is less than half and the degree of substitution, γ, is less than the certain
threshold value. A small value of β means that the supplier’s bargaining power over Eretailer is strong, and therefore (1 − r∗ ) is large. At that time, the supplier prioritizes thesales revenue of the e-book, (1 − r∗ )pe qe , over the wholesale revenue of the paper book,wt qt . The supplier tries to weaken the degree of competition and earn larger sales revenue
from the e-book by raising both wt and pe . Because the increase in wt is greater thanthat of pe , Proposition 2 holds when β is small. We will examine the partial derivativesof several parameters including wt∗ and p∗e with respect to β in the next subsection.
A small value of γ corresponds to the situation where the retail competition is moderate. This case also makes the supplier focus on its sales revenue from the e-book and islikely to cause the implementation of below-wholesale-price retail pricing.

4.4

Effects of countervailing power

To take a more in-depth look at the equilibrium characteristics of the baseline model, we
analyze how a change in β affects the equilibrium results in this subsection. We derive
the following proposition.
Proposition 3 An increase in E-retailer’s bargaining power lowers the retail price of thee-book. Moreover, this increases T -retailer’s profit as well as E-retailer’s profit; however,it reduces the supplier’s profit. Specifically,
∂p∗e
∂wt∗
∂πt∗
∂πe∗
∂πs∗
< 0,
< 0,
> 0,
> 0,
< 0.
∂β
∂β
∂β
∂β
∂β

(13)

First, we can confirm that countervailing power leads to a lower retail price in our model.
11Second, it may be more surprising that T -retailer improves its profit from an increase of
E-retailer’s bargaining power. These two effects arise from the supplier’s reaction to anincrease in β. In the previous subsection, we examined the supplier’s action when β issmall. Now, when β increases, the supplier places more weight on the wholesale revenueof the paper book over the retail revenue of the e-book. As a result, the supplier lowers
both pe and wt , that is, ∂p∗e /∂β < 0 and ∂wt∗ /∂β < 0.3 Even though the retail price ofthe paper book, pt , also decreases, both (pt − wt ) and qt increase. Consequently, T -retailer
can earn more profit when E-retailer’s bargaining power becomes strong.
As an aside, in addition to the supplier’s profit, total sales of the e-book decrease inβ, specifically, ∂p∗e qe∗ /∂β < 0. In our model, an increase in E-retailer’s bargaining power
does not promote e-book sales, but rather suppresses e-book sales because, for its profit,
the supplier comes to depend more on the wholesale revenue of the paper book when β
becomes large.

5Effects of self-regulation on below-wholesale-price retail
pricing

Proposition 2 in the previous section shows the possibility that the wholesale price forT -retailer is higher than the retail price of E-retailer even if we have assumed that themarginal costs of the two books are zero. The higher wholesale price causes T -retailer
to complain that the supplier’s pricing policy significantly limits the competitiveness ofT -retailer in the retail market.
In this section, we consider a simple way to escape the imbalance between the wholesale
price and the retail price of E-retailer, by examining the idea in the context of price/marginsqueezes (Bouckaert and Verboven, 2004; Jullien et al., 2014). We impose on the supplierthe following self-regulation regarding wt and pe : wt ≤ pe , which prevents the supplierfrom setting a wt that is higher than pe . We will derive new equilibrium results with thisself-regulation and compare them with those of the baseline model.
3This mechanism is very similar to those revealed in Chen (2003) and Matsushima and Yoshida (2018).

In their papers, a supplier, which deals with a dominant retailer and fringe retailers under wholesale
contracts, responds to an increase in the dominant retailer’s bargaining power by lowering the wholesale
price for fringe retailers to boost its sales through the fringe retailers.

12

5.1

Results under self-regulation

In the same vein as the baseline model, we derive a subgame perfect Nash equilibrium bybackward induction. After this, we focus on the case when β = 1/2 to derive a uniqueequilibrium. By comparing the results with those of the baseline model, we first derive
the following proposition about the equilibrium prices.
Proposition 4 In the equilibrium of the self-regulated supplier case,• the retail price of the e-book is set equal to the wholesale price of the paper book;• the wholesale price is higher than that of the baseline model;• the retail prices are also higher than those of the baseline model.
Specifically, for γ ∈ (0, 1),RpR
e = wt =α> wt∗ ,
2

(14)

∗
R
∗
pR
e > pe and pt > pt , where the superscript ‘R’ represents the equilibrium outcome in the

self-regulated supplier case.
Proposition 4 tells us that the regulation, which seemingly lowers the wholesale price
wt , has anti-competitive effects on the retail competition. The supplier anticipates the
expected outcome of Stage 3, in which the wholesale price set in Stage 2 is the lower
bound of its retail price set in Stage 3. Setting a higher wholesale price allows the supplier
to commit itself to set a high retail price of the e-book in Stage 3.
Next, we check the effects of the regulation on the firms’ profits.
Proposition 5 The supplier’s self-regulation, wt ≤ pe ,• increases the profit of the supplier and that of E-retailer;• decreases the profit of T -retailer.
That is, for γ ∈ (0, 1),
πsR > πs∗ , πeR > πe∗ , πtR < πt∗ .

(15)With the self-regulation, the supplier and E-retailer earn more profit and T -retailer earns
less profit compared with the baseline model. These results may be apparent from Proposition 4. The self-regulated supplier can commit to set a higher pe when it sets a higher wt .

13

The supplier controls the competitive environment in the downstream market by setting ahigher wt , which leads to a weaker competitive environment for E-retailer. As a result, thesupplier and E-retailer can improve their profits. By contrast, because of such a higher
wholesale price, T -retailer cannot improve its profit although the downstream competition
becomes moderate.

5.2

Welfare analysis

Finally, we examine the effect of the self-regulation on social welfare and consumer surplus.
Before checking the welfare effect, we examine the effect on industry profits. Regarding
industry profits, we have the following result.
Proposition 6 The supplier’s self-regulation, wt ≤ pe , increases industry profits when
the degree of substitution is higher than the specific value, γ̂;πsR + πtR + πeR > πs∗ + πt∗ + πe∗ if γ̂ < γ < 1,(16)

where γ̂ ≃ 0.727. Otherwise, if 0 < γ < γ̂, industry profits decrease.
The self-regulation can be detrimental to the industry profit although it benefits the profits
of some firms.
Now we discuss consumer surplus and social welfare. We define consumer surplus as:

CS ≡∑ {∫ qii=t,e}(α − xi − γqj − pi ) dxi ,

(17)

0

where j ̸= i, and social welfare is
SW ≡ CS + πs + πt + πe .

(18)Comparing those of the baseline model and those of the self-regulated supplier case, we
can derive the following proposition.
Proposition 7 The supplier’s self-regulation, wt ≤ pe , decreases both consumer surplus
and social welfare, that is, for γ ∈ (0, 1),
CS ∗ > CS R ,SW ∗ > SW R .

14

(19)

In addition to the increase in the retail prices, the retail quantities are lower for mostvalues of γ. Therefore, the introduction of the regulation reduces the consumer surplus.
Moreover, even though the regulation may increase industry profits, it decreases social
welfare for all γ.

6Discussion

6.1

Price competition

We now develop a modified model in which the two retailers compete in price insteadof the price–quantity competition. When we introduce price competition into the retailmarket, (i) the supplier does not use below-wholesale-price retail pricing and (ii) the selfregulation, wt ≤ pe , does not have any effect on the outcome. To examine these results,
we solve the self-regulation case with price competition and show that the constraint is
not binding, wt < pe , in equilibrium.
The maximization problems of T -retailer and the self-regulated supplier in the retail
pricing stage are:max πt = (pt − wt )qt ,pt

max π̃s = wt qt + (1 − r)pe qe + λ(pe − wt ),
pe

(20)

where λ ≥ 0 is a Lagrange multiplier. The first-order conditions are:∂πtα(1 − γ) − 2pt + γpe + wt
=
= 0,
∂pt
1 − γ2∂ π̃sα(1 + γ)(1 − r) − 2(1 − r)pe + γ(1 + r)pt + γwt=− λ = 0.
∂pe
(1 − γ 2 )(21)Note that the supplier internalizes the wholesale revenue contrary to the price–quantity
model; the supplier’s first-order condition includes wt , although that in equation (4) does
not include. This consideration for the wholesale revenue in the retail pricing stage differsfrom the supplier’s pricing in the baseline model, and it increases the retail price of theE-retailer.4 From equation (21), we obtain optimal retail prices and the condition for the4

From equation (4), T -retailer’s reaction function in the baseline case is qt (pe ) = {(1 − γ)α + γpe −wt }/2(1−γ 2 ), and we can see that ∂wt qt (pe )/∂pe > 0 for all γ ∈ (0, 1). Therefore, the lack of consideration
for the wholesale revenue makes the supplier more aggressive, and decreases pe to less than the optimallevel for the supplier who cares about the wholesale revenue.

15

constraint, wt ≤ pe , is binding. The constraint is binding if and only if:λ=−α(2 − γ − γ 2 )(1 − r) + {4 − 3γ − γ 2 − (4 − γ − γ 2 )r}wt> 0,2(1 − γ 2 )(22)

in other words, if and only if
4 − 3γ − γ 2≡ r̄, and4 − γ − γ2α(2 − γ − γ 2 )(1 − r)
≡ w̄t .
wt ≥4 − 3γ − γ 2 − (4 − γ − γ 2 )r
0<r≤

(23)

We consider two cases in Stage 2: (Case A) wt ≥ w̄t (the constraint in Stage 3 can bebinding); (Case B) wt ≤ w̄t (the constraint in Stage 3 is binding if and only if wt = w̄t ).
Case A (wt ≥ w̄t )In this case, the optimal retail prices are:α(1 − γ) + (1 + γ)wt,
2
pbe (wt ) = wt .
pbt (wt ) =(24)

Taking these prices as given, the supplier sets wt to maximize its profit subject to theconstraint (23); the supplier solves the following maximization problem.

max πs (pbt (wt ), pbe (wt )) + λb (wt − w̄t ) ,
wt

(25)

where λb ≥ 0. Then, the optimal wholesale price and the Lagrange multiplier are:α(2 − γ − γ 2 )(1 − r)
= w̄t ,
4 − 3γ − γ 2 − (4 − γ − γ 2 )rαγ{1 − γ + r(1 + γ)}{3 + γ − r(2 + γ)}.
λb =4 − 3γ − γ 2 − (4 − γ − γ 2 )r
wtb =

(26)

We can also check that λb is always positive for any r ∈ (0, r̄]. In the range wt ≥ w̄t ,wt = w̄t is optimal in Stage 2.
Case B (wt ≤ w̄t )When wt ≤ w̄t , the constraint in Stage 3, wt ≤ pe , is not binding.

The optimal retail prices are derived by substituting λ = 0 into the first-order conditions
in equation (21):16α(2 − γ − γ 2 )(1 − r) + {2(1 − r) + γ 2 }wt,(4 − γ 2 )(1 − r)α(2 − γ − γ 2 )(1 − r) + γ(3 − r)wt
pne (wt ) => wt .
(4 − γ 2 )(1 − r)pnt (wt ) =(27)

Given these prices, the supplier solves the following problem,
max πs (pnt (wt ), pne (wt )) + λn (w̄t − wt ) ,
wt

(28)

where λn ≥ 0. We can obtain an interior solution in this case; the constraint, wt ≤ w̄t , isslack. The optimal wholesale price and the Lagrange multiplier are:wtn =α(1 − γ)(2 + γ)(1 − r){4 + 2γ(1 − r) − γ 2 + γ 3 }< w̄t ,
2{8(1 − r) − γ 2 (7 − 8r − r2 ) + γ 4 }(29)

λn = 0.
From the discussions in Cases A and B, the supplier prefers the interior solution in Case
B to the corner solution in Case A, which is the same as the corner in Case B. This result
implies that the supplier does not set wt that induces the retail price of the E-retailer, pe ,to be binding to wt . Therefore, the self-regulation, wt ≤ pe , does not affect the equilibrium
prices and profits in price competition. Furthermore, the retail price of the E-retailer is
not lower than the wholesale price of the T -retailer, wt , in equilibrium. We can conclude
that the price–quantity competition is crucial to obtaining the anti-competitive effect of
the self-regulation.

6.2

The contract between the supplier and E-retailer

We have assumed that the supplier and E-retailer are under agency contract because
major online retailers such as Amazon and Apple adopt agency contracts to distributee-books. Following the literature on agency contracts (e.g., Foros et al., 2017; Johnson,
2017; Tan and Carrillo, 2017; Zennyo, 2019; Maruyama and Zennyo, 2020), we investigate
which contract form is preferable for the suppliers and E-retailers to distribute the e-book:an agency contract or a wholesale contract.
We modify the model and assume the following timeline. In Stage 1, the supplier andE-retailer determine the wholesale price, we , through bargaining. Next, in Stage 2, thesupplier unilaterally sets a wholesale price, wt , for T -retailer. In Stage 3, T -retailer sets

17

its quantity, qt , and E-retailer sets its price, pe , simultaneously.5
By comparing the equilibrium profits of this wholesale-wholesale model with those of
the baseline model, we conclude that both the supplier and E-retailer prefer the agency
contract if the E-retailer’s bargaining power, β, is lower than β̂ ≃ 0.913 (a sufficientcondition). Their preferences for adopting an agency contract are perfectly consistentbecause of the nature of Nash bargaining: maximizing the total profits first, then splitting
them between the players.
Compared with the wholesale contract, the agency contract has an advantage and adisadvantage for their total profits: averting the double-marginalization problem and the
supplier’s internalization problem discussed in Subsection 4.1. The latter disadvantage
comes from the nature of the price–quantity competition: the supplier does not internalize
the wholesale revenue from T -retailer when it sets pe , and therefore it cannot coordinate
the revenue from E-retailer and that from T -retailer. However, if the supplier uses thewholesale contracts with both retailers, it will care about the two revenue sources. Whenβ is very high, we is at a very low level, implying that the double-marginalization problem
is negligible. Employing a wholesale contract is better for both the supplier and E-retailer
when β exceeds the threshold value β̂. On the other hand, the agency contract between
the supplier and E-retailer has a detrimental effect on T -retailer’s profit for any β and γ.
Related to the two discussions in this section, Zennyo (2019) focuses on the equilibrium
contractual form between the supplier and E-retailer in price–price competition under asimilar market structure. Here, we briefly describe his model and results, as well as thedifferences with our paper.
The channel structure is the same as in our paper: there is a monopoly supplier,a traditional retailer (T -retailer), and an e-commerce retailer (E-retailer). The gameproceeds as follows. In Stage 1, E-retailer unilaterally offers the royalty rate r to themonopoly supplier. In Stage 2, if the supplier accepts it, the two firms employ the agency
contract, in which the supplier sets the retail price of E-retailer in Stage 3, and the supplierunilaterally sets a wholesale price wt to T -retailer. Otherwise, the supplier unilaterally
sets wholesale prices wt and we for both retailers under the wholesale contract, in which
T -retailer sets its retail price in Stage 3. In Stage 3, T -retailer and the designated firm
under the contract offer their retail prices simultaneously.6
5

The timeline is consistent with the setting where the decisions on wt and we are in Stage 1, and the

supplier re-determines wt if the negotiation on we breaks down.
6

He also endogenizes the choice of whether the supplier uses E-retailer or not and shows that the18

In his study, because of the advantage of the agency contract, the supplier and Eretailer always employ the agency contract in equilibrium, and thus the realized market
situation becomes the same as ours.7 The differences between his study and ours are as
follows. First, T -retailer’s strategic variable is price in Zennyo (2019) and quantity in
our paper; second, the procedure for determining the royalty rate is a unilateral offer in
Zennyo (2019) and Nash bargaining in our paper; third, the main focus is the equilibrium
contract form in Zennyo (2019) and the market outcomes under price–quantity competitionand self-regulation in our paper. Despite these similar situations, we emphasize that ourdifferent (but natural) assumptions yield very different outcomes and rich implications.
In this sense, we believe that his study and our own complement each other.

7

Conclusion

Per the recent advancement of online platforms facilitating digital content sales, we investigate a model in which a monopoly supplier distributes two types of its product througha traditional retailer with a wholesale price contract and an online retailer with an agency
contract. The supplier and the online retailer negotiate the royalty rate through Nashbargaining. A notable feature of our model is assuming that the traditional retailer andthe supplier, via the online retailer, compete in quantity and price, respectively. We believe that the assumption of price–quantity competition is consistent with the standard
view on when price and quantity are strategic variables of firms (e.g., the textbook by
Belleflamme and Peitz (2015), Section 3.3.3 on page 67). We also discuss self-regulationby the supplier such that the retail price of the online retailer is not smaller than thewholesale price for the traditional retailer, seemingly helping the traditional retailer.
Our findings in the baseline model are the following. The equilibrium royalty rate has apositive correlation to the online retailer’s bargaining power over the supplier. An increasein the online retailer’s bargaining power over the supplier benefits the two retailers but
harms the supplier. The wholesale price for the traditional retailer can be higher than the
online retailer’s retail price in equilibrium. The additional discussion on self-regulation by
the supplier leads to the following results. The wholesale price is strictly higher than that
supplier always uses the retailer in addition to T -retailer in equilibrium.
7

In addition to the advantage of the agency contract discussed above, E-retailer prefers the contract

to the wholesale contract because he can obtain a first-mover advantage. See Johnson (2017) for moredetails.

19

in the baseline model. The retailers’ prices are also strictly higher than those in the baselinemodel. The retail price of the online retailer is always binding by the constraint. The selfregulation benefits the supplier and the online retailer but harms the traditional retailer.
The consumer and total surpluses are lower than those in the baseline model. The results
should be viewed with an eye toward whether content suppliers (e.g., publishers, gameproducers) employ the remedy discussed here with the excuse that they are attempting toprotect traditional retailers using “fair trading terms.”

20

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8

Appendix
Table 1: Equilibrium outcome for the baseline case and the selfregulation case when β = 1/2.
Baseline case{r

Self-regulation case√−(8−2γ−5γ 2 )2 +βγ 2 (16−16γ+γ 2 )+(8−2γ−5γ 2 )βγ 2}(8−2γ−5γ 2 )2 −2(1−β)βγ 2 (16−16γ+γ 2 )(16−8γ−7γ 2 )

1
2+γ

wt

α{8−4r∗ γ−2(4−r∗ )γ 2 +(1+2r∗ )γ 3 }2{8−γ 2 (7−r∗ )}

α
2

pe

α(8−2γ−5γ 2 )2{8−γ 2 (7−r∗ )}

α
2

pt

α{12−2γ(2+r∗ )−2γ 2 (6−r)+5γ 3 }2{8−γ 2 (7−r∗ )}α(3−γ)4qeα(8−2γ−5γ 2 )2{8−γ 2 (7−r∗ )}α(2+γ)
4(1+γ)qt

α{2−γ(2−r∗ )}8−γ 2 (7−r∗ )α4(1+γ)πsα2 {12−8r∗ −4γ(2−r∗ )−γ 2 (3−4r∗ )}4{8−(7−r∗ )γ 2 }α2 (2+γ)8(1+γ)

2

πe
πt
CS
SW

α2 (8−2γ−5γ 2 ) r∗4{8−(7−r∗ )γ 2 }2α28(1+γ)α2 (1−γ 2 ){2−γ(2−r∗ )}2{8−(7−r∗ )γ 2 }2α2 (1−γ)16(1+γ)α2 {80−16γ(4−r∗ )−4γ 2 (15+4r∗ −(r∗ )2 )+20γ 3 +25γ 4 }8{8−γ 2 (7−r∗ )}2

α2 {304−16γ(16−3r∗ )−4γ 2 (69+(r∗ )2 )+4γ 3 (49−16r∗ +2(r∗ )2 )+5γ 4 (7+4r∗ )}8{8−γ 2 (7−r∗ )}225

α2 (5+4γ+γ 2 )32(1+γ)2α2 (19+20γ+3γ 2 )32(1+γ)2