Discussion Paper No. 978

EXCLUSIVE CONTRACTSAND
BARGAINING POWER

Hiroshi Kitamura
Noriaki Matsushima
Misato Sato

September 2016

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

Exclusive Contracts and Bargaining Power∗
Hiroshi Kitamura†

Noriaki Matsushima‡

Misato Sato§

September 8, 2016

Abstract
This study constructs a simplest model to examine anticompetitive exclusive
contracts that prevent a downstream buyer from buying input from a new upstream supplier. Incorporating Nash bargaining into the standard one-buyer-onesupplier framework in the Chicago School critique, we show a possibility that aninefficient incumbent supplier can deter a socially efficient entry through exclusivecontracts.

JEL classifications code: L12, L41, L42, C72.
Keywords: Antitrust policy; Entry deterrence; Exclusive contracts; Nash bargaining.

∗This paper is a divided part of Kitamura et al. (2016b) “Exclusive Contracts with ComplementaryInput.” We extract Section 4.2 in Kitamura et al. (2016b) and revise it. We gratefully acknowledge
financial support from JSPS KAKENHI Grant Numbers JP15H03349, JP15H05728, and JP15K17060,
and the 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 5670047, Japan. Email: nmatsush@iser.osaka-u.ac.jp§
Department of Economics, The George Washington University, 2115 G street, NW Monroe Hall340 Washington DC 20052, USA. Email: smisato@gwmail.gwu.edu

1Introduction

Among the issues of vertical restraints (e.g., exclusive contracts, loyalty rebates, slotting
fees, resale price maintenance, quantity fixing, and tie-ins),1 exclusive contracts havelong been controversial, especially since the Chicago School critique (Posner, 1976;Bork, 1978), which argue that the rational buyer does not sign such a contract to detera more efficient entrant.2
By incorporating additional players into the baseline setting in the Chicago School,
many papers examine possibilities of signing anticompetitive exclusive contracts (e.g.,scale economies (Rasmusen, Ramseyer, and Wiley, 1991; Segal and Whinston, 2000)
and competition between the buyers (Simpson and Wickelgren, 2007; Abito and Wright,2008)).3 By contrast, we show a possibility that an anticompetitive exclusive contract
attains under a one-buyer-one-supplier framework with one potential supplier. The
key factor of our model is incorporating Nash bargaining into the baseline setting in
the Chicago School.4 Under the extended setting, upstream competition through entry does not generate enough buyer profits if the buyer has weaker bargaining power.
Anticipating the outcome, the buyer agrees with an exclusive contract offered by theincumbent. This contrasts with the Chicago School’s setting in which entry generates
fierce upstream Bertrand competition that induces the buyer to reject an exclusive offer.
Fumagalli et al. (2012) is also the study which shows a possibility that an anticompetitive exclusive contract attains under a one-buyer-one-supplier framework with one
potential supplier. The novelty of their model is incorporating incumbent’s investments
1Excellent surveys of vertical restraints are available in Rey and Tirole (2007) and Rey and Vergé
(2008).
2Motta (2004) and Whinston (2006) explain discussions on the impact of the Chicago School
argument on antitrust policies.
3Aghion and Bolton (1987) is the pioneering work that shows a possibility that an anticompetitive
contract attains.
4

In the context of vertical relations, Nash bargaining has been used in many papers (e.g., recently,
Aghadadashli et al., 2016).

1

which improve the value of ex-post trade into the traditional one-buyer-one-suppliermodel.5 The differences between Fumagalli et al. (2012) and ours are as follows. We
do not take into account incumbent’s investments. We instead change the bargaining
process, which generates a crucial difference when two suppliers are active. Fumagalli etal. (2012) assume Nash bargaining with random proposers in which the homogeneous
Bertrand competition occurs if two suppliers make price offers. In their setting, exclusion never occurs in the absence of investments because the buyer can earn large profit
when entry occurs. By contrast, we assume that the buyer sequentially negotiates with
two suppliers. More concretely, it first negotiates with an efficient entrant supplier. It
then negotiates with an inefficient incumbent supplier if the previous negotiation breaks
down. This implies that the incumbent supplier becomes an outside option of the buyer
if the entrant exists. Under the modified framework, the competition between suppliers
for the case of socially efficient entry is less intense than under homogeneous Bertrand
competition, which leaves room for exclusion even in the absence of investments.
The rest of this paper proceeds as follows. Section 2 introduces the model. Section
3 then presents the main results.

2ModelThis section develops the basic model. The upstream market consists of an upstream
incumbent UI with constant marginal cost cI > 0 and an upstream entrant UE with constant marginal cost cE ∈ [0, cI ). Each of them is able to supply input to a downstreambuyer D which is able to produce one unit of final product by using one unit of input.
The downstream demand is given by Q(p), which is continuous and Q0 (p) < 0. We
assume that (p − z)Q(p) is strictly and globally concave in p; 2Q0 (p) + (p − z)Q00 (p) < 0.
The model contains four stages. In Stage 1, UI offers an exclusive contract to D.
This contract involves some fixed compensation x ≥ 0. D decides whether to accept
5Kitamura et al. (2016a) shows a possibility that an exclusive contract attains under a one-buyerone-supplier framework with one potential buyer.

2this offer.
In Stage 2, after observing D’s decision, UE decides whether to enter the upstream
market. We assume that the fixed cost of entry f (> 0) is sufficiently small, such that
if UE is active, it could earn positive profits.
In Stage 3, existing firms negotiate and make contracts for two-part tariffs. We
assume that the outcome of every negotiation is given by Nash bargaining solution andthat the bargaining power of D over each upstream firm β ∈ (0, 1). Depending on D’s
decision in Stage 1, two scenarios can emerge. If D accepts the offer, D negotiateswith UI , and makes contracts for the two-part tariffs consisting of a linear wholesale
price and an upfront fixed fee (wIa , FIa ) if they reach an agreement. If the negotiation
between them breaks down, they gain nothing. By contrast, if D rejects the offer, thetwo suppliers are active. In this case, D first negotiates with UE , and makes contracts
for the two-part tariffs (wEr , FEr ), if they reach an agreement.6 If the negotiation between
them breaks down, UE exits. Then, D negotiates with UI , and makes contracts for thetwo-part tariffs (wIr , FIr ) if they reach an agreement. If the negotiation between thembreaks down, they gain nothing.
In Stage 4, D determines its price if a negotiation is reached with one of the upstream
firms.
Given the equilibrium outcomes in the subgame following Stage 1, we derive theessential conditions for an exclusive contract. Let πij be the profit of i (i = D, UI )under state j (j = a, r, where a and r indicate ‘Accept’ and ‘Reject’). For an exclusion
equilibrium, the equilibrium transfer x∗ must satisfy the following two conditions.
First, it must satisfy the individual rationality for UI ; that is, UI must earn higher
operating profits under exclusive dealing, such thatπUa I − x∗ ≥ πUr I or x∗ ≤ πUa I − πUr I .

(1)Second, it must satisfy the individual rationality for D; that is, the compensation
6

It is not optimal for D to bargain first with UI .

3amount x must induce D to accept the exclusive offer, such thatarrax ∗ + πD
≥ πDor x∗ ≥ πD− πD.

(2)

From the above conditions, it is easy to see that an exclusion equilibrium exists if andonly if inequalities (1) and (2) hold simultaneously. That is, an exclusion equilibrium
exists, if the highest value of x∗ in inequality (1) is larger than or equal to the lowest
value of x∗ in inequality (2). This is equivalent to the following condition:arπUa I + πD
≥ πD+ πUr I .

(3)

Condition (3) implies that for the existence of anticompetitive exclusive contracts, wemust examine whether exclusive agreements increase the joint profits of D and UI .

3ResultWe solve the game by using backward induction. In Stage 4, given the agreed wholesale
price w, D sets p(w) to maximize its profit, such thatp(w) ≡ arg max (p − w)Q(p).
pFor notational convenience, we define the gross downstream profit given w as Π(w) ≡(p(w) − w)Q(p(w)). The rest of this section is organized as follows. We first consider
the case in which D accepts the exclusive offer in 3.1. We then explore the case in which
D rejects the exclusive offer in 3.2. Finally, we examine the existence of anticompetitive
exclusive contracts in 3.3.

3.1

D accepts the exclusive offer

The bargaining problem between D and UI in Stage 3 is given as(wIa , FIa ) = arg max β log[(p(w) − w)Q(p(w)) − F ] + (1 − β) log[(w − cI )Q(p(w)) + F ].
w,F4Assuming (w − cI )Q(p(w)) is strictly and globally concave in w, the maximization
problem leads to the following two equations:(1 − β){Q(p(wIa )) + (wIa − cI )Q0 (p(wIa ))p0 (wIa )}βQ(p(wIa ))= 0,+Π(wIa ) − FIa(wIa − cI )Q(p(wIa )) + FIaβ(1 − β)−= 0.
+ aaa
Π(wI ) − FI
(wI − cI )Q(p(wIa )) + FIa−

Substituting the second equation into the first one, we obtain−Q(p(wIa )) + Q(p(wIa )) + (wIa − cI )Q0 (p(wIa ))p0 (wIa ) = 0.
Thus, we have wIa = cI . Substituting it into the second equation, we obtain
FIa = (1 − β)Π(cI ).
The resulting profits of D and UI , excluding the fixed compensation x, are given asaπD= βΠ(cI ), πUa I = (1 − β)Π(cI ).

3.2(4)

D rejects the exclusive offer

Anticipating the outcome after the breakdown of the first negotiation, D and UE negotiate their trading term. Note that for the breakdown of the first negotiation between Dand UE , D negotiates with UI . Therefore, the bargaining outcome for the breakdown of
the first negotiation coincides with the bargaining outcome in the previous subsection;anamely, D’s outside option under bargaining with UE is πD. The bargaining problem

between D and UE is given asa(wEr , FEr ) = arg max β log[(p(w)−w)Q(p(w))−F −πD]+(1−β) log[(w−cE )Q(p(w))+F ].
w,FThe maximization problem leads to the following two equations:βQ(p(wEr ))(1 − β){Q(p(wEr )) + (wEr − cE )Q0 (p(wEr ))p0 (wEr )}+= 0,aΠ(wEr ) − FEr − πD
(wEr − cE )Q(p(wEr )) + FEr
β(1 − β)+ r
= 0.
−rra
Π(wE ) − FE − πD (wE − cE )Q(p(wEr )) + FEr−5Substituting the second equation into the first one, we obtain−Q(p(wEr )) + Q(p(wEr )) + (wEr − cE )Q0 (p(wEr ))p0 (wEr ) = 0.
Thus, we have wEr = cE . Substituting it into the second equation, we obtainaFEr = (1 − β)(Π(cE ) − πD).

By using outcomes in (4), the resulting profits of firms are given asr= βΠ(cE ) + (1 − β)βΠ(cI ), πUr I = 0, πUr E = (1 − β)(Π(cE ) − βΠ(cI )).
πD

3.3(5)

Comparison

We now consider the game in Stage 1. From the outcomes in (4) and (5), we derive thecondition that D accepts the exclusive offer by UI . Substituting (4) and (5) into (3),
we obtain(1 − β)Π(cI ) + βΠ(cI ) ≥ (βΠ(cE ) + (1 − β)βΠ(cI )) + 0,
⇒ (1 − β(1 − β))Π(cI ) ≥ βΠ(cE ).
From this condition, we obtain the following proposition:
Proposition 1 Suppose that upstream suppliers adopt two-part tariffs and that industry profits are allocated by bilateral Nash bargaining between D and upstream suppliers.
UI can deter socially efficient entry as a unique equilibrium outcome if and only if
Π(cE )/Π(cI ) ≤1 − β(1 − β)≡ Γ(β).
βNote that for all β ∈ (0, 1), we have Γ(β) > 1, Γ0 (β) < 0, and Γ00 (β) > 0 and that
Γ(β) → ∞ as β → 0 and Γ(β) → 1 as β → 1 (See Figure 1).
[Figure 1 about here]6

To understand our result, we compare sequential Nash bargaining characterized herewith Nash bargaining with random proposers in Fumagalli et al. (2012). Regardlessof bargaining types, the joint profits between UI and D become Π(cI ) when D accepts
the exclusive offer.
The crucial difference arises when D rejects the exclusive offer. Under the case of
random proposers, UI and UE become homogeneous Bertrand competitors with probability 1 − β, while D makes the price offer with probability β. More importantly, when
suppliers compete, UI offers its best term (cI , 0). As a result, Nash bargaining withrandom proposers induces D to earn βΠ(cE ) + (1 − β)Π(cI ), which is strictly larger
than Π(cI ). Therefore, exclusion never occurs in the absence of investments.
Sequential bargaining here, however, allows UI to offer (cI , (1 − β)Π(cI )) off theequilibrium path. Hence, the competition between suppliers is less intense than underhomogeneous Bertrand competition. This prevents D from earning higher profits for thecase of entry and thus there is room of exclusion outcomes; exclusion occurs even in theabsence of investments.7 In addition, as D’s bargaining power is weak, it earns lower
profits; namely, the possibility of exclusion is higher when D has limited bargaining
power.
Our result provides an important policy implication for antitrust agencies; the possibility of anticompetitive exclusive dealing depends highly on the bargaining process
when a downstream buyer negotiates with upstream suppliers. More concretely, anticompetitive exclusive dealing occurs if the buyer needs to negotiate with suppliers
sequentially. Such exclusion is more likely to be observed in the case where the buyer
faces some time constraints, which reduce its bargaining power, and limitations of negotiation opportunity.
7

We can extend the analysis here to the case in which N entrants exist and show the possibility ofexclusion exists for the finite number of upstream suppliers. The proof of this result can be available
upon request.

7References
Abito, J.M., and Wright, J., 2008. Exclusive Dealing with Imperfect Downstream Competition. International Journal of Industrial Organization 26(1), 227–246.
Aghadadashli, H., Dertwinkel-Kalt, M., and Wey, C., 2016. The Nash Bargaining Solution in Vertical Relations with Linear Input Prices. Economics Letters 145,291–294.
Aghion, P., and Bolton, P., 1987. Contracts as a Barrier to Entry. American Economic
Review 77(3), 388–401.
Bork, R.H., 1978. The Antitrust Paradox: A Policy at War with Itself. New York:Basic Books.
Fumagalli, C., Motta, M., and Rønde, T., 2012. Exclusive Dealing: Investment Promotion May Facilitate Inefficient Foreclosure. Journal of Industrial Economics 60(4),599–608.
Kitamura, H., Matsushima, N., and Sato, M., 2016a. How Does Downstream Firms’ Efficiency Affect Exclusive Supply Agreements? mimeo.
http://ssrn.com/abstract=2306922
Kitamura, H., Matsushima, N., and Sato, M., 2016b. Exclusive Contracts with Complementary Input. mimeo.
http://ssrn.com/abstract=2547416
Motta, M., 2004. Competition Policy. Theory and Practice. Cambridge: Cambridge
University Press.
Posner, R.A., 1976. Antitrust Law: An Economic Perspective. Chicago: University ofChicago Press.
8

Rasmusen, E.B., Ramseyer, J.M., and Wiley Jr., J.S., 1991. Naked Exclusion. American Economic Review 81(5), 1137–1145.
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., 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., 2000. Naked Exclusion: Comment. American Economic Review 90(1), 296–309.
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.

9Π (𝑐𝐸 )Π (𝑐𝐼 )54

Γ(𝛽)Entry3Exclusion
210.00.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

𝛽

Figure 1: Results of Proposition 110