Introduction Model Results Conclusions
Exclusive dealing with commitment problem
Rostislav Stan¥k
March 13, 2013
Rostislav Stan¥k
Exclusive dealing with commitment problem
Introduction Model Results Conclusions
Exclusive dealing
Exclusive dealing refers to contracts that require to purchase
products or services for a period of time exclusively from one
retailer.
• Exclusive dealing can have anti-competitive eect. It allows
dominant rm to deter ecient entry (foreclosure practice).
• There can be also eciency gains.
• It protects specic investment against opportunistic behaviour
(Segal, Whinston 2000).
• Stimulate investment into retailers services (Besanko, Perry
1993)
The ability of an incumbent to deter entry by writing exclusionary
contracts with customers has been subject of contention in the
antitrust literature.
Rostislav Stan¥k
Exclusive dealing with commitment problem
Introduction Model Results Conclusions
Chicago school argument
1 In order to sign an exclusive contract a buyer has to be
compensated for the loss it suers.
2 This loss amounts to the dierence between consumer surplus
under competitive price and consumer surplus under monopoly
price.
3 This equals monopoly prot plus the deadweight loss.
Conclusion:
The incumbent cannot protably use exclusive contacts to deter
entry. Eciency considerations explain the use of exclusive
contracts.
Rostislav Stan¥k
Exclusive dealing with commitment problem
Introduction Model Results Conclusions
Literature review
• Segal, Whinston (1996). Entrant needs to supply minimum
number of buyers to cover its xed costs. Incumbent can
exploit buyers' lack of coordination and deter entry.
• Fumagalli, Motta (2004). Exclusive contract do not involve
nal consumers but rms. Anticompetitive eect of exclusive
contacts depends on the intensity of competition in the
downstream market.
• Abito, Wright (2008). Exclusive contacts deter entry when
markets are more competitive under linear pricing. Exclusive
contacts deter entry regardless of the extent of competition
under two-part tari.
Rostislav Stan¥k
Exclusive dealing with commitment problem
Introduction Model Results Conclusions
Abito, Wright (2008)
Assumptions:
1 Incumbent proposes exclusive contact to the two retailers.
2 Entrant enjoys lower marginal costs.
3 The manufacturers make oers to available retailers. The
contracts are secret and retailers conjectures are symmetric. It
excludes commitment problem from their model.
4 Degree of competition between retailers is parameterized.
Conclusions
1 Under linear prices exclusive dealing causes foreclosure
regardless of entry costs if degree of competition is high.
2 Under two-part tari exclusive dealing causes foreclosure
regardless of entry costs and degree of competition.
Rostislav Stan¥k
Exclusive dealing with commitment problem
Introduction Model Results Conclusions
Commitment problem
Manufacturer faces a commitment problem when dealing with
retailer.
Consider a case of one manufacturer and two retailers. Contracts
specifying quantity and price are publicly observed. Manufacturer
credibly oers contract
(q1, T1) = (q2, T2) = (
qM
2
,
pMqM
2
)
Sticking to this contract is not credible if contracts are secret.
Manufacturer has an incentive to oer more than qM/2.
Rostislav Stan¥k
Exclusive dealing with commitment problem
Introduction Model Results Conclusions
Conjecture assumption
• Symmetric conjectures. Retailers assume that manufacturer
makes the same oer to them. This assumptin solves the
commitment problem. It is credible to oer
(q1, T1) = (q2, T2) = (
qM
2
,
pMqM
2
)
This assumption is not very realistic (Rey, Tirole 2007).
• Passive conjectures. Each retailer keeps assuming that the
manufacturer oers the equilibrium oer to its rival. This
assumption creates commitment problem.
• Warry conjectures (Rey, Verge (2004)). Retailer anticipates
that manufacturer oers contract that is best for
manufacturer.
Rostislav Stan¥k
Exclusive dealing with commitment problem
Introduction Model Results Conclusions
Model
• Consumers
• Consumers have quadratic utility function
• Demand function Qi =
1−β−pi +βpj
1−β2
• Inverse demand function Pi = 1 − qi − βqj
• Firms
• Incumbent manufacturer (I) produces a good at a constant
marginal cost cI
• A potential entrant (E) has lower marginal cost cE < cI.
Entrant faces xed cost of entry equal to F > 0
• The good is used by two retailers as input to produce a nal
good. The only retailers' cost is the wholesale price wi
Rostislav Stan¥k
Exclusive dealing with commitment problem
Introduction Model Results Conclusions
Competition
The degree of competition is measured by parameter β ∈ [0, 1). As
β → 1, product dierentiation disappears.
Cournot competition reects a situation in which the manufacturer
produce before the nal consumers formulate their demand. The
downstream rms are capacity constrained.
Bertrand competition reects a situation in which the manufacturer
produce after the nal consumers formulate their demand.
Rostislav Stan¥k
Exclusive dealing with commitment problem
Introduction Model Results Conclusions
Timing
1 Incumbent oers exclusive contract which involves xed
compenstaion x
2 Entrant makes entry decision
3 Manufacturers oer contract specifying wi under linear
wholesale contract or (wi, Ti) under two-part tari.
4 Retailers compete for cosumers by setting prices pi or
quantities qi
Rostislav Stan¥k
Exclusive dealing with commitment problem
Introduction Model Results Conclusions
Passive conjectures
Price contracts are secret and retailers have passive conjectures,
when receiving out-of-equilibrium oer. Retailers do not revise their
beliefs.
• Reaction function under Cournot competition
Qi(wi) = argmax(Pi(qi, qe
j ) − wi)qi
• Reaction function under Bertrand competition
Pi(wi) = argmax(pi − wi)D(pi, pe
j )
Quantity sold by retailer is
qi = Di(P1(w1), P2(w2))
Rostislav Stan¥k
Exclusive dealing with commitment problem
Introduction Model Results Conclusions
Cournot with linear wholesale prices
• Wholesale contract determines linear wholesale price w1 and
w2
• Retailers compete by setting quantity q1 and q2
What happens in each of possible subgames following exclusive
contracts being signed?
Let S denote the number of retailers that sign the contract.
Rostislav Stan¥k
Exclusive dealing with commitment problem
Introduction Model Results Conclusions
Cournot with linear wholesale prices, S=2
• With passive conjectures, each retailer anitcipates that its rival
receives the equilibrium oer and puts equilibrium quantity qe
j
on the market. Its best repsonse function is
qi(wi) =
1 − wi − βqe
j
2
• Incumbent then chooses wholesale prices w1 and w2 to
maximize ΠI = (w1 − cI)q(w1) + (w2 − cI)q(w2)
• It holds for the compesation fees that x1 + x2 ≤ ΠI
• Πmax = ΠR + ΠI/2 denotes maximum retailer's prot
including the compensation fee x under the condition that
other retaler obtains the same prot.
Πmax
S=2 =
(1 − c)2(3 − 2β)2
(4 − β)2
Rostislav Stan¥k
Exclusive dealing with commitment problem
Introduction Model Results Conclusions
Cournot with linear wholesale prices, S=1
1 Entrant does not enter. The situation is the same as before.
Retailer which does not signed an exclusive contract (R2) does
not obtain compensation.
2 Entrant enters.
• Entrant sell through R2 with wholesale price w2 = cI. w1 is
given by maximizing (w1 − cI)q1(w1)
• Compensation fee x ≤ ΠI. R1's maximum prot including
compesation fee is Πexc
S=1 = (1−c)23(2−β)2
(8−β2)2
• R2's prot is Πfree
S=1 = (1−c)2(4−β)2
(8−β2)2 .
• It holds that Πexc
S=1 < Πfree
S=1
Rostislav Stan¥k
Exclusive dealing with commitment problem
Introduction Model Results Conclusions
Cournot with linear wholesale prices, S=0
• Both retailers buy through E at a common price
w1 = w2 = cI. Otherwise I could protably attract retailers.
• Both retailers obtain prot
ΠS=0 =
(2 − β)2(1 − c)2
(4 − β)2
Rostislav Stan¥k
Exclusive dealing with commitment problem
Introduction Model Results Conclusions
Cournot with linear wholesale prices
Suppose that entrant's xed costs are low enough.
F ≤
(cE − cI)(1 − cI)(4 − β)2
(8 − β2)
This implies that E enters in case S = 1.
exclusive free
exclusive Πmax
S=2,Πmax
S=2 Πexc
S=1,Πfree
S=1
free Πfree
S=1,Πexc
S=1 ΠS=0,ΠS=0
Table: Exclusive contract
It holds Πfree
S=1 > ΠS=0 > Πmax
S=2 > Πexc
S=1
Rostislav Stan¥k
Exclusive dealing with commitment problem
Introduction Model Results Conclusions
Cournot with linear wholesale prices
Suppose that entrant's xed costs are high.
F >
(cE − cI)(1 − cI)(4 − β)2
(8 − β2)
This implies that E does not enter in case S = 1.
exclusive free
exclusive Πret
S=2 + x,Πret
S=2 + x Πret
S=2 + x,Πret
S=2
free Πret
S=2,Πret
S=2 + x ΠS=0,ΠS=0
Table: Exclusive contract
For any given x > 0, there is an equilibrium where both retailers
sign exclusive contract. There is no entry equilibrium because
incumbent can oer contract to retailer such that
Πret
S=2 + x > ΠS=0.
Rostislav Stan¥k
Exclusive dealing with commitment problem
Introduction Model Results Conclusions
Cournot with two-part tari
• Two-part tarrif contract determines linear wholesale price w1
and w2 and xed fee T1 and T2
• Retailers compete by setting quantity q1 and q2
What happens in each of possible subgames following exclusive
contracts being signed?
Rostislav Stan¥k
Exclusive dealing with commitment problem
Introduction Model Results Conclusions
Cournot with two-part tari, S=2
• Passive conjectures leads to best repsonse function
qi(wi) = argmax(P(qi, qe
j ) − wi)qi
• Incumbent then chooses wholesale prices w1 and w2 to
maximize ΠI = (w1 − cI)q1(w1) + F1 + (w2 − cI)q@(w2) + F2
where Fi is retailer's prot Fi = (P(qi(wi), qe
j ) − wi)qi(wi)
• Incumbent chooses w1 = w2 = cI. Incumbent's prot is equal
to the sum of Cournot's prots ΠI = 2ΠC(cI, cI)
• Compensaiton fees cannot exceed incumbent's prot
x1 + x2 ≤ ΠI
• Maximum retailer's prot including the compensation fee x is
Πmax
S=2 = ΠC(cI, cI)
Rostislav Stan¥k
Exclusive dealing with commitment problem
Introduction Model Results Conclusions
Cournot with two-part tari, S=1
1 Entrant does not enter. The situation is the same as before.
Retailer which does not signed an exclusive contract (R2) does
not obtain compensation.
2 Entrant enters.
• Entrant sell through R2 with wholesale price w2 = cE.
• Incumbent is ready to oer contract characterized by wI,2 = cI
and T = 0 to R2. Hence, Πfree
S=1 = ΠC(cI, cI)
• Compensation fee x ≤ ΠI. R1's maximum prot including
compesation fee is Πexc
S=1 = ΠC(cI, cE)
• Entrant obtains prot ΠE
S=1 = ΠC(cE, cI) − ΠC(cI, cI)
Rostislav Stan¥k
Exclusive dealing with commitment problem
Introduction Model Results Conclusions
Cournot with two-part tari, S=0
• Both retailers buy through E at a common price
w1 = w2 = cE.
• Incumbent is ready to oer contract characterized by wI,i = cI
and T = 0. Retailer's prot is therefore ΠS=0 = ΠC(cI, cE).
• Entrant's prot is ΠE
S=0 = 2(ΠC(cE, cE) − ΠC(cI, cE)).
Rostislav Stan¥k
Exclusive dealing with commitment problem
Introduction Model Results Conclusions
Cournot with two-part tari - entry
Compare entrant's prot ΠE
S=1 and ΠE
S=0
ΠE
S=0 =
(2 − β)2(1 − cE)2
(4 − β2)
−
(2(1 − cI) − β(1 − cE))2
(4 − β2)
ΠE
S=1 =
(2(1 − cE) − β(1 − cI))2
(4 − β2)
−
(2 − β)2(1 − cI)2
(4 − β2)
Because prot function is convex it holds that ΠE
S=1 > ΠE
S=0
It is impossible to deter entry because of lack of coordination
Rostislav Stan¥k
Exclusive dealing with commitment problem
Introduction Model Results Conclusions
Cournot with two-part tari
exclusive free
exclusive Πmax
S=2,Πmax
S=2 Πexc
S=1,Πfree
S=1
free Πfree
S=1,Πexc
S=1 ΠS=0,ΠS=0
Table: Exclusive contract
It holds Πfree
S=1 > ΠS=0 > Πmax
S=2 > Πexc
S=1
Dominant startegy is to be a free buyer
Rostislav Stan¥k
Exclusive dealing with commitment problem
Introduction Model Results Conclusions
Conclusions
• Linear wholesale prices
• There is only entry equilibrium if xed costs are low enough.
• There is only exclusion equilibrium if xed costs are high
enough.
• Entrant's prot is decreasing in β
• Two-part tari
• If it is protable to enter when S = 0, it is also protable to
enter when S = 1
• There is only entry equilibrium.
• It is not possible to deter entry by exclusive dealing.
Rostislav Stan¥k
Exclusive dealing with commitment problem
Introduction Model Results Conclusions
Conclusions
• Conclusions are dierent from Abito, Wright (2008)
• Two-part tari: Only exclusion equilibria X No exclusion
equilibria
• Linear prices: Only exclusion equilibria if β < 1/2 X Depends
on xed costs
• Introducing a commitment problem changes the results
substantially.
• Incumbent cannot exploit its market power. Compensation fee
has to be lower which makes exclusive contract less protable.
Rostislav Stan¥k
Exclusive dealing with commitment problem
Introduction Model Results Conclusions
Conclusions
Thank you for your attention.
Rostislav Stan¥k
Exclusive dealing with commitment problem