Discussion Paper No. 918

EXCLUSIVE CONTRACTS
WITH
COMPLEMENTARY INPUTS

Hiroshi Kitamura
Noriaki Matsushima
Misato Sato

January 2015
Revised September 2015

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

Exclusive Contracts with Complementary Inputs∗
Hiroshi Kitamura†

Noriaki Matsushima‡

Misato Sato§

August 25, 2015
Abstract
This study constructs a model of anticompetitive exclusive contracts in the presenceof complementary inputs. A downstream firm transforms multiple complementary inputs
into final products. When complementary input suppliers have market power, upstream
competition within a given input market benefits not only the downstream firm but also
complementary input suppliers by raising complementary input prices. The downstream
firm is thus unable to earn higher profits even when socially efficient entry is allowed.
Hence, the inefficient incumbent supplier can deter socially efficient entry by using exclusive contracts even in the absence of scale economies, downstream competition, andrelationship-specific investment.

JEL classifications code: L12, L41, L42, C72.
Keywords: Antitrust policy; Complementary inputs; Exclusive dealing; Multiple inputs.
∗

We thank Eric Avenel, Chiara Fumagalli, Toshihiro Matsumura, Patrick Rey, Dan Sasaki, and Tetsuya
Shinkai for their insightful comments. We also thank Akifumi Ishihara, Akira Ishii, Akihiko Nakagawa, Ryoko
Oki, Noriyuki Yanagawa, conference participants at EARIE 2014 (Bocconi University) and the Japanese Economic Association (Seinan Gakuin University), and seminar participants at Kwansei Gakuin University, Kyoto
University, Kyoto Sangyo University, Osaka University, The University of Rennes 1, and Yokohama National
University for helpful discussions and comments. We would also like to thank Shohei Yoshida for his research
assistance. The second author thanks the warm hospitality at MOVE, Universitat Autònoma de Barcelona, wherepart of this paper was written and acknowledges financial support from the “Strategic Young Researcher Overseas
Visits Program for Accelerating Brain Circulation” of JSPS. We gratefully acknowledge financial support from
JSPS KAKENHI Grant Numbers 22243022, 24530248, 24730220, 15H03349, 15H05728, and 15K17060 andthe program of the Joint Usage/Research Center for Behavioral Economics at ISER, Osaka University. The usual
disclaimer applies.
†
Faculty of Economics, Kyoto Sangyo University, Motoyama, Kamigamo, Kita-Ku, Kyoto, Kyoto 603-8555,
Japan. Email: hiroshikitamura@cc.kyoto-su.ac.jp‡
Institute of Social and Economic Research, Osaka University, 6-1 Mihogaoka, Ibaraki, Osaka 567-0047,
Japan. Email: nmatsush@iser.osaka-u.ac.jp§
Department of Economics, The George Washington University, 2115 G street, NW Monroe Hall 340 Washington DC 20052, USA. Email: smisato@gwmail.gwu.edu

1Introduction

In vertical supply chain relationships, firms often engage in contracts including vertical restraints, such as exclusive contracts, loyalty rebates, slotting fees, resale price maintenance,
quantity fixing, and tie-ins.1 Among vertical restraints, exclusive contracts have long been
controversial.2 Once signed, exclusive contracts deter efficient entrants; they thus may appear
to be anticompetitive. However, scholars from the Chicago School oppose this view by arguing, based on analytic models, that rational economic agents do not sign contracts to deter
more efficient entrants (Posner, 1976; Bork, 1978).3 In rebuttals of this argument after Aghion
and Bolton (1987), several researchers present market environments in which anticompetitive
exclusive dealing occurs (e.g., Bernheim and Whinston, 1998). These studies introduce, forinstance, scale economies in the sense that an entrant needs to trade with a certain numberof buyers to offset its fixed costs (Rasmusen, Ramseyer, and Wiley, 1991; Segal and Whinston, 2000a) and downstream competition (Simpson and Wickelgren, 2007; Abito and Wright,
2008).
The present study, by taking into account complementary inputs, provides an economic
environment within which anticompetitive exclusive dealing occurs. In a real-world businesssituation, final-good producers often transform multiple inputs into final products. More importantly, there exist complementary input suppliers with market power. In the Intel antitrust
case, for example, Microsoft is a supplier with strong market power.4 Therefore, when applying analysis of anticompetitive exclusive dealing to real-world situations, the interaction
between complementary input suppliers cannot be neglected.
In this study, we develop a model of anticompetitive exclusive dealing in the presence
1

The pioneering Rey and Tirole (1986) comprehensively considers these topics. More recently, Asker andBar-Isaac (2014) use a repeated game to consider the matter. Excellent surveys of vertical restraints are provided
by Rey and Tirole (2007) and Rey and Vergé (2008).
2
Setting exclusive territories is a typical example of exclusive-dealing agreements. For instance, Mathewson
and Winter (1984), Rey and Stiglitz (1995), and Matsumura (2003) discuss this matter.
3
For analysis of the impact of this argument on antitrust policies, see Motta (2004) and Whinston (2006).
4Intel was accused of awarding rebates and various other payments to major original equipment
manufacturers (e.g., Dell and HP). In a single quarter in 2007, conditional rebates and paymentsfrom Intel amounted to 76% of Dell’s operating profit (Gans, 2013).
See also Japan Fair Trade
Commission (2005): http://www.jftc.go.jp/eacpf/cases/intel.pdf and the European Commission (2009):
http://ec.europa.eu/competition/sectors/ICT/intel.html.

1

of complementary inputs. In our model, an upstream incumbent supplier offers an exclusive
contract to a single downstream firm to deter an entrant supplier that is more efficient than
the incumbent supplier—and would thus constitute a socially efficient entry. Because there
are neither scale economies nor downstream competition, the incumbent supplier cannot detersocially efficient entry with exclusive contracts, as in the frameworks of previous studies. The
new dimension in our model is that the downstream firm produces a final product using not
only an input produced by the incumbent supplier but also a complementary input produced
by a supplier with market power.
In a simple setting with linear demand and linear wholesale pricing, we first show that theexistence of a complementary input supplier with market power allows the incumbent supplier
to deter socially efficient entry via exclusive contracts, even in the case of a single downstream
firm. To intuitively understand this result, consider the effects of socially efficient entry. Socially efficient entry into an input market generates competition, which reduces the input’s
price and thus allows the downstream firm to earn higher profits. Under the Chicago School
argument, this effect prevents the incumbent supplier from profitably compensating the downstream firm; Chicago School scholars thus conclude that exclusion is impossible. However,when there is a complementary input supplier with market power, socially efficient entry into
one input market increases the demand for the complementary input, which benefits the complementary input supplier by increasing the complementary input price. Hence, comparedwith the case in which there is no complementary input supplier with market power, sociallyefficient entry leads to a smaller increase in the downstream firm’s profits. This allows theincumbent supplier to profitably compensate the downstream firm, and therefore exclusion ispossible.
We also check the robustness of the above exclusion outcome and show that it can beobserved in a broad range of settings. First, introducing non-linear demand, we show thatthe exclusion outcome results as long as the demand curve for final products is not overly
convex; that is, exclusion is more likely to be observed under inelastic demand. Second, aunique exclusion equilibrium occurs in a context of non-linear wholesale pricing and a generaldemand function. Third, in the appendix, we show that when the inputs of incumbent and entrant suppliers are vertically differentiated, as discussed in Argenton (2010), a complementary2

supplier with market power is essential for deriving an exclusion equilibrium. Therefore, theexclusion outcome identified in this study can be widely applied to diverse real-world vertical
relationships.
This study is related to the literature on anticompetitive exclusive contracts (Rasmusen,
Ramseyer, and Wiley, 1991; Segal and Whinston, 2000a; Simpson and Wickelgren, 2007;
Abito and Wright, 2008).5 These studies share a common feature: reaching the exclusion result
requires multiple downstream buyers.67 In contrast, this study shows that anticompetitive
exclusive contracts can be signed even under a single-buyer model.
In terms of a single-buyer model of anticompetitive exclusive contracts, this study is closest to Fumagalli, Motta, and Rønde (2012), who explore a model in which exclusive dealing can both promote relationship-specific investment and foreclose a more efficient supplier.
They show that if relationship-specific investment is possible, inefficient market foreclosure
occurs even in the single-buyer model because competition between suppliers diminishes theinvestment level of the incumbent supplier, which leaves room for the efficient supplier to set
a higher input price, thereby harming the downstream buyer. In contrast, exclusion in thepresent study arises because a complementary input supplier directly deprives the downstream
firm of some additional profits generated through competition in another complementary input market. Although a third party’s rent extraction is the key factor required for deriving theexclusion outcomes in both studies, the mechanism of rent extraction in the present study isquite different from that in Fumagalli, Motta, and Rønde (2012). Moreover, the main result in
5

In addition, certain studies examine pro-competitive exclusive dealings; e.g., non-contractible investments(Marvel, 1982; Besanko and Perry, 1993; Segal and Whinston, 2000b; de Meza and Selvaggi, 2007; de Fontenay,
Gans, and Groves, 2010), industry R&D and welfare (Chen and Sappington, 2011), risk sharing (Argenton andWillems, 2012), and adverse selection (Calzolari and Denicolò, 2013). Exclusive dealing is also considered away to solve the commitment problem posited by Hart and Tirole (1990), which arises when a single upstream
firm sells to multiple retailers with two-part tariffs under unobservable contracts. See also O’Brien and Shaffer(1992), McAfee and Schwartz (1994), and Rey and Vergé (2004).
6
In the literature on exclusion with downstream competition, Fumagalli and Motta (2006) show that the existence of participation fees to remain active in the downstream market plays a crucial role in exclusion if buyers
are undifferentiated Bertrand competitors. See also Wright’s (2009) study, which corrects the result of Fumagalli
and Motta (2006) in the case of two-part tariffs.
7
For extended models of exclusion with downstream competition, see Wright (2008), Argenton (2010), andKitamura (2010, 2011). Whereas these studies all show that the resulting exclusive contracts are anticompetitive,
Gratz and Reisinger (2013) show potentially pro-competitive effects if downstream firms compete imperfectly
and contract breaches are possible. See also DeGraba (2013), who adapts the model to cover a situation in whicha small rival that is more efficient at serving a portion of the market can make exclusive offers.

3the present study does not wholly depend on the negotiation procedure between suppliers andthe downstream buyer, whereas the outcome in Fumagalli, Motta, and Rønde (2012) partly
depends on the negotiation procedure employed there.8
This study is also related to the literature on vertical relationships involving complementary inputs, such as the work of Laussel (2008), Matsushima and Mizuno (2012, 2013), andReisinger and Tarantino (2013).9 These studies demonstrate that vertical integration is notnecessarily profitable because the complementary input supplier extracts the majority of the
profits generated as a result of eliminating double marginalization through vertical integration.
The present study extends this work, showing that these ideas can be applied to the literatureon entry deterrence via exclusive contracts.
The remainder of this paper is organized as follows. Section 2 constructs the basic model.
Section 3 presents the main results under linear wholesale pricing and extends the basic modelin several dimensions. Section 4 provides analysis under non-linear wholesale pricing, while
Section 5 offers concluding remarks. Appendix A presents proofs of the results. Appendixes
B and C provide extended analysis.

2

Model

This section develops the basic model environment. We first explain players’ characteristics
and the game’s timing in Section 2.1. Section 2.2 then introduces the design of the anticompetitive exclusive contracts.

2.1

Basic environment

The upstream market is composed of two complementary input markets: A and B (Figure 1).
Input A is exclusively produced by supplier U A with a constant marginal cost c > 0. In contrast,
input B is produced by an incumbent supplier U IB and an entrant supplier U EB . Following
the Chicago School model, U IB and U EB produce an identical product but with differing cost
8

In Appendix B, we present a bargaining procedure in which the main result of our model still holds whereasthat of Fumagalli, Motta, and Rønde (2012) does not.
9
See also Arya and Mittendorf (2007) and Laussel and Long (2012).

4

efficiencies; namely, U EB is more efficient than U IB , with a constant marginal cost cE ∈ [0, c)
as opposed to U IB ’s constant marginal cost c > 0.10
The downstream market is composed of a single firm. This modeling strategy clarifies therole of U A as having market power; that is, the prevention of socially efficient entry occurs
even in the absence of scale economies and downstream competition, both of which require
more than one downstream firm. A downstream monopolist D transforms inputs A and B intoa final product. D uses Leontief production technology: one unit of the final product is madewith one unit of input A and one unit of input B:11
Q = min{qA , qB },(1)

where qi is the amount of input i ∈ {A, B}. Equation (1) implies that the two inputs are essential
to produce a final product in a downstream market—i.e., they are perfect complements.12 The
payment for qi units of input i ∈ {A, B} is given as wi qi , where wi is input i’s price. To simplify
the analysis, we assume that D incurs no production costs aside from paying for the two inputs.
Thus, per unit production cost of D is given by
cD = wA + w B .
We assume that the inverse demand for the final product P(Q) is given by a simple linear
function:P(Q) = a − bQ,(2)where Q is the output of the final product supplied by D, a > 2(2c − cE ), and b > 0. (In Section
4, we consider a general demand case.) The first inequality implies that U EB ’s monopoly priceis higher than c; namely, the existence of U IB always acts as a constraint on the pricing of U EB
when U EB enters the market for input B.13
10

In Appendix C, we extend the setting to a case in which the inputs are vertically differentiated, as in Argenton(2010).
11
Introducing asymmetric production technology where one unit of the final product is made with h > 0 units
of input A and m > 0 units of input B does not qualitatively change the results.
12
Such production technology can be widely observed in real-world manufacturing. For example, producing a
PC requires a CPU and an operating system, and producing a car requires a body and tires.
13
Exclusion will still exist even when U EB is more efficient, but the analysis becomes more complicated.

5

We assume that D cannot merge with U A ; this assumption can be justified as follows.14
First, a vertical merger with common suppliers is sometimes prohibited by antitrust authorities
because such a vertical merger can generate a foreclosure problem. Second, we can regard U A
as an industry-wide labor union of downstream firms. In the literature on oligopoly models
incorporating labor unions, the labor union is usually assumed to maximize the wage leveland number of employees, which can be interpreted as wA and qA in this study. Under thisinterpretation, D cannot merge with U A .
The model contains four stages (Figure 2). In Stage 1, U IB makes an exclusive offer to
D with fixed compensation x ≥ 0. D decides whether to accept the offer.15 D immediately
receives x if it accepts the offer. In Stage 2, U EB decides whether to enter the market for input
B. We assume that the fixed entry cost is sufficiently small that U EB can earn positive profits. In
Stage 3, active suppliers offer linear input prices to D. (In Section 4, we introduce non-linear
pricing.) We assume that if U EB enters the market for input B, then U IB and U EB become
homogeneous Bertrand competitors. The equilibrium price of input i ∈ {A, B} when D accepts(rejects) the exclusive offer is denoted by wai (wri ) where the superscript ‘a’ (‘r’) indicates thatthe exclusive offer is accepted (rejected). In Stage 4, D orders inputs and sells the final productto consumers. Uk ’s profit in the case where D accepts (rejects) the exclusive offer is denotedby πak (πrk ), where k ∈ {A, IB, EB}. D’s profit in the case when it accepts (rejects) the exclusive
offer is denoted by πaD (πrD ).

2.2

Design of exclusive contracts

For an exclusion equilibrium to exist, the equilibrium transfer x∗ must satisfy the following
two conditions.
First, it must satisfy individual rationality for U IB ; that is, U IB earns higher profits under
exclusive dealing:
πaIB − x∗ ≥ πrIB .
14(3)

See Matsushima and Mizuno (2013) for a more detailed discussion of the justifications for this assumption.
Rasmusen, Ramseyer, and Wiley (1991) and Segal and Whinston (2000a) point out that price commitments
are unlikely if the product’s nature is not precisely described in advance. In the naked exclusion literature,
it is known that if the incumbent can commit to wholesale prices, then anticompetitive exclusive dealings areenhanced. See Yong (1999) and Appendix B of Fumagalli and Motta (2006).
15

6

Second, the exclusive contract must satisfy individual rationality for D; that is, the amountof compensation x induces D to accept the exclusive offer:
πaD + x∗ ≥ πrD .

(4)From the above conditions, it is evident that a unique exclusion equilibrium exists if andonly if inequalities (3) and (4) simultaneously hold. This is equivalent to the following condition:
πaIB + πaD ≥ πrIB + πrD .

(5)Condition (5) implies that to determine whether anticompetitive exclusive contracts exist, wemust examine whether exclusive contracts increase the joint profits of U IB and D.

3

Linear wholesale pricing

This section analyzes the existence of anticompetitive exclusive contracts under linear wholesale pricing. To intuitively understand the importance of a complementary input supplier having market power, we first discuss a benchmark case in which complementary input A is competitively provided (Section 3.1). We then explore the case in which complementary input A is
supplied by a monopolistic supplier and also examine how the curvature of the inverse demand
function influences the result (Section 3.2). Finally, Section 3.3 discusses how market powerin input market A influences the result in Section 3.2.

3.1

Benchmark: When a complementary input is competitively supplied

Assume that complementary input A is competitively provided. Then, input A’s price does
not depend on whether the exclusive offer is accepted in Stage 1; i.e., waA = wrA = c. In thissetting, the Chicago School model can be interpreted as a special case in which D can purchasecomplementary input A for free; i.e., waA = wrA = 0.16 Therefore, as the Chicago School argues,
U IB cannot deter socially efficient entry.
16

Although a buyer is the final consumer in the Chicago School model, the result does not qualitatively change
if we assume that the buyer is a downstream monopolist. See Lemma 1 of Kitamura, Sato, and Arai (2014).

7

Proposition 1. Suppose that inverse demand is given by a linear function and upstream suppliers adopt linear wholesale pricing. When complementary input A is competitively provided,
U IB cannot deter socially efficient entry by using exclusive contracts.
The result here can be explained using logic similar to that underlying the Chicago School
argument. When D accepts the exclusive offer in Stage 1, it purchases input B from U IB at ahigher input price, which allows U IB to earn monopoly profits. However, under linear wholesale pricing, U IB and D cannot maximize their joint profits because of the double marginalization problem. Thus, the left-hand side of inequality (5) is quite small.
In contrast, when D rejects the exclusive offer in Stage 1, U EB enters the market for input
B in Stage 2. In Stage 3, U IB and U EB compete to manage D. Compared with the case of
exclusive dealing, upstream competition in the B market reduces input B’s price, which solves
the double marginalization problem. Thus, D earns considerably higher rejection profits; thatis, the right-hand side of inequality (5) becomes large. In the absence of scale economies anddownstream competition, U IB cannot profitably compensate D, implying that there is no x thatsimultaneously satisfies participation constraints (3) and (4). Therefore, when the downstream
market consists of a monopolist, anticompetitive exclusive dealing cannot occur if complementary input A is competitively supplied.

3.2

When a complementary input is provided by a monopolist

We now assume that complementary input A is provided exclusively by U A . Input A’s price
now depends on whether entry into the market for input B occurs, unlike in the previous subsection. As in the case in which complementary input A is provided competitively, entry into
the market for input B generates competition within it, reducing input B’s price. To understandthe pricing behavior of U A when input B’s price decreases, we first examine the relationshipbetween entry into the B market and input A’s price. The following lemma summarizes therelationship:
Lemma 1. When U A has market power, socially efficient entry into the market for input B
raises the equilibrium price of input A—that is, wrA > waA .

8

To understand this result, consider the reaction function of the monopolistic supplier of
input i given input j’s price w j ;wi (w j ) =a + c − wj,
2bwhere i, j ∈ {A, B} and i , j. It is easy to see that the strategic interaction between the twomonopolistic suppliers is strategic substitute; that is, raising input A’s price is the best response
for U A when input B’s price decreases.17 Therefore, entry into the market for input B induces
U A to raise input A’s price and enjoy higher profits. The following proposition shows that thisrelationship between entry into the market for input B and input A’s price allows U IB to deter
efficient entry by using exclusive contracts.
Proposition 2. Suppose that inverse demand is given by a linear function and upstream suppliers adopt linear wholesale pricing. If U A is the monopolist for input A, U IB can deter sociallyefficient entry as a unique exclusionary equilibrium outcome.
Note that the crucial difference as compared to the benchmark case exists in the sub-gamein which D rejects the exclusive offer. As in the case in which input A is competitively supplied, entry into the market for input B generates upstream competition in this market, which
benefits D. However, Lemma 1 implies that entry into this market also benefits U A by increasing input A’s price, which prevents D from earning considerably higher profits upon rejecting
the exclusive offer; that is, the right-hand side of inequality (5) does not become sufficiently
large. This allows U IB to profitably compensate D using its profits under exclusive dealing.
Therefore, the existence of a complementary supplier with market power leads to anticompetitive exclusive dealing even in the absence of scale economies and downstream competition.
Remark (Non-linear demand)

The previous results rest on the assumption of a linear in-verse demand function. We now relax this assumption to extend Section 3.2’s analysis with a
non-linear inverse demand function:
P(Q) = a − bQα .
17(6)

If inputs A and B were substitutes, a reduction in input B’s price would decrease demand for input A, andthus U A would be required to lower A’s price. In contrast, if inputs A and B are complements, a reduction in input
B’s price increases demand for input A.

9

We assume that α > 0 so that the firms’ second-order conditions are satisfied. We also assume
that a > ((1 + α)(c − cE ) + 2αc)/α so that U EB ’s monopoly price is higher than c. Comparing
equations (2) and (6) reveals clearly that the linear demand case considered in the previous
subsections is a special case in which α = 1. The price elasticity of demand is given by
−

dQ/Q
p
=
.
d p/p
α(a − p)(7)

Equations (6) and (7) imply that as α increases (decreases), the demand curve becomes concave(convex) or inelastic (elastic). The following proposition shows that the likelihood of exclusion
depends on the curve’s shape.
Proposition 3. Suppose that upstream suppliers adopt linear wholesale pricing. If U A is themonopolistic supplier of input A, U IB can deter socially efficient entry as a unique equilibriumoutcome as long as the demand curve for the final product is not overly convex, α ≥ α '0.40692.
This result has an important implication: exclusion is more likely to be observed when
demand is inelastic. The curvature of the inverse demand curve influences the degree of demand expansion following socially efficient entry. When the inverse demand curve is concave(α > 1), the demand-expansion effect of a new upstream entrant is weak; as a result, sociallyefficient entry does not lead to a large increase in D’s profits, allowing U IB to profitably compensate D. However, as the inverse demand curve becomes convex, the demand-expansion
effect becomes significant; in other words, the double marginalization problem is more serious
in the case of convex inverse demand. This leads to a large increase in D’s profits, preventing
U IB from profitably compensating D.

3.3

Discussion

To probe how the monopoly power of a complementary input supplier influences the previous
subsection’s outcome, we briefly discuss the case in which a competitor also supplies complementary input A. We suppose that input A is produced by not only an incumbent supplier, U IA ,but also an inefficient supplier, U EA . The marginal cost of U EA is dA ∈ (c, a/2). We assume
that U EA enters the market for input A in Stage 2, that U IA and U EA are homogeneous Bertrand
10competitors, and that the fixed cost of entry is zero, enabling U EA to enter the market for input
A.18 Note that the analyses in Sections 3.1 and 3.2 can be interpreted as the cases in which
dA = c and dA ≥ a/2, respectively. The following proposition shows that the likelihood of exclusion depends on the difference in efficiency between the suppliers of complementary input
A.19
Proposition 4. Suppose that input A can be produced by U IA and U EA . U IB can deter sociallyefficient entry as a unique equilibrium outcome if the efficiency difference between the suppliersof complementary input A is sufficiently large—that is, dA ≥ d A where
dA = a − c −a − 2c√ .
3Note that c < d A < a/2. The result here fills the gap between Propositions 1 and 2
and confirms the significance of the complementary input supplier being able to control its
input price. When U EA ’s efficiency is high (that is, dA is close to c), the existence of U EA
acts as a constraint on the pricing of U IA and significantly dampens the monopoly power of
U IA . This implies that U IA does not extract sufficient profits from D, regardless of whether
U IB ’s exclusive offer is accepted. In this environment, engaging in exclusive dealing with U IB
significantly reduces D’s profit through double marginalization.
In contrast, when U EA is sufficiently inefficient (that is, dA ∈ ((a + c)/3, a/2)), the existenceof U EA does not necessarily constrain the pricing of U IA . On the one hand, if U IB ’s exclusive
offer is accepted, the existence of U EA never influences U IA ’s pricing decisions. On the other,
if U IB ’s exclusive offer is rejected, the existence of U EA does constrain U IA ’s pricing decisions.
In this case, input A’s price depends on U EA ’s efficiency, dA . As noted in Section 3.2, thestronger the monopoly power of U IA , the lower D’s profitability if U IB ’s exclusive offer isrejected. Therefore, if U EA ’s efficiency is low enough that dA ≥ d A , then U IB and D engage in18

If the entry cost is positive, U EA does not enter the market for input A because it anticipates zero operating
profits and cannot cover this fixed cost. It may be harder to justify this assumption. However, U EA might entereven if it had to incur the fixed cost. For example, this might occur if there were upstream differentiation in themarket for input A. Alternatively, if U EA is already established and operating in other industries, it could supply
input A without additional fixed costs.
19
The result does not change even if we assume that both U IA and U IB independently and simultaneously makeexclusive offers to D with fixed compensation xA (≥ 0) and xB (≥ 0), respectively.

11

anticompetitive exclusive dealing even in the presence of competition in the complementary
input market.
Interpretation of these results yields an important policy implication for antitrust agencies: an increase in the cost efficiency of a dominant input supplier can facilitate anticompetitive exclusive dealing in complementary input markets. As the dominant input supplierbecomes more efficient, industry output usually increases, which is socially efficient. However, if we consider the possibility of exclusive contracts in complementary input markets, animprovement in the efficiency of the dominant input supplier may trigger exclusion outcomesin complementary input markets, which is socially inefficient. Therefore, when consideringreal-world exclusive contracts, antitrust agencies should pay attention to not only the structureof the market in which the exclusive contracts are signed but also structural changes in related
complementary input markets.

4

Non-linear wholesale pricing

In this section, we extend the analysis of the model in Section 3.2 to the case in which upstream
suppliers use two-part tariffs in Stage 3. Two-part tariffs consist of a linear wholesale price andan upfront fixed fee; the two-part tariff offered by input supplier Ui when D accepts (rejects)
the exclusive offer is denoted by (wai , Fia ) ((wri , Fir )), where i ∈ {A, IB, EB}. Under non-linear
pricing, the double marginalization problem is avoidable, and the joint profit is maximized
within the technological endowments available to firms. For notational convenience, we defineΠ∗ (z) as follows:Π∗ (z) ≡ max(p − z − c)Q(p),pwhere z ≥ 0 and Q(p) is a general demand function. Π∗ (z) can be interpreted as the maximum
joint profit when input B is supplied with marginal cost z. When entry does not occur (occurs),
we have z = c (z = cE ). Hence, the difference between Π∗ (cE ) and Π∗ (c) depends on the
difference between the efficiencies of U EB and U IB . To simplify the analysis, we assume thatΠ∗ (z) is continuous and strictly decreasing in z.
The rest of this section is organized as follows. In Section 4.1, we explore the case inwhich suppliers make take-it-or-leave-it offers. In Section 4.2, we explore the case in which
12the industry profit is allocated by bilateral Nash bargaining.

4.1

Take-it-or-leave-it offers

We first consider the case in which the exclusive offer is accepted in Stage 1. There are multipleaaequilibria in which U A and U IB respectively offer (c, F Aa ) and (c, F IB
) such that F Aa + F IB=

Π∗ (c). The firms’ equilibrium profits, excluding the fixed compensation x, are
0 ≤ πaA ≤ Π∗ (c), 0 ≤ πaIB ≤ Π∗ (c), πaD = 0,awhere πaA + πaIB = Π∗ (c). Multiple equilibria consist of any F Aa ≥ 0 and F IB
≥ 0 such thata
F Aa + F IB
= Π∗ (c).

We next consider the case in which the exclusive offer is rejected in Stage 1. In Stage 2,
U EB then enters the market for input B. In Stage 3, U IB offers its best term (c, 0). Anticipatingrr
this term, U A and U EB respectively offer (c, F Ar ) and (cE , F EB), which satisfy Π∗ (cE )−F EB−F Ar ≥rΠ∗ (c) − F Ar if F Ar ≤ Π∗ (c) and Π∗ (cE ) − F EB
− F Ar ≥ 0 if F Ar > Π∗ (c). The inequalities thatr
include F EB
indicate that D either prefers U EB ’s offer to that of U IB or treats them equally.
r
By arranging the condition, we conclude that (c, F Ar ) and (cE , F EB
) satisfy the following: 0 ≤rr
F EB≤ Π∗ (cE ) − Π∗ (c) and F Ar + F EB
= Π∗ (cE ). Firms’ equilibrium profits are then given as

follows:Π∗ (c) ≤ πrA ≤ Π∗ (cE ), πrIB = πrD = 0, 0 ≤ πrEB ≤ Π∗ (cE ) − Π∗ (c),where πrA + πrEB = Π∗ (cE ). Multiple equilibria consist of any Π∗ (c) ≤ F Ar ≤ Π∗ (cE ) andrr
0 ≤ F EB≤ Π∗ (cE ) − Π∗ (c) such that F Ar + F EB
= Π∗ (cE ).

Finally, we check for the existence of exclusion. Because we have πaIB + πaD − (πrIB + πrD ) ≥ 0
with equality for πaIB = 0, inequality (5) always holds. Therefore, exclusion is always anequilibrium outcome.
Proposition 5. Suppose that upstream suppliers adopt two-part tariffs and make take-it-orleave-it offers. If U A has market power, then U IB can deter socially efficient entry as a uniqueequilibrium outcome.
There are a few remarks that must be made regarding this subsection’s analysis. First, as
pointed out above, there exist multiple equilibria in Stage 3. Second, the profit allocation is13

not consistent with the linear wholesale pricing case. When complementary input suppliers
adopt two-part tariffs, D earns zero operating profits regardless of its decision in Stage 1.
Hence, the main intuition of the Chicago School argument, in which the downstream buyer
enjoys a large surplus, cannot be applied. Third, if D is able to make take-it-or-leave-it offers,
exclusion cannot be an equilibrium outcome because D can extract all of Π∗ (cE ) by offering(c, 0) to U A and (cE , 0) to U EB in the case of U EB ’s entry. Hence, we must reconsider the
analysis in a situation of more general bargaining power. In the next subsection, we provide abilateral Nash Bargaining outcome with the following properties: a unique Stage 3 equilibriumoutcome exists; D enjoys a larger surplus when entry occurs; and the possibility of exclusion
can be explored with respect to the degree of bargaining power.

4.2

Bilateral Nash bargaining

Under our bargaining assumptions, when the exclusive offer is accepted in Stage 1, D andexisting suppliers, U A and U IB , negotiate and make contract(s) for the two-part tariffs in Stage
3. We consider a form of simultaneous bilateral negotiation; that is, when negotiating with
two suppliers, D simultaneously bargains with each of them separately.20 Each bargaining
session aims at contracting the two-part tariff D will transfer to the supplier. We assume thatthe outcome in Stage 3 is determined as follows. First, the outcome of each negotiation is
given by the Nash bargaining solution, based on the belief that the outcome of bargaining withthe other party is determined in the same way. Second, the net joint surplus is divided between
D and the supplier in the proportion β to 1 − β, where β ∈ (0, 1) represents D’s bargaining
power.
By contrast, when the exclusive offer is rejected in Stage 1, U EB enters the market for input
B in Stage 2. In Stage 3, D simultaneously negotiates separately with each of the suppliers, U A
and U EB , and makes contract(s) for the two-part tariffs. If D and U EB cannot reach an agreement, then D can bargain with U IB given the contract (wrA , F Ar ).21 The assumptions governing
each bargaining procedure are the same as those applying in the case in which the exclusive
20

For an application in the industrial organization literature in which industry profits are allocated according
to bilateral Nash bargaining, see, for instance, Matsushima and Shinohara (2014) and references therein.
21
It is not optimal for D to bargain first with U IB .

14

offer is accepted.
We first consider the case in which the exclusive offer is accepted in Stage 1 and then U EB
does not enter in Stage 2. In Stage 3, D simultaneously negotiates with each of the suppliers,a
U A and U IB , separately and makes contract(s) for the two-part tariffs, (c, F Aa ) and (c, F IB). Notethat we do not discuss explicitly how the wholesale price is determined in each instance of
bargaining because we can easily show that marginal cost pricing is achieved in both cases.
For notational simplicity, we omit the discussion of how to determine the suppliers’ wholesale
prices. Given the contract (c, F aj ), the bargaining problem between D and Ui is described by
the payoff pairs (Π∗ (c)− Fia − F aj , Fia ) and the disagreement point (0, 0) (i, j ∈ {A, IB} and i , j).
The solution is given by:
Fia = arg max β log[Π∗ (c) − Fi − F aj ] + (1 − β) log Fi .
Fi

The firms’ equilibrium profits, excluding the fixed compensation x, are(1 − β)Π∗ (c)aaπA = πIB =,2−ββΠ∗ (c)
a
πD =
.
2−β

(8)

We next consider the case in which the exclusive offer is rejected in Stage 1 and then U EB
enters the market for input B in Stage 2. In Stage 3, D simultaneously negotiates separately
with each of the suppliers, U A and U EB , and makes contracts for the two-part tariffs, (c, F Ar )rand (cE , F EB). If D and U EB cannot reach an agreement, then D can bargain with U IB given thecontract (c, F Ar ). We derive solutions by backward induction.
We first explore bargaining between D and U IB off the equilibrium path. Given (c, F Ar ),the bargaining problem between D and U IB off the equilibrium path is described by the payoff
r(o)
r(o)
pairs (Π∗ (c) − F Ar − F IB
, F IB) and the disagreement point (0, 0). The solution is given by:
r(o)
F IB
= arg max β log[Π∗ (c) − F Ar − F IB ] + (1 − β) log F IB .
F IB

(9)

By solving this problem, D earns β(Π∗ (c) − F Ar ), which becomes D’s outside option underbargaining with U EB .22
Under the negotiation characterized here, U IB offers (c, (1 − β)(Π∗ (c) − F Ar )) and does not offer its best terms,(c, 0). Hence, the competition between suppliers of input B is less intense than under homogeneous Bertrand
competition. In Appendix B, we extend the analysis here to the case in which N entrants exist. We show that thenegotiation (competition) among input B suppliers described here becomes more severe as the number of entrants
increases and coincides with homogeneous Bertrand competition as a limiting case; even in such a case, however,
the existence of U A allows U IB to deter socially efficient entry.
22

15

We now explore the bargaining between D and Uk on the equilibrium path, where k ∈r), the bargaining problem between D and U A is described by the payoff{A, EB}. Given (cE , F EBr
, F Ar ) and the disagreement point (0, 0). The solution is given by:pairs (Π∗ (cE ) − F Ar − F EBr
F Ar = arg max β log[Π∗ (cE ) − F A − F EB
] + (1 − β) log F A .
FA

(10)

By contrast, the bargaining problem between D and U EB given (c, F Ar ) is described by therr) and the disagreement point (β(Π∗ (c) − F Ar ), 0). The, F EB
payoff pairs (Π∗ (cE ) − F Ar − F EB

solution is given by:r
F EB= arg max β log[Π∗ (cE ) − F Ar − F EB − β(Π∗ (c) − F Ar )] + (1 − β) log F EB .
F EB

(11)

By solving problems (10) and (11), the equilibrium firms’ profits are given as follows:
πrA =
πrD =

(1 − β)(Π∗ (cE ) + (1 − β)Π∗ (c)), πrIB = 0,
β2 + 3(1 − β)β(Π∗ (cE ) + (1 − β)Π∗ (c))(1 − β)((2 − β)Π∗ (cE ) − Π∗ (c))
r
,
π
=
.
EB
β2 + 3(1 − β)β2 + 3(1 − β)Note that for all β ∈ (0, 1), πrD − πaD = β((2 − β)Π∗ (cE ) − Π∗ (c))/(2 − β)(β2 + 3(1 − β)) > 0
and πrA − πaA = (1 − β)((2 − β)Π∗ (cE ) − Π∗ (c))/(2 − β)(β2 + 3(1 − β)) > 0, which implies thatsocially efficient entry increases not only D’s profits but also U A ’s profits. Thus, the negotiation
characterized here leads to a similar profit allocation in the case of linear wholesale pricing.
We finally consider the existence of exclusion. Condition (5) holds if and only if
πaIB + πaD − (πrIB + πrD ) =(1 + (1 − β)2 (2 − β))Π∗ (c) − β(2 − β)Π∗ (cE )≥ 0.
(2 − β)(β2 + 3(1 − β))From this condition, we obtain the following proposition:
Proposition 6. Suppose that upstream suppliers adopt two-part tariffs and that industry profits
are allocated by bilateral Nash bargaining between D and upstream suppliers. If U A has
market power, U IB can deter socially efficient entry as a unique equilibrium outcome if there isa sufficiently small difference in efficiency between U IB and U EB and D has limited bargaining
power; that is, Π∗ (cE )/Π∗ (c) ≤ φ(β), whereφ(β) ≡

1 + (1 − β)2 (2 − β).
β(2 − β)16

Note that for all β ∈ (0, 1), we have φ(β) > 1, φ0 (β) < 0, and φ00 (β) > 0 and that φ(β) → ∞as β → 0 and φ(β) → 1 as β → 1.
Figure 3 summarizes the result of Proposition 6, showing that the possibility of exclusion
is higher when D has less bargaining power. The intuition behind this result is as follows.
When D has limited bargaining power, U A extracts most of the increase in the firms’ joint
profits from U EB ’s entry whereas D enjoys a smaller increase in profits, which increases thepossibility of exclusion. By contrast, when D has strong bargaining power, D obtains a larger
increase in profits from U EB ’s entry whereas U A enjoys a smaller increase in profits. Hence,
there is less possibility of exclusion.

5

Concluding remarks

This study has explored the existence of anticompetitive exclusive dealing, extending the workof previous studies to consider the role of complementary inputs in the upstream market. It isessential that this interaction between complementary input suppliers not be neglected, as it iscommon for real-world downstream firms to transform multiple inputs into final products.
Our analysis showed that seemingly small differences in the model’s setting can have crucial ramifications for the results. If the complementary input supplier has market power, thenthe inefficient incumbent supplier can deter socially efficient entry by using exclusive contracts
even under the Chicago School argument’s framework in which there is a single downstreambuyer. On checking the robustness of our exclusion outcome, we showed that it does not depend on the assumption of linear demand or linear wholesale pricing; that is, our results remain
valid when the final product demand curve is not too convex or when non-linear wholesalepricing is introduced. This study’s analysis can thus be widely applied to real-world vertical
relationships.
Our results also have novel and important implications for antitrust agencies: it is necessary
to take into account the existence of complementary inputs when considering the possibility ofanticompetitive exclusive dealing. If we discuss the anticompetitiveness of exclusive contracts
while ignoring the existence of complementary input suppliers with market power, we mightover-emphasize the results of the Chicago School argument. This study’s results suggest that17

rational economic agents can easily engage in anticompetitive exclusive dealing in a market
requiring multiple inputs to produce a downstream product for which demand is inelastic.
Moreover, if the complementary input supplier considered here is interpreted as an industrywide labor union, our results imply that the existence of unions plays a role in facilitating
anticompetitive exclusive dealing.
Despite these contributions, there remain several outstanding issues requiring further research. The first involves extensions of our model to encompass other facets of the anticompetitive dealing literature. For example, we assume that the downstream firm is a monopolist.
We predict that, as Simpson and Wickelgren (2007) and Abito and Wright (2008) discuss,adding downstream competition to our model would increase the likelihood of reaching an exclusion equilibrium. A second area for further analysis concerns the generality of our results.
For example, the present study’s analysis assumed Leontief production technology. While
this might be appropriate for analyzing certain real-world situations, such as the Intel antitrust
case, the result might also remain valid under more general production technologies. In addition, in Section 3.3 we assumed that the complementary input suppliers are homogeneous
Bertrand competitors. If we were to add differentiation between the complementary input suppliers to our model, the likelihood of an exclusion equilibrium would increase. A real-world
example of this is the case of Eastman Kodak v. Fuji, in which Kodak complained of exclusive contracts between Fuji and Japanese wholesalers that prevented Kodak from successfully
entering Japan’s photographic film market.23 The Japanese camera market, which complements the film market, is characterized by dominant manufacturers such as Canon and Nikon.
These manufacturers are somewhat differentiated and have market power because consumers
face switching costs when considering changing cameras. Extensions and applications of ourmodel can thus help researchers and policymakers address similar real-world issues.

23

See, for example, Nagaoka and Goto (1997).

18

Appendix
A

Proofs of All Results

Proof of Proposition 1
Before proceeding to the proof, we explain D’s maximization problem. Given input prices wA
and wB , the problem is given as
max (a − bQ − wA − wB )Q.
Q(12)The level of output of the final product supplied by D and the demand for each input are givenbya − wA − w B
.
(13)
2b
When input A is competitively provided, we have waA = wrA = c. We first explore the caseqA = qB = Q(wA , wB ) ≡in which the exclusive contract is accepted in Stage 1. The outcome in Stage 4 is given in (13).
In Stage 3, U IB sets the input price:
waB = arg max(wB − c)Q(c, wB ).
wB

The equilibrium input prices are waB = a/2 and waA = c. From (13), the equilibrium productionlevels are Qa (c, a/2) = qaA = qaB = (a − 2c)/6b. The firms’ equilibrium profits, excluding the
fixed compensation x, are
πaA = 0, πaIB =(a − 2c)2(a − 2c)2, ΠaD =
.
8b
16b

(14)

We next explore the case in which the exclusive offer is rejected in Stage 1. Then, U EB
enters the B market in Stage 2. In Stage 3, competition in the B market reduces input B’s
price to U IB ’s marginal cost; i.e., wrB = c. From (13), the equilibrium production levels are
Qr (c, c) = qrA = qrB = (a − 2c)/2b. The equilibrium profits are
πrA = πrIB = 0, πrD =(a − 2c)2
.
4b

(15)

Finally, we check the existence of an exclusion equilibrium. From (14) and (15), we haveπaIB + πaD − (πrIB + πrD ) = −19(a − 2c)2< 0,
16bwhich implies that condition (5) never holds.
Q.E.D.

Proof of Lemma 1
Suppose first that the exclusive offer is accepted in Stage 1. The maximization problem faced
by D in Stage 4 is given by (12). The output of the final product supplied by D and the demandfor each input are given by (13). The maximization problem of input i supplier in Stage 3 isgiven asmax(wi − c)Q(wi , w j ),
wi ≥c

(16)

where i, j ∈ {A, B} and i , j. The first-order conditions lead to the equilibrium input prices:a+cwaA = waB =.
(17)
3
From (13), the equilibrium production levels are Qa = qaA = qaB = Q((a + c)/3, (a + c)/3) =(a − 2c)/6b. The firms’ equilibrium profits, excluding the fixed compensation x, are(a − 2c)2(a − 2c)2, πaD =
.
(18)
18b
36b
Suppose next that the exclusive offer is rejected in Stage 1. In this case, U EB enters the B
πaA = πaIB =market in Stage 2. The maximization problem faced by D in Stage 4 is given by (12). The
output of the final product supplied by D and the demand for each input are given by (13).
The competition in the B market in Stage 3 leads to wrB = c. By contrast, the maximization
problem of U A in Stage 3 is given by (16). The equilibrium price of input A isa(19)
wrA = .
2
From (13), the equilibrium production levels are Qr = qrA = qrB = (a − 2c)/4b. The equilibrium
profits of firms are(a − 2c)2(a − 2c)2, πrIB = 0, πrD =.
8b16bFrom (17) and (19), we have the following relation:a − 2cwaA − wrA = −< 0.
6Therefore, entry into the B market increases input A’s price.
πrA =

(20)

Q.E.D.
20

Proof of Proposition 2
From (18) and (20), we haveπaIB + πaD − (πrIB + πrD ) =(a − 2c)2> 0,
48bwhich implies that condition (5) always holds.
Q.E.D.

Proof of Proposition 3
We first consider the case in which the exclusive offer is accepted in Stage 1. The firms’
equilibrium profits, excluding the fixed compensation x, are
πaA = πaIB =α((1 + α)b) α1

a − 2c1 + 2α

! 1+α
α

,

πaD =

α(a − 2c)
(1 + α)(1 + 2α)

α
1

bα

! 1+α
α

.

We next consider the case in which the exclusive offer is rejected in Stage 1. The equilibrium profits of the firms are given byπrA =α((1 + α)b) α1

a − 2c
1+α

! 1+α
α

,

πrIB = 0,

πrD =

α
1

bα

a − 2c(1 + α)2

! 1+α
α

.

Finally, we consider the existence of exclusion. By using above results, we haveα(a − 2c)πaIB + πaD − (πrIB + πrD ) =
1

1+α
α

1+α

2(1+α)(1 + α) α (2 + α) − ((1 + α)(1 + 2α)) α3(1+α)(1 + α) α (1 + 2α) α

bα

1+α

≥ 0,

if and only if α ≥ α. Therefore, condition (5) holds if and only if α < α.
Q.E.D.

Proof of Proposition 4
We first consider the case in which U IB ’s exclusive offer is accepted in Stage 1. The existenceof U EA acts as a constraint on the pricing of U IA although U IA is the supplier of input A on theequilibrium path. U IB monopolistically sets input B’s price. The maximization problem faced
by D in Stage 4 is given by (12). The output of the final product supplied by D and the demand21

for each input are as in (13). The maximization problems of U IA and U IB in Stage 3 are givenbya − wA − w B, s.t. wA ≤ dA ,wA2ba − wA − w B.
max (wB − c)wB
2bmax (wA − c)These maximization problems lead to


a+c
a+c
a + c − dA






,
d
if
c
<
d
<
if c < dA <
,


A
A




3
2
3
a
w
=
waA = 

B


a+c
a+c


a+c
a+c




if dA ≥,
if dA ≥
.


3
3
3
3
The equilibrium production levels are a−d −c
a+c

A


, if c < dA <
,



4b
3
qaA = qaB = Qa = 
a+ca − 2c
,
if dA ≥.
6b
3
The equilibrium profits, excluding the fixed compensation x, are given by(dA − c)(a − dA − c)
a+c



if c < dA <
,



4b
3
a
πIA = 
(a − 2c)2
a+c



,
if dA ≥
,

18b
3


a+c
(a − dA − c)2
if c < dA <
,



8b
3
πaIB = (a − 2c)2a+c
if dA ≥
.

18b
3


a+c
(a − dA − c)2
if c < dA <
,



16b
3
a
πD = 
(a − 2c)2a+c
if dA ≥,

36b
3Second, we consider the case in which U IB ’s exclusive offer is rejected in Stage 1. As in
the first case, the existence of U EA acts as a constraint on the pricing of U IA . The equilibrium
supplier of input B is U EB , and its price is wrB = c. The maximization problem faced by D in
Stage 4 is given by (12). The output of the final product supplied by D and the demand foreach input are given by (13). The maximization problem of U IA in Stage 3 is given as
max (wA − c)wAa − wA − c, s.t. wA ≤ dA .
2b
22

This maximization problem leads toa
dA if c < dA < ,2
wrA = aa

if dA ≥ .
2
2
The equilibrium production levels are a−d −c
a

A


,
if
c
<
d
<

A


2b
2
qrA = qrB = Qr = 


a
−
2c
a



,
if dA ≥ .
4b
2
The equilibrium profits are

πrIA
πrIB
πrD



a
(dA − c)(a − dA − c)



,
if
c
<
d
<
A



2b
2
= 

2

a
(a − 2c)
,
if dA ≥ ,

8b
2
= 0.


a
(a − dA − c)2, if c < dA <



4b
2
= 

2

(a − 2c)a
,if dA ≥ ,

16b
2

From now on, we explore the existence of exclusion. Applying the above results, we haveπaIB + πaD − (πrIB + πrD )a+c(a − dA − c)2
if c < dA <
,
−



16b
3



o
√ n
√ on
√


 3 dA − ((a − c) − (a − 2c)/ 3) (a − 2c) + 3(a − dA − c)
a+c
a
= 


if
≤
d
<
,
A



12b
3
2



(a − 2c)2a
if dA ≥ .
48b
2
It is easy to see that condition (5) holds if and only if dA ≥ d A .
Q.E.D.

23

B

Nash bargaining under N entrants

This appendix extends Section 4.2’s analysis to the case of N entrants. Entrants here aredenoted by U EB(n) , where n ∈ {1, 2, .., N}.24 For simplicity, we assume that U EB(n) has thesame marginal cost cE and that, as in Section 3.3, the fixed cost of entry is zero, enabling N
entrants to enter the market for input B. By extending the analysis of Section 4.2, we consider
the following competition among input B suppliers. When the exclusive offer is rejected inStage 1, N entrants enter the market for input B in Stage 2. In Stage 3, D simultaneously
negotiates with each of equilibrium suppliers, U A and U EB(N) , separately and makes contract(s)for the two-part tariffs. If D and U EB(N) cannot reach an agreement, then D can bargain with
U EB(N−1) given the contract (c, F Ar ). If D and U EB(N−1) cannot reach an agreement, then D canbargain with U EB(N−2) given (c, F Ar ). In this way, bargaining off the equilibrium path continues.
After N bargaining failures, D can bargain with U IB , which is the final bargaining partner. To
understand the importance of a complementary input supplier, we first discuss a benchmark
case in which input A is not required for producing the final product in B.1. In B.2, we thenexplore the case in which input A is required to produce the final product.

B.1

Benchmark: When input A is not required for final-good production

In this subsection, we assume that input A is not required to produce the final product and that
D uses production technology Q = qB under which one unit of the final product is made with
one unit of input B. As in Section 4.2, we define Π∗∗ (z) as follows:Π∗∗ (z) ≡ max(p − z)Q(p).
pΠ∗∗ (z) can be interpreted as the maximum joint profit when input B is supplied with marginal
cost z. When entry does not occur (occurs), we have z = c (z = cE ). As in Section 4.2, we
assume that Π∗∗ (z) is continuous and strictly decreasing in z.
We first consider the case in which the exclusive offer is accepted in Stage 1. In Stagea3, D negotiates with U IB and makes a contract for the two-part tariffs, (c, F IB). The bargain24

Multiple entrants are introduced by Kitamura (2010). By extending the model of Abito and Wright (2008),
Kitamura (2010) explores the case of multiple entrants and shows that the possibility of exclusion decreases insuch an environment.

24

a
a
ing problem between D and U IB is described by the payoff pairs (Π∗∗ (c) − F IB
, F IB) and thedisagreement point (0, 0). The solution is given by:a
F IB= arg max β log[Π∗∗ (c) − F IB ] + (1 − β) log F IB .
F IB

The firms’ equilibrium profits, excluding the fixed compensation x, areπaIB = (1 − β)Π∗∗ (c), πaD = βΠ∗∗ (c).
We next consider the case in which the exclusive offer is rejected in Stage 1. In Stage2, N entrants enter the market for input B. In Stage 3, D negotiates with U EB(N) and makes arcontract for the two-part tariffs (cE , F EB(N)). As in Section 4.2, we derive solutions by backward

induction. The bargaining problem between D and U IB off the equilibrium path is described by
r(o)
r(o)
the payoff pairs (Π∗∗ (c) − F IB
, F IB) and the disagreement point (0, 0). The solution is given

by:
r(o)
F IB
= arg max β log[Π∗∗ (c) − F IB ] + (1 − β) log F IB .
F IB

Solving this problem, D earns βΠ∗∗ (c), which becomes D’s outside option under bargaining
with U EB(1) . The bargaining problem between D and U EB(1) off the equilibrium path is der(o)r(o)
scribed by the payoff pairs (Π∗∗ (cE ) − F EB(1), F EB(1)) and the disagreement point (βΠ∗∗ (c), 0).

The solution is given byr(o)F EB(1)= arg max β log[Π∗∗ (cE ) − F EB(1) − βΠ∗∗ (c)] + (1 − β) log F EB(1) .
F EB(1)

Solving this problem, D earns Π∗∗ (cE ) − (1 − β)(Π∗∗ (cE ) − βΠ∗∗ (c)), which becomes D’s outside
option under bargaining with U EB(2) . In this way, we can obtain firms’ equilibrium profits forthe case of N entrants:
πrIB = 0, πrD = Π∗∗ (cE ) − (1 − β)N (Π∗∗ (cE ) − βΠ∗∗ (c)), πrEB(N) = (1 − β)N (Π∗∗ (cE ) − βΠ∗∗ (c)).
Note that πrD is strictly increasing in N whereas πrEB(N) is strictly decreasing in N; this implies
that the competition characterized here is like Cournot competition in that it becomes more
severe as the number of entrants increases. In addition, as N → ∞, we have πrD → Π∗∗ (cE ) >πaD and πrEB(N) → 0; namely, the competition characterized here coincides with homogeneous
Bertrand competition in which each entrant offers (cE , 0) as a limiting case.
25

We finally consider the existence of exclusion. Condition (5) holds if and only if
πaIB + πaD − (πrIB + πrD ) = −(Π∗∗ (cE ) − Π∗∗ (c)) + (1 − β)N (Π∗∗ (cE ) − βΠ∗∗ (c)) ≥ 0.
From this condition, we obtain the following proposition:
Proposition B.1. Suppose that upstream suppliers adopt two-part tariffs and industry profits
are allocated by bilateral Nash bargaining between D and upstream suppliers. If D’s production technology is Q = qB , U IB cannot deter socially efficient entry by using exclusive contracts
for an infinite number of entrants. More concretely, exclusion is possible if the difference inefficiency between U IB and U EB is sufficiently small and D has limited bargaining power; thatis, Π∗ (cE )/Π∗ (c) ≤ η(β, N) where1 − β(1 − β)N
η(β, N) =.
1 − (1 − β)N
Note that for all N ∈ N and β ∈ (0, 1), η(β, N) > 1, η(β, N) < η(β, N − 1), and ∂η(β, N)/∂β < 0
and that η(β, N) → 1 as N → ∞ or β → 1.
The results here imply that the analysis in Section 4.2 is imperfect at clarifying that theexistence of U A plays an essential role in deterring socially efficient entry because the competition among the finite number of input B suppliers characterized here is weaker than homogeneous Bertrand competition. To see this, consider the case of N = 1, which corresponds with the framework of Section 4.2. In this case, condition (5) holds if and only ifΠ∗∗ (cE )/Π∗∗ (c) ≤ η(β, 1) = (1 − β(1 − β))/β > 1 for all β ∈ (0, 1). Thus, for N = 1, the exclusion equilibrium exists even in the absence of U A if the efficiency difference between input
B suppliers is sufficiently small and D has limited bargaining power. Therefore, we need to
explore whether the result in Section 4.2 holds for the infinite number of entrants.25
25

Multiple entrants cannot be neglected in the model of Fumagalli, Motta, and Rønde (2012). If we introduce
multiple entrants or bilateral Nash bargaining under an infinite number of entrants into the model of Fumagalli,
Motta, and Rønde (2012), socially inefficient exclusion does not occur. The main reason why exclusion is possible
under their model is that the competition between the incumbent supplier and the entrant supplier diminishes
the investment level of the incumbent supplier, which allows the efficient entrant supplier to set a higher input
price. When multiple entrants exist, entrants cannot set a higher input price; this allows the downstream buyer
to earn higher profits. Appendix B.2 shows that the existence of a complementary input supplier with strong
market power leads to socially inefficient exclusion even for an infinite number of entrants, thereby clarifying theessential role of the complementary input supplier with market power.

26

B.2

When input A is required for final-good production

We now assume that input A, supplied by U A , is required to produce the final product andthat D uses production technology Q = min{qA , qB }. We first consider the case in which theexclusive offer is accepted in Stage 1. Because the bargaining problem when the exclusive
offer is accepted coincides with the one in Section 4.2, equilibrium firms’ profits are given by(8).
We next consider the case in which the exclusive offer is rejected in Stage 1. In Stage2, N entrants enter the market for input B. In Stage 3, D simultaneously negotiates witheach of the suppliers, U A and U EB(N) , and makes contracts for the two-part tariffs, (c, F Ar )rand (cE , F EB(N)). We derive solutions by backward induction. We first explore the bargaining

problem between D and input B suppliers off the equilibrium path. From the discussion in
Section 4.2, the bargaining problem between D and U IB and that between D and U EB(1) off theequilibrium path given (c, F Ar ) are given by (9) and (11), respectively. Solving these problems
yields the result that D earns Π∗ (cE )− F Ar −(1−β)(Π∗ (cE )−βΠ∗ (c)−(1−β)F Ar ), which becomes
D’s outside option under bargaining with U EB(2) . In this way, the bargaining between D andr(O)U EB(N−1) off the equilibrium path given (c, F Ar ) enables D to earn Π∗ (cE ) − F Ar − F EB(N−1), wherer(O)F EB(N−1)= (1 − β)N−1 (Π∗ (cE ) − βΠ∗ (c) − (1 − β)F Ar ). We now explore the bargaining between

D and Uk on the equilibrium path, where k ∈ {A, EB(N)}. The bargaining problem between Drr
and U EB(N) given (c, F Ar ) is described by the payoff pairs (Π∗ (cE ) − F Ar − F EB(N), F EB(N)) and ther(O)disagreement point (Π∗ (cE ) − F Ar − F EB(N−1), 0). The solution is given by:r(o)rF EB(N)= arg max β log[Π∗ (cE )−F Ar −F EB(N) −(Π∗ (cE )−F Ar −F EB(N−1))]+(1−β) log F EB(N) . (21)F EB(N)r
By contrast, the bargaining problem between D and U A given (cE , F EB(N)) is described by therpayoff pairs (Π∗ (cE ) − F Ar − F EB(N), F Ar ) and the disagreement point (0, 0). The solution is given

by:r
F Ar = arg max β log[Π∗ (cE ) − F A − F EB(N)] + (1 − β) log F A .
FA

(22)

By solving problems (21) and (22), we can obtain equilibrium firms’ profits for the case of N
entrants:πrA =(1 − β)(Π∗ (cE ) − (1 − β)N (Π∗ (cE ) − βΠ∗ (c))), πrIB = 0,
1 − (1 − β)2+N27

β(Π∗ (cE ) − (1 − β)N (Π∗ (cE ) − βΠ∗ (c)))
r
πD =
,
2+N

β(1 − β)πrEB =((2 − β)Π∗ (cE ) − Π∗ (c)).
1 − (1 − β)
1 − (1 − β)2+N
Note that as N → ∞, πrEB(N) → 0, πrD → βΠ∗ (cE ) > πaD , and πrA → (1 − β)Π∗ (cE ) > πaA ; asN

in the linear pricing case, socially efficient entry increases not only D’s profits but also U A ’s
profits.26
We finally consider the existence of exclusion. Condition (5) holds if and only if
πaIB + πaD − (πrIB + πrD ) =(1 − (1 − β)N (β + (1 − β)3 ))Π∗ (c) − β(2 − β)(1 − (1 − β)N )Π∗ (cE )≥ 0.
(2 − β)(1 − (1 − β)2+N )From this condition, we obtain the following proposition:
Proposition B.2. Suppose that upstream suppliers adopt two-part tariffs and industry profits
are allocated by bilateral Nash bargaining between D and upstream suppliers. If input A,
supplied by U A , is required to produce the final product, U IB can deter socially efficient entry
as a unique equilibrium outcome even for an infinite number of entrants. More concretely,
exclusion is possible given a sufficiently small difference in efficiency between U IB and U EB(n)and limited bargaining power for D; that is, Π∗ (cE )/Π∗ (c) ≤ ψ(β, N) whereψ(β, N) =1 − (1 − β)N (β + (1 − β)3 ).
β(2 − β)(1 − (1 − β)N )Note that for all N ∈ N, ψ(β, N) > 1 and ψ(β, N) < ψ(β, N − 1) and that ψ(β, 1) = φ(β) andψ(β, N) → 1/β(2 − β) as N → ∞.
The result here implies that the exclusion result under linear wholesale pricing is valid evenwhen we apply the general demand function and a profit allocation rule based on bilateral Nashbargaining with an infinite number of entrants. B.1’s model showed that in the absence of U A ,D is the unique player obtaining all benefits in the case of the entry of an infinite number ofentrants, which makes exclusion impossible. Hence, the Chicago School argument can apply.
However, B.2 showed that the existence of U A prevents D from being the only player to obtain
all of these benefits even for an infinite number of entrants, which makes exclusion possible.
Therefore, we can conclude that the existence of U A plays an essential role in deterring sociallyefficient entry.
Both inequalities hold if and only if (2 − β)Π∗ (cE ) − Π∗ (c) > 0. It is easy to see that this condition holds forall β ∈ (0, 1).
26

28

C

Vertical product differentiation

In this appendix, we extend Section 3.2’s analysis to the case in which input B suppliers produce vertically differentiated inputs. The basic model structure here follows Argenton (2010),
who explores a model of anticompetitive exclusive contracts when upstream suppliers’ products are vertically differentiated. Although Argenton (2010) explores the case of two downstream firms with no complementary input supplier, we explore the case of a single downstream firm with a complementary input supplier.
The quality of the final product for which input B is supplied by Ui is denoted by µi , wherei ∈ {IB, EB}. Following Argenton (2010), we assume that U EB produces a higher quality input,µEB > µIB , and that for simplicity all firms’ marginal costs are zero; that is, cIB = cEB = cA = 0.
Consumer preferences follow the standard in the literature on vertical product differentiation.
There is a unit mass of consumers, indexed by θ, which is uniformly distributed on the interval[0, 1]. Consumers decide whether to purchase one unit of one of the final products. To purchaseone unit of the final product with quality µi , a consumer of type θ pays pi and enjoys consumer
surplus θµi − pi . The consumer is assumed to purchase a given final product if and only if theconsumer surplus is nonnegative; i.e., max{θµIB −pIB , θµEB −pEB } ≥ 0. Moreover, the consumerpurchases the final product with quality µi if θµi − pi ≥ θµ j − p j , where i, j ∈ {IB, EB} andi , j.
Demand for each final product depends on the results of Stage 1. First, when the exclusive
offer is accepted in Stage 1, only U IB supplies input B. Thus, demand for the final productwith quality µIB becomesQIB (pIB ) = 1 −

pIB
.
µIB

Second, when the exclusive offer is rejected in Stage 1, U IB and U EB supply input B andcompete in input prices. In this case, demand for the final product with quality µEB becomesQEB (pIB , pEB ) = 1 −pEB − pIB.
µEB − µIB

By contrast, demand for the final product with quality µIB becomesQIB (pIB , pEB ) =pEB − pIB pIB−.
µEB − µIB µIB

29

The rest of this appendix is organized as follows. To understand the importance of a complementary input supplier, we first discuss a benchmark case in which input A is not requiredfor producing the final product in C.1. We then explore the case in which input A is requiredfor producing the final product in C.2.
Before we discuss the suppliers’ pricing, we derive the demand for the products given thedetermined input prices. First, we consider a case in which D produces the low-quality productthat includes the input of U IB . The maximization problem faced by D is given bymax (pIB − wA − wIB )QIB (pIB ).
pIB

The price of the final product and demand for input B are given bypIB (wA , wIB ) =µIB + wA + wIBµIB − wA − wIB, QIB (wA , wIB ) =
.
2
2µIB

(23)

Second, we consider a case in which D produces both low- and high-quality final products that
include, respectively, the inputs of U IB and U EB . The maximization problem faced by D isgiven bymax (pIB − wA − wIB )QIB (pIB , pEB ) + (pEB − wA − wEB )QEB (pIB , pEB ).

pIB ,pEB

The price of each final product and demand for each input are given byµIB + wA + wIBµEB + wA + wEB, pEB (wA , wEB ) =,22µIB wEB − µEB wIB − (µEB − µIB )wA
QIB (wA , wIB , wEB ) =.
2µIB (µEB − µIB )µEB − µIB − wEB + wIB
QEB (wIB , wEB ) =,2(µEB − µIB )pIB (wA , wIB ) =

C.1

(24)
(25)

Benchmark: When input A is not required for final-good production

In this subsection, we assume that input A is not required for producing the final product andthat D uses production technology Q = qB , which corresponds to a case in which D canpurchase input A for free; waA = wrA = 0.
We first consider the case in which the exclusive offer is accepted in Stage 1. Using the outcome in (23), we solve the maximization problem of U IB and can then obtain the equilibrium30input price and firms’ profits, excluding the fixed compensation x:
waIB =µIBµIBµIB, πaIB =, πaD =.
2
8
16

We next consider the case in which the exclusive offer is rejected in Stage 1. Using theoutcome in (24) and (25), we solve the maximization problems of U IB and U EB and then obtain
the equilibrium input prices and firm profits:µIB (µEB − µIB )2µEB (µEB − µIB ), wrEB =,4µEB − µIB
4µEB − µIBµ2EB (4µEB + 5µIB )2µ2EB (µEB − µIB )µEB µIB (µEB − µIB )rrπrIB =
,
π
=
,
π
=
.
D
EB
2(4µEB − µIB )24(4µEB − µIB )2(4µEB − µIB )2
wrIB =

Finally, we consider the existence of exclusion. By using the above results, we haveπaIB + πaD − (πrIB + πrD ) = −4µEB (µEB − µIB ) + 3µ2IB< 0,16(4µEB − µIB )which implies that condition (5) never holds. Hence, we obtain the following proposition:
Proposition C.1. Suppose that the products of the suppliers of input B are vertically differentiated and that upstream suppliers adopt linear wholesale pricing. If D’s production technology
is Q = qB , U IB cannot deter socially efficient entry by using exclusive contracts for any degreeof product differentiation.

C.2

When input A is required for final-good production

We now assume that input A, supplied by U A , is required to produce the final product and D
uses production technology Q = min{qA , qB }.
We first consider the case in which the exclusive offer is accepted in Stage 1. Using theoutcome in (23), we solve the maximization problems of U A and U IB and then obtain theequilibrium input prices and firm profits, excluding the fixed compensation x:
waA = waIB =

µIB
µIB
µIB
, πaA = πaIB =, πaD =.
3
18
36

We next consider the case in which the exclusive offer is rejected in Stage 1. Using theoutcome in (24) and (25), we solve the maximization problems of U A , U IB , and U EB and then31

have the equilibrium input prices and firm profits:µEB − µIB
µIB
, wrIB = 0, wrEB =
,
2
2
µIB
µEB
µEB − µIBπrA =, πrIB = 0, πrD =, πrEB =
.
8
16
8
wrA =

We finally consider the existence of exclusion. Condition (5) holds if and only if
πaIB + πaD − (πrIB + πrD ) =4µIB − 3µEB
≥ 0.
48

From this condition, we obtain the following proposition:
Proposition C.2. Suppose that the products of the suppliers of input B are vertically differentiated and that upstream suppliers adopt linear wholesale pricing. If D’s production technology
is Q = min{qA , qB } and U A is the monopolistic supplier of input A, U IB can deter sociallyefficient entry as a unique equilibrium outcome for a sufficiently small degree of product differentiation; that is, µEB /µIB ≤ 4/3.

References
Abito, J.M., and Wright, J., 2008. Exclusive Dealing with Imperfect Downstream Competition. International Journal of Industrial Organization 26(1), 227–246.
Aghion, P., and Bolton, P., 1987. Contracts as a Barrier to Entry. American Economic Review
77(3), 388–401.
Arya, A., and Mittendorf, B., 2007. Interacting Supply Chain Distortions: The Pricing of Internal Transfers and External Procurement. Accounting Review 82(3), 551–580.
Argenton, C., 2010. Exclusive Quality. Journal of Industrial Economics 58(3), 690–716.
Argenton, C., and Willems, B., 2012. Exclusivity Contracts, Insurance and Financial Market
Foreclosure. Journal of Industrial Economics 60(4), 609–630.
Asker, J., and Bar-Isaac, H., 2014. Raising Retailers’ Profits: On Vertical Practices and the
Exclusion of Rivals. American Economic Review 104(2), 672–686.
32

Bernheim, B.D., and Whinston, M.D., 1998. Exclusive Dealing. Journal of Political Economy 106(1), 64–103.
Besanko, D.P, and Perry, M.K., 1993. Equilibrium Incentives for Exclusive Dealing in a Differentiating Products Oligopoly. RAND Journal of Economics 24(4), 646–668.
Bork, R.H., 1978. The Antitrust Paradox: A Policy at War with Itself. New York: Basic Books.
Calzolari, G., and Denicolò, V., 2013. Competition with Exclusive Contracts and Market-Share
Discounts. American Economic Review 103(6), 2384–2411.
Chen, Y., and Sappington, D.E.M., 2011. Exclusive Contracts, Innovation, and Welfare. American Economic Journal: Microeconomics 3(2), 194–220.
de Fontenay, C.C., Gans, J.S., and Groves, V., 2010. Exclusivity, Competition, and the Irrelevance of Internal Investment. International Journal of Industrial Organization 28(4),336–340.
DeGraba, P., 2013. Naked Exclusion by an Input Supplier: Exclusive Contracting Loyalty
Discounts. International Journal of Industrial Organization 31(5), 516–526.
de Meza, D., and Selvaggi, M., 2007. Exclusive Contracts Foster Relationship-Specific Investment. RAND Journal of Economics 38(1), 85–97.
Fumagalli, C., and Motta, M., 2006. Exclusive Dealing and Entry, When Buyers Compete.
American Economic Review 96(3), 785–795.
Fumagalli, C., Motta, M., and Rønde, T., 2012. Exclusive Dealing: Investment Promotion may
Facilitate Inefficient Foreclosure. Journal of Industrial Economics 60(4), 599–608.
Gans, J.S., 2013. Intel and Blocking Practices. The Antitrust Revolution: Economics, Competition, and Policy. 6th Edition, edited by J. Kwoka and L. White, New York: Oxford
Univ Press.
Gratz, L. and Reisinger, M., 2013. On the Competition Enhancing Effects of Exclusive Dealing Contracts. International Journal of Industrial Organization 31(5), 429-437.
33

Hart, O., and Tirole, J., 1990. Vertical Integration and Market Foreclosure. Brooking Papers
on Economic Activity: Microeconomics, 205–286.
Kitamura, H., 2010. Exclusionary Vertical Contracts with Multiple Entrants. International
Journal of Industrial Organization 28(3), 213–219.
Kitamura, H., 2011. Exclusive Contracts under Financial Constraints. B.E. Journal of Economic Analysis & Policy 11, Article 57.
Kitamura, H., Sato, M., and Arai, K., 2014. Exclusive Contracts when the Incumbent can Establish a Direct Retailer. Journal of Economics 112(1), 47–60.
Laussel, D., 2008. Buying Back Subcontractors: The Strategic Limit of Backward Integration. Journal of Economics & Management Strategy 17(4), 895–911.
Laussel, D., and Long, N.V., 2012. Vertical Disintegration: A Dynamic Markovian Approach.
Journal of Economics & Management Strategy 21(3), 745–771.
Marvel, H.P., 1982. Exclusive Dealing. Journal of Law and Economics 25(1), 1–25.
Mathewson, G.F., and Winter, R.A., 1984. An Economic Theory of Vertical Restraints. RAND
Journal of Economics 15(1), 27–38.
Matsumura, T., 2003. Consumer-Benefiting Exclusive Territories. Canadian Journal of Economics 36(4), 1007–1025.
Matsushima, N., and Mizuno, T., 2012. Equilibrium Vertical Integration with Complementary
Input Markets. B.E. Journal of Economic Analysis & Policy 12, Article 26.
Matsushima, N., and Mizuno, T., 2013. Vertical Separation as a Defense against Strong Suppliers. European Journal of Operational Research 228(1), 208–216.
Matsushima, N., and Shinohara, R., 2014. What Factors Determine the Number of Trading
Partners? Journal of Economic Behavior & Organization 106, 428–441.
McAfee, R.P., and Schwartz, M., 1994. Opportunism in Multilateral Vertical Contracting: Nondiscrimination, Exclusivity, and Uniformity. American Economic Review 84(1), 210-230.
34

Motta, M., 2004. Competition Policy. Theory and Practice. Cambridge: Cambridge University Press.
Nagaoka, S., and Goto, A., 1997. Vertical Restraints and Market Access. Emprica 24(1-2),
21–36.
O’Brien, D., and Shaffer, G., 1992. Vertical Control with Bilateral Contracts. RAND Journalof Economics 23(3), 299–308.
Posner, R.A., 1976. Antitrust Law: An Economic Perspective. Chicago: University of Chicago
Press.
Rasmusen, E.B., Ramseyer, J.M., and Wiley Jr., J.S., 1991. Naked Exclusion. American Economic Review 81(5), 1137–1145.
Reisinger, M., and Tarantino, E., 2013. Vertical Integration with Complementary Inputs. mimeo.
Rey, P., and Stiglitz, J., 1995. The Role of Exclusive Territories in Producers’ Competition.
RAND Journal of Economics 26(3), 431–451.
Rey, P., and Tirole, J., 1986. The Logic of Vertical Restraints. American Economic Review
76(5), 921–939.
Rey, P., and Tirole, J., 2007. A Primer on Foreclosure. Handbook of Industrial Organization,
Volume 3 Ch. 33, edited by M. Armstrong and R.H. Porter, 2145–2220, Amsterdam:
North Holland.
Rey, P., and Vergé, T., 2004. Bilateral Control with Vertical Contracts. RAND Journal of Economics 35(4), 728–746.
Rey, P., and Vergé, T., 2008. Economics of Vertical Restraints. Handbook of Antitrust Economics Ch. 9, edited by P. Buccirossi, 353–390, Boston: MIT Press.
Segal, I.R., and Whinston, M.D., 2000a. Naked Exclusion: Comment. American Economic
Review 90(1), 296–309.

35

Segal, I.R., and Whinston, M.D., 2000b. Exclusive Contracts and Protection of Investments.
RAND Journal of Economics 31(4), 603–633.
Simpson, J., and Wickelgren, A.L., 2007. Naked Exclusion, Efficient Breach, and Downstream
Competition. American Economic Review 97(4), 1305–1320.
Whinston, M.D., 2006. Lectures on Antitrust Economics. Cambridge: MIT Press.
Wright, J., 2008. Naked Exclusion and the Anticompetitive Accommodation of Entry. Economics Letters 98(1), 107–112.
Wright, J., 2009. Exclusive Dealing and Entry, when Buyers Compete: Comment. American
Economic Review 99(3), 1070–1081.
Yong, J.S., 1999. Exclusionary Vertical Contracts and Product Market Competition. Journalof Business 72(3), 385-406.

36

Input A Market

Input B Market

𝑼𝑨

𝑼𝑰𝑩

wA

𝑼𝑬𝑩

wB

𝑫

Figure 1: Market Structures

Stage 1

Stage 2

Stage 3

Stage 4

𝑈𝐼𝐵 makes an
exclusive offer.

𝑈𝐸𝐵 makes
entry decision.

Active suppliers
make input priceoffers.

𝐷 orders inputs 𝐴 and 𝐵
and produces final products.

𝐷 decides.

Figure 2: Timeline37 * (c E ) * (c )5 ( )
4

Entry

3

Exclusion
2

1
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0


Figure 3: Results of Proposition 638