The Use of Exclusive Contracts to Deter Entry

John Simpson

Federal Trade Commission

and

Abraham Wickelgren

Federal Trade Commission

June 27, 2001

This article reflects the opinion of the authors and is not intended to represent the position of the

Federal Trade Commission or the views of any individual Commissioner. Ezra Friedman, Ian

Gale, David Reiffen, Louis Silvia, and John Yun provided helpful comments.
Abstract

This paper shows that an upstream monopolist that sells to competing downstream firms can

profitably use exclusive contracts to deter entry even where scale economies are absent. By

offering downstream firms a discount if they sign an exclusive contract covering later periods,

the incumbent monopolist can often place each downstream firm in a prisoner’s dilemma. 

Because a downstream firm that refuses to sign the exclusive contract loses profit to downstream

firms that sign the exclusive contract, downstream firms will sign exclusive contracts even when,

over the long-term, they would obtain the upstream good at a lower price if they all refused to

sign.
1

I. Introduction

U.S. antitrust law treats exclusive contracts, which require that a buyer make all of its

purchases of a particular good from a single seller, under a rule of reason standard in which

possible economic efficiencies are balanced against possible anticompetitive harm. “Chicago

School” scholars (Richard A. Posner (1976, p. 212) and Robert H. Bork (1978, p. 309)),

however, have argued that U.S. antitrust law should treat exclusive contracts as per se legal. 

They first note that the excluding firm imposes harm on consumers equal to its monopoly profit

plus some deadweight loss. They then assume that the excluding firm can not get buyers to sign

exclusive contracts except by fully compensating buyers for this harm. Given this assumption,

they note that, since the excluding firm only gains the monopoly profit from using exclusive

contracts, the excluding firm can not profitably induce buyers to sign exclusive contracts. Based

on this, they conclude that efficiency considerations, rather than anticompetitive motives, explain

the use of exclusive contracts.

In arguing that exclusive contracts are unlikely to be anticompetitive, the Chicago School

model implicitly assumes that buyers are final consumers rather than competing downstream

firms and that a buyer does not impose externalities on other parties when it signs an exclusive

contract. This paper shows that when these two assumptions are relaxed, an upstream incumbent

monopolist can often use exclusive contracts to deter entry. Unlike several previous papers (e.g.,

Eric B. Rasmusen et al. (1991), Illya R. Segal & Michael D.Whinston (2000a)), we show that this

is true even where upstream scale economies are absent. 

In this paper, we consider a model where an entrant can not initially supply a buyer at the

same cost as the incumbent monopolist. This condition would hold if “learning by doing”
1The entrant may not be able learn without a buyer since what it needs to learn may be

something specific to the industry that only a buyer can provide.

2

enabled upstream firms to produce at lower cost over time. It would also hold if downstream

firms required some period of testing before they would commit to obtain a substantial portion of

their inputs from a new entrant. Next, we assume that this entrant can supply buyers with the

input at the same cost as the incumbent firm after the initial period as long as exclusive contracts

have not shut it out of the industry. Exclusive contracts can do this if they preclude the

incumbent from producing in the initial period, thereby preventing “learning by doing”1

 or

product testing.

Given these assumptions, the incumbent firm can create a prisoner’s dilemma for the

downstream firms by offering these firms discounts for signing an exclusive contract. A

downstream buyer that refuses to sign the exclusive contract foregoes the discount. Foregoing

the discount puts the non-signing firm at a cost disadvantage relative to any downstream

competitor that signs the exclusive contract. As a consequence, the non-signing firm loses profit

to the signing firm(s) during the interim period. When the entrant comes in, both the non-signing

firm and the signing firms obtain the upstream good at a duopoly price. This increases the profits

of both the non-signing firm and the signing firms equally over their pre-entry profits. In this

payoff structure it is profitable for the incumbent to offer a discount such that all downstream

firms sign the exclusive contract even though, over the long-term, they would obtain the

upstream good at a lower price and earn a higher profit if they all refused to sign. Thus, the

incumbent monopolist can use exclusive contracts to deter efficient entry.

We also consider a slight variation of the above model where the entrant does not exist in
2Note, neither the price matching clause nor the ability to commit to a future price (at or

above cost) will alone deter entry since there is no entry cost. The exclusive contract is necessary

for entry deterrence.

3

period 1 but can produce the input at the same cost and at the same scale as the incumbent in

period 2. In this model, the incumbent monopolist can use its control over period 1 input prices

to induce downstream firms to pay it a monopoly price in period 2 if it can use long-term

contracts. Specifically, instead of requiring that buyers agree to only buy from the incumbent in

the first period, the incumbent requires buyers to sign exclusive contracts that force them to

purchase only from the incumbent in the second period. In order to create the prisoner’s

dilemma for the downstream competitors, the contract must ensure that a downstream firm that

signs the contract does not pay a higher input price than any firms that do not sign the contract if

entry occurs. This can be accomplished either by a price matching clause or by committing to

supply the input at or near cost whenever not all downstream competitors have signed the

exclusive contract.2 With such a contract, the logic of the original model guarantees that there

will be a first period discount for exclusive dealing that will induce all firms to sign the contract,

eliminating any market for the entrant’s product (see Section V).

This type of contract can also be thought of as a tying agreement where the tie is across

periods. If the incumbent produced two (not completely complementary) products that are both

used by competing downstream firms, a similar tying agreement between the two products would

profitably exclude competition in one market. Thus, the model not only shows that exclusive

contracts can profitably deter entry when an incumbent is selling to downstream competitors, it

also shows that tying contracts can be both anticompetitive and profitable in this circumstance as

well.
4

Three critical differences between our basic model and that of the Chicago School

generate the entry deterring effect of exclusive contracts. The first is that we allow the

incumbent monopolist to compensate the buyers for signing the exclusive contract through lower

unit prices rather than just lump-sum transfers. As a result, the cost of the compensation to the

incumbent is less than the benefit to the buyers (lower prices reduce the dead weight loss). 

Second, our model is a multi-period model rather than a one-period model. The monopolist has

a period to reward (punish) buyers who sign (do not sign) the exclusive contract during which a

non-signer cannot reap the benefits of competition. Third, as mentioned above, the Chicago

School model assumes that there are no externalities among buyers. In contrast, we assume that

the buyers are competing against each other in a downstream market. Thus, when one buyer pays

a higher unit price for the product, other buyers have a competitive advantage in that market. 

This gives the incumbent an extra way to reward (punish) buyers for signing (not signing) the

exclusive contract. Essentially, it can force a non-signing buyer to bear some of the cost of

compensating a signer for signing the contract.

By relaxing the Chicago School’s assumption that a buyer does not impose externalities

on other parties when it signs an exclusive contract, several recent papers have also shown that

an incumbent monopolist can use exclusive contracts to deter entry. Rasmusen et. al. (1991) and

Segal and Whinston (2000a) show that exclusion can be profitable assuming the following: 1) an

incumbent monopolist sells to diffuse buyers; 2) a potential entrant would need to make sales to

more than one buyer; and 3) a potential entrant’s minimum viable scale is large relative to
3For example, assume that an incumbent monopolist sells to 100 buyers of equal size, and

that this incumbent, by signing exclusive contracts with 61 buyers, can prevent an entrant from

attaining its minimum viable scale. Given these assumptions, exclusion would be profitable if

the monopoly profit from all 100 buyers exceeded the required compensation to 61 buyers.

5

industry sales.3

 In these papers, buyers who sign exclusive contracts prevent the entrant from

attaining its minimum viable scale. This, in turn, imposes an externality on buyers who do not

sign exclusive contracts. Our paper is similar to these papers in that we also rely on externalities

to show that exclusive contracts can deter entry. Our paper differs from these papers in that we

show an incumbent monopolist can use exclusive contracts to deter entry even in the absence of

scale economies.

B. Douglas Bernheim and Whinston (1998) consider a model with the following

assumptions: 1) a single market is served by a single retailer; 2) with time, a second retail market

becomes viable; and 3) a manufacturer must serve more than one market to achieve important

scale economies. Given these assumptions, Bernheim and Whinston show that in certain

circumstances a manufacturer can gain a monopoly in the second retail market by signing an

exclusive contract with the first retailer. Thus, in the Bernheim and Whinston model, a

manufacturer and the first retailer form a coalition to extract monopoly profit from the second

retailer. As with the Rasmusen et al. and Segal and Whinston papers, the Bernheim and

Whinston paper relies on the assumption that an upstream firm must make sales to more than one

buyer in order to obtain important scale economies. As noted above, our paper does not make

this assumption.

Finally, Phillippe Aghion and Patrick Bolton (1986) consider a model with the following

assumptions: 1) an incumbent monopolist sells to a single buyer; 2) absent exclusive contracts, a
6

new seller would enter if it had lower costs than the incumbent; 3) absent exclusive contracts,

this entrant would gain as surplus the difference between his cost of production and the

incumbent’s cost of production. Given these assumptions, Aghion and Bolton note that the

incumbent monopolist and the buyer can sign a contract with liquidating damages that would

force the entrant to pay some of his surplus to the incumbent/buyer coalition. While this would

sometimes deter efficient entry, the incumbent/buyer coalition only benefits from the exclusive

contract when entry actually occurs. To get this result, the Aghion and Bolton model relies on

the assumption that the entrant has lower costs than the incumbent. In contrast, our model

explains the use of exclusive contracts when the incumbent and the entrant have similar costs. 

The remainder of this paper is organized as follows: Section II presents a simple two

period model in which an incumbent monopolist can profitably use exclusive contracts to deter

entry. Section III extends this result to the infinite horizon case. Section IV considers whether

an entrant can successfully counter the incumbent monopolist’s use of exclusive contracts. 

Section V analyzes the basic model assuming that both the incumbent and entrant can sign longterm contracts, and Section VI concludes.
4Throughout this paper, we use the term monopolist as shorthand for a dominant firm.

5While, this may not be the optimal form for the exclusive contract, we only need to show

that there exists an exclusive contract that can profitably deter entry.

7

II. Simple Two-Period Model

Our model relies on the following assumptions:

1. There are two periods, with no discounting.

2. An upstream monopolist4

 (the incumbent) sells to two downstream competitors. 

3. Entry requires no fixed cost, but in the first period in which it enters, an entrant’s

production must be very small (so that buyers can test its product).

4. If the entrant can make sales in period 1, then in period 2 the entrant can produce

at the same cost as the incumbent. Thus, the entrant can attain his minimum

viable scale in period 2 by selling to a single downstream firm in period 1.

The sequence of actions is the following:

1. The upstream monopolist offers downstream buyers a choice between a nonexclusive contract at the monopoly price or an exclusive contract that offers a

discounted price for purchases in period 1.5

2. The downstream firms independently decide which contract to accept.

Because of assumption (3), in the entrant’s first period of existence the incumbent’s

myopically optimal strategy is to price at the monopoly level. Thus, if both downstream firms

sign the exclusive contract, then the incumbent sells to them at the discounted price in period 1
6

It is possible that the non-signer’s demand curve is slightly altered when the signer

receives the input at the discounted price, thus changing the optimal monopoly price for that

consumer. As will become clear, taking this into account would not affect the results.

8

and charges them the monopoly price in period 2. If one of the downstream firms refuses to sign

the exclusive contract, then, in period 1, the monopolist sells to the signer at the discounted price

and sells to the non-signer at the monopoly price. (This contract is renegotiation proof since, in

period 1, the entrant’s low production (assumption 3) ensures that the monopolist’s best response

to entry is to charge the non-signer the monopoly price.6) In period 2, the entrant and the

monopolist compete in some duopoly pricing game yielding a price somewhere in between

marginal cost and the monopoly price.

Define: Bm = the downstream firm’s profit when it and its competitor pay a monopoly 

upstream price. 

BD

 = the downstream firm’s profit when it and its competitor pay a discounted

monopoly price to the upstream firm.

Bh = the downstream firm’s profit when it pays a discounted monopoly price to

the upstream firm and its competitor pays the monopoly price.

Bl = the downstream firm’s profit when it pays the monopoly price to the

upstream firm and its competitor pays a discounted price.

Be = the downstream firm’s profit when entry creates upstream duopoly

competition. 

Thus, the payoffs for the downstream firms are as follows. If both downstream firms sign

exclusive contracts with discounts, then both downstream firms earn BD

 in the first period and Bm
9

in the second period. If neither downstream firm signs an exclusive contract then an entrant

enters in period 1, and both downstream firms earn Bm in period 1 and Be in period 2. If one firm

signs the exclusive and one does not, then an entrant enters in period 1,and the signer earns Bh in

period 1 and Be

 in period 2. The non-signer earns Bl

 in period 1 and Be

 in period 2. These

payoffs are related as follows:

(1) Be > Bm > Bl and Bh > BD > Bm > Bl

Downstream firms earn greater profits when both can buy their inputs at the duopoly

price than at the monopoly price. A downstream firm earns more profits when it can buy the

input at a discounted price while its rival has to pay the monopoly price than when both get the

discounted price (this is due to the fact that these firms are competitors). When both get the

input at the discounted price, however, they each earn greater profits then when both have to pay

the monopoly price. And, a firm earns more profits when both pay the monopoly price than

when it pays the monopoly price while its rival gets a discount (again, due to competition). We

will show below that the discounted price will be weakly greater than the duopoly price, so Be

 >

BD, but this is not an assumption of the model.
10

Given these payoffs, the following prisoner’s dilemma game represents the situation

faced by the downstream firms when deciding whether or not to sign the exclusive contract.

downstream firm 2

sign don’t sign

downstream

firm 1

sign BD+Bm

, BD+Bm Bh+Be

, Bl+Be

don’t sign Bl+Be, Bh+Be Bm+Be, Bm+Be

payoffs to: (downstream firm 1, downstream firm 2)

For each downstream firm, signing the exclusive contract is a dominant strategy as long as the

following conditions hold:

Condition 1: Bh+Be $ Bm+Be or Bh $ Bm

This condition requires that the downstream firm’s profit when it gets a discount and its

competitor pays the monopoly price exceeds its profit when both it and its competitor pay the

monopoly price. This condition holds for any positive discount.

Condition 2: BD+Bm $ Bl+Be

 or Bm

 - Bl $ Be

 - BD

Since Bm - Bl is positive, Be - BD can also be positive. This, in turn, implies that the downstream

firms’ profits with the discount can be less than their profits with duopoly. That is, the
11

incumbent monopolist’s discounted price can exceed the duopoly price. 

Finally, offering the exclusive contracts with the discount is profitable for the incumbent

monopolist as long as his profit with the discount exceeds his profit with duopoly. 

Condition 3: BI,D $ BI,d

This condition holds because, as noted above, downstream firms will accept a discounted

price that exceeds the duopoly price. Thus, we have proved the following result.

Proposition 1. Whenever there is some competition between the two downstream firms (i.e.,

payoffs are given by (1)), then the monopolist can profitably offer a discount for signing an

exclusive contract that both downstream firms will sign, and, thus, deter entry.
12

 Period 1 Period 2

 

 

 

pm pm 

 

 A1 B1 A2 B2

 

pe pe 

 

 Qm Qe Qm Qe 

 

To give some intuition to our model, it is useful to return to the basic argument of Posner

and Bork. The figure on the left shows the upstream market in period 1, and the figure on the

right shows the upstream market in period 2. Let us assume for now that downstream buyers do

not compete at all. Posner and Bork argue that an incumbent monopolist in period 1 could only

get buyers to sign exclusive contracts by offering to compensate them for the area A2 + B2. 

However, according to Posner and Bork, this would be unprofitable for the monopolist because it

only obtains A2 by using exclusive contracts.

This analysis, however, overlooks an important feature of this two period model: The

incumbent monopolist is in a unique position to compensate buyers for signing exclusive

contracts. By lowering its prices in period 1 from the monopoly price to the price after entry (the

duopoly price), the monopolist can compensate the buyers an amount A1 + B1 at a cost of only
13

A1 to itself. Thus absent competition among downstream buyers, the monopolist can offer

downstream buyers who sign exclusive contracts a discount equal to the difference between the

monopoly price and the duopoly price. This would fully compensate downstream buyers for their

second period losses without imposing overall (period 1 + period 2) losses on itself. Essentially,

the incumbent deters entry by giving the buyers a period of duopoly pricing and a period of

monopoly pricing (exactly what they would get with entry) if they sign the exclusive contract.

Let us now add downstream competition. With downstream competition, a downstream

firm with lower costs than its rival earns more profit than its rival for two reasons: It has lower

costs, and these lower costs enable it to capture a disproportionate amount of market share at the

expense of its rival. Consequently, the desire to gain market share at its rival’s expense and to

prevent its rival from gaining market share at its expense gives downstream competitors a strong

incentive to sign an exclusive contract and obtain a discount. For this reason, even a small

amount of downstream competition would enable the monopolist to get downstream firms to sign

exclusive contracts even when it offers them a discount that leaves its first period price above the

duopoly level. 

Of course, the amount of anticompetitive harm from the use of exclusive contracts in this

model depends on the size of this discount. If the discount is very large (the first period price is

close to the duopoly level), then the anticompetitive harm from using exclusive contracts to deter

entry is comparatively small. If the discount is small (the first period price is close the monopoly

level), then the anticompetitive harm from using exclusive contracts to deter entry will be larger. 

As we discussed above, when the downstream firms do not compete at all, exclusive contracts

can deter entry, but they do not affect the total input prices paid by the downstream buyers (they
14

only reverse the periods when monopoly and duopoly prices are paid). If the downstream firms

engage in Bertrand competition (with undifferentiated products), however, the incumbent can

come arbitrarily close to the monopoly outcome in both periods. This occurs because the

downstream buyers do not care at all about the level of the input price, only its relation to the

input price paid by their rival. So, they both earn zero profits in period 2 whether there is entry

or not (since both pay the same input prices in that period). Thus, each buyer will sign the

exclusive contract for any arbitrarily small discount. 

Whether this relationship between downstream competition and the size of the discount

holds everywhere is more problematic. The incumbent will offer an exclusive contract with a

discount that meets Condition 2 with equality:

(2) BD

 + Bm

 = Bl

 + Be

 

or

(2*) (Be - BD) - (Bm - Bl ) = 0

We now rewrite Bm and Be as a function of downstream competition (2) and rewrite BD and Bl as

a function of both downstream competition (2) and the size of the discount (D): 

(2**) (Be (2) - BD (2,D)) - (Bm (2) - Bl (2,D)) = 0

Differentiating (2**) with respect to 2 gives the following 

(3) 0={M(Be

 (2) - BD

 (2,D))/M2 - M(Bm

 (2) - Bl

 (2,D))/M2} - (MD/M2)[M( BD

 (2,D)- Bl

 (2,D))/MD]

which can be rewritten as:

(4) (MD/M2) = {M(Be

 (2) - BD

 (2,D))/M2- M(Bm

 (2) - Bl

 (2,D))/M2}/ M( BD

 (2,D)- Bl

 (2,D))/MD

The denominator of this expression, (M(BD (2,D)- Bl (2,D))/MD), is positive. A larger

discount increases a firm’s profit when both it and its rival get the discount but reduces a firm’s
15

profit when its rival gets the discount but it does not. The first term in the numerator (M(Be (2) -

BD (2,D))/M2) is negative. As downstream competition intensifies, the benefit to a firm from

getting an input at the duopoly price rather than the higher discounted monopoly price is

competed away. 

The sign of the second term in the numerator ( M(Bm (2) - Bl (2,D))/M2) is more

problematic. Certainly, starting from the point of no competition (the two products are

unrelated) the sign must be positive since increasing the degree of downstream competition must

increase the difference Bm (2) - Bl (2,D). (This difference is zero when the products are unrelated

since my rival’s output price (and, thus input price) does not affect my profits, but is positive

when there is some competition.) When the two products become very close substitutes,

however, this sign may be negative. If the firm paying the lower input price chooses to price at

the marginal cost of the firm paying the higher input price, then increased competition would

have no effect on Bl(2,D), while continuing to reduce Bm (2). 

If the second term in the numerator were always positive, then the total expression would

always be negative. This would imply that the discount that the incumbent must pay falls as

downstream competition intensifies. However, because the second term will sometimes be

negative, we cannot rule out the possibility that, for some downstream demand functions, there is

a region where greater downstream competition does not reduce the required discount. That said,

we conjecture that such regions either only exist for very peculiar demand functions or do not

exist at all. 
16

III. An Infinite Horizon Model

In this section, we show that the main results of the two period model are still valid in an

infinite horizon setting. We assume that the entrant can enter at any period and that long term

exclusive contracts are not feasible. As was true above, if exclusive contracts deter entry in this

case, they will still deter entry when the menu of possible exclusive contracts is expanded. We

now introduce a discount rate, $ and let V represent the downstream firm’s value function. This

value function will depend only on whether or not there is a fully qualified entrant (an entrant

that has already had one period of (tiny) sales). As before, Condition 1 always holds. The

analogue of Condition 2 requires that in any no entry state (NE), a downstream firm will sign an

exclusive when its rival has signed the exclusive. That is:

Condition 2N: BD+$*V(NE) $ Bl+$*V(E) or BD- Bl $ $*(V(E)-V(NE))

(We allow the discount in this model to differ from the discount in any prior model.) If the

incumbent monopolist finds it profitable to offer a discount that satisfies this condition in any

given period, it will find it profitable to do so in every period. Thus, one can write the previous

expression as follows: 

(5) BD

- Bl

 $($ /1-$)*(Be

-BD

) or BD $ $*Be+ (1-$)*Bl

From this, it is easy to see that as the discount factor increases (it takes the entrant less time to be

able to compete with the incumbent on an equal footing) the required discount must increase. In

the limit, as the discount factor approaches one, the incumbent must offer the downstream firms

duopoly prices to get them to continue to agree to the exclusive contract.
17

Finally, offering the exclusive contracts with the discount is profitable for the incumbent

monopolist as long as his profit with the discount exceeds his profit with duopoly. 

Condition 3N: (1/1-$) BI,D $ BI,m + ($/1-$)*BI,d or BI,D $(1-$)* BI,m + $*BI,d 

The following proposition shows that exclusive contracts can still deter entry in this infinitehorizon setting.

Proposition 2. As long as the downstream market is characterized by some degree of

competition, it is profitable for the incumbent to offer a discount for an exclusive contract that

deters entry.

Before proving this result, we first establish the following lemma.

Lemma 1. The discount necessary to induce the downstream firms to sign the exclusive is

increasing in the discount factor.

Proof. Differentiating (5) at equality and rearranging terms gives the following:

(6) MpD/M$ = (Be- Bl)/[-(1-$)B2(pm,pD)+(B1(pD,pD) +B2(pD,pD))]

Here (and in the proof of Proposition 2), the B function with two arguments is the profit of the

downstream firm where the first argument is the input price it is paying and the second is the

input price its rival pays. Numerical subscripts on this function represent partial derivatives. 
18

Hence, B2(pm,pD) is the derivative with respect to the rival’s input price of the profit of the

downstream firm when he is paying the monopoly price for the input and his rival is paying the

discounted price. The denominator is negative since increasing the discounted price increases

the profit of a firm whose rival is paying that price when he is not, and increasing the price both

downstream firms pay reduces their profits. The numerator is positive by (1). So, if the

discounted price is decreasing in the discount factor, the discount is increasing. Q.E.D.

Proof of Proposition 2. We can rewrite condition 3N making the dependence of profits on price

explicit as follows:

(7) BI

(pD

)-((1-$)* BI

(pm

) + $*BI

(pe

)/2)>0

Here, pD

 represents the discounted price, pe

 the post-entry (duopoly) price, and pm

 the monopoly

price. BI is the function that gives total upstream profits for a given price. Thus, in the duopoly

case I divide by two since the incumbent only gets half the upstream profits after entry. 

However, if the following inequality holds then so will (7):

(7*) BI(pD)-((1-$)* BI(pm) + $*BI(pe))>0

Differentiating the left hand side of (7*) with respect to $ gives the following:

(8) (MpD/M$) BIN(pD)+BI(pm) -BI(pe)

Substituting the explicit expression for MpD

/M$ obtained in Lemma 1 into the above expression

gives the following:

(9) {[B(pe

,pe

) -B(pm

,pD

)] BI

N(pD

)-(BI

(pm

) -BI

(pe

))[(1-$)B2

(pm

,pD

)-(B1

(pD

,pD

) +B2

(pD

,pD

))]}

{1/[-(1-$)B2

(pm

,pD

)+(B1

(pD

,pD

) +B2

(pD

,pD

))]}
19

The denominator in (9) is negative (it is just the denominator of MpD/M$). To determine the sign

of the numerator we first rewrite it as follows:

(10) {[B(pe,pe) -B(pm,pm)+B(pm,pm)-B(pm,pD)] BIN(pD)-(BI(pm) -BI(pe))

[(1-$)B2(pm,pD)-(B1(pD,pD)+B2(pD,pD))]}

Now, we make the following Taylor’s approximations:

B(pe

,pe

) -B(pm

,pm

) .-(pm

-pe

)(B1

(pD

,pD

) +B2

(pD

,pD

))

(11) B(pm,pm)-B(pm,pD) .-(pm-pD)B2(pm,pD)

BI(pm) -BI(pe) .-(pm-pe)BIN(pD)+BI(pe)

With these approximations, the numerator simplifies to the following:

(12) BIN(pD)B2(pm,pD){pe- pD+$ (pm-pe)}

This expression has the sign of the term in curly braces (so long as B2

(pm

,pD

)>0, which is true

whenever the two downstream firms compete to some degree). Since MpD

/M$<0, this term is

decreasing in $. At $=0 it is negative since pe<pD. As $61 it is positive since (5) guarantees that

pD6pe when $61. Thus, for small values of $, (7) is increasing in $, while for large values it is

decreasing in $. Thus, (7) must reach its minimum at either $=0 or 1. At $=0, (7) is zero since

Condition 2O says that pD=pm in this case. Similarly, as $61 it approaches zero since Condition

2O says that pD6pe in that case. So, for any possible value of $, the monopolist can do at least as

well by offering an exclusive contract and deterring entry as by acquiescing to entry. Q.E.D.
7See Robert Innes and Richard J. Sexton (1994) and Ilya R. Segal and Michael D.

Whinston (2000b) for discussions of counter-strategies that entrants can use in the exclusion

theories discussed earlier.

20

IV. Entrant Counter-Strategies7

In this section, we consider whether an incumbent monopolist can use exclusive contracts

to increase overall prices in cases where a prospective entrant can make side payments to a

downstream firm for refusing to sign the exclusive contract. In considering this, we focus on

cases where the incumbent monopolist’s discounted price equals or exceeds the duopoly price,

since the incumbent actually increases welfare if it offers a discount below the duopoly price.

The maximum side payment that the entrant will offer is its (duopoly) profit after entry in

period 2, BE,e. If the entrant can make sales in period 1, it can compete on an equal footing with

the incumbent in period 2. Thus, BE,e=BI,e. Given this, the various conditions become: 

Condition 1O: Bh+Be $ Bm+Be +BI,e or Bh $ Bm +BI,e

Condition 2O: BD+Bm $ Bl+Be +BI,e or Bm - Bl $ Be - BD + BI,e

Condition 3O: BI,D $ BI,e

If the monopolist can strictly deter entry with a discount price equal to the post entry price, then it

can deter entry with a slightly larger discounted price (slightly smaller discount). Thus, if the

monopolist offers a discount price equal the duopoly price, Condition 2O becomes Bm - Bl $ BI,e.

Notice that if Condition 2O holds in this case, Condition 1O (Bh

 - Bm

 $ BI,e ) also (strictly) holds. 

This follows because total profits of downstream firms will be at least as large when one firm

gets a discount as when neither firm gets a discount. Thus, Bh+ Bl

 > Bm

 + Bm

, which can be
21

rewritten as Bh - Bm > Bm - Bl which is greater than BI,e by Condition 2O. Condition 3O will also

hold (strictly, so long as duopoly profits are positive) since we are restricting ourselves to cases

where the incumbent’s discounted price equals or exceeds the duopoly price. Given this, if a

prospective entrant can make side payments to a downstream firm, the incumbent can strictly

deter entry and decrease social welfare if and only if: 

(13) Bm - Bl > BI,e.

We can rewrite (13) as 

(13N) B(pm,pm) - B(pm,pe) > BI(pe)/2

where pe replaces pD in the second term since we allow the incumbent to offer a discounted price

as low as the duopoly price and where BI

(pe

) equals BE,e + BI,e.

The inequality in (13N) will clearly hold whenever upstream competition takes the

Bertrand form since, in that case, upstream duopoly profits are zero. As the duopoly price

increases, the left hand side of (13N) decreases while the right hand side increases. Thus, at the

other extreme, the inequality in (13N) will clearly not hold if the entrant and the incumbent can

collude perfectly since the duopoly price equals the monopoly price. Given this, there must be

some price p* such that if pe < p*, then the incumbent can use an exclusive contract that

decreases welfare to deter entry even when the entrant is allowed to make side payments to a

buyer who refuses to sign the exclusive contract. That is, exclusive contracts are more likely to

deter entry as upstream duopoly competition becomes more intense. Thus, while the ability of

the entrant to make side payments in period 1 limits the ability of the monopolist to deter entry, it

does so precisely in those situations where entry contributes the least to social welfare. 
22

Moreover, as we show in the next section, if long-term contracts are available, then entrant side

payments no longer limit the ability of exclusive contracts to deter entry.

V. Long-Term Contracts

In the two-period model described in section II, the incumbent monopolist is able to use

its power over period 1 prices to induce downstream firms to pay it a monopoly price in period 2. 

In that model, the exclusive contract has this effect because of our assumption about the

technology. If the entrant could not make any sales in period 1, the entrant could not compete on

an equal footing with the incumbent in period 2. Thus, by signing exclusive contracts with the

incumbent in period 1, downstream firms committed themselves to pay the incumbent a

monopoly price in period 2. In this section, we show that we can relax this assumption about

technology if we assume instead that firms can sign long-term contracts in period 1 that set the

period 2 price.

Consider a two period model in which an incumbent monopolist is the only seller in

period 1 and an entrant can enter in period 2. Suppose that both firms can sign long-term

contracts before the start of period 1 that would commit them to sell at a set price in period 2. In

this case, the results in section II guarantee that an incumbent monopolist can still use exclusive

contracts to deter entry. To see this, recall that the incumbent selects his discount by working

back from the period 2 duopoly state. Allowing the entrant to commit to some price in period 2

forces the period 2 duopoly price lower and forces the incumbent to offer a larger discount. 

However, since we have shown that the incumbent can profitably use discounted exclusive
23

contracts to deter entry for any period 2 duopoly price, the incumbent can still use exclusive

contracts to deter entry.

As mentioned in the introduction, this type of contract has characteristics of a tying

contract where the tied product is the same product purchased in the next period. The same

reasoning, of course, would apply if the incumbent were an un-threatened monopolist in one

input and faced competition for a second input, both of which are used by downstream

competitors. Thus, downstream competition also provides an anticompetitive explanation for

tying contracts.

This same insight also shows that the incumbent’s strategy of bribing a downstream firm

not to sign an exclusive contract (or a tying contract) will not work when the incumbent can sign

long term contracts. The incumbent can costlessly guarantee marginal cost pricing in a duopoly

market with the following contract. It offers a downstream firm a discount for signing an

exclusive contract and promises it a second period price equal to marginal cost unless the

incumbent can show that both downstream firms signed this contract. Thus, if the entrant does

induce a buyer not to sign the exclusive, it can enter but will not earn any profits in the second

period. So, it is not willing to pay a positive bribe to a buyer who does not sign the exclusive

contract. We are now in the basic two period model where duopoly prices are Bertrand prices, so

Proposition 1 applies. Of course, the discount the incumbent must offer increases, which reduces

the anti-competitive impact of the exclusive (or tying) contract. But, when the buyers do

compete downstream, the discount will not have to equal the Bertrand price, so there is still some

anticompetitive impact.
24

V. Conclusion

The basic model presented in this paper relies on three assumptions: an incumbent

monopolist sells to competing downstream firms; an entrant can not initially supply a buyer at

the same cost as the incumbent; and this entrant can supply buyers at the same cost as the

incumbent if it can make some sales during an interim period to at least one firm. Where these

assumptions hold, this paper shows that an incumbent monopolist can profitably deter entry by

offering discounts to firms that sign exclusive contracts. Where the incumbent monopolist can

offer a long-term exclusive contract, this paper shows that an incumbent monopolist can deter

future entry even when the entrant does not need to make sales during the interim period in order

to compete later on an equal footing with the incumbent.

The anticompetitive harm that results from such an exclusionary strategy depends on

several factors. As the time required for entry decreases, the incumbent monopolist will need to

offer downstream firms progressively larger discounts. Thus, the anticompetitive harm from this

exclusionary strategy decreases as the length of the interim period decreases. As the intensity of

downstream competition lessens, we believe that the incumbent monopolist will need to offer

downstream firms progressively larger discounts to get them to sign the exclusive contracts. If

we are correct, then the anticompetitive harm from this exclusionary strategy will also decrease

as downstream competition decreases.

In some cases involving a single entrant, the entrant can counter the incumbent

monopolist’s use of exclusive contracts simply by compensating a downstream firm for its losses

during the interim period. In other cases involving a single entrant, this will not be the case. 
25

Finally, we want to stress that since exclusive contracts can help induce efficient investments

(see Segal and Whinston (2000b)), we are certainly not advocating a per se rule against exclusive

contracts. In some cases, even where exclusive contracts deter entry, these efficiency benefits

may outweigh any anticompetitive harm from the use of exclusive contracts.

References

Aghion, Phillippe and Bolton, Patrick. “Contracts as a Barrier to Entry.” American Economic

Review, June 1987, 77(3), pp. 388-401.

Bernheim, B. Douglas, and Whinston, Michael D., “Exclusive Dealing.” Journal of Political

Economy, February 1998, 106(1), pp. 64-103.

Bork, Robert H., The Antitrust Paradox, New York: Basic Books, 1978.

Innes, Robert, and Richard J. Sexton, “Strategic Buyers and Exclusionary Contracts,” American

Economic Review, June 1994, 84(3), pp. 566-84.

Posner, Richard A., Antitrust Law: An Economic Perspective, Chicago: University of Chicago

Press, 1976.

Rasmusen, Eric B., Ramseyer, J. Mark and Wiley, John Shepard Jr., “Naked Exclusion.”

American Economic Review, December 1991, 81(5), pp. 1137-45.

Segal, Ilya R. and Whinston, Michael D. “Naked Exclusion and Buyer Coordination.” American

Economic Review, March 2000a, 90(1) pp. 296-309.

------. “Exclusive Contracts and Protection of Investments.” The RAND Journal of Economics,

Winter 2000b, 31(4), pp. 603-33.