Vertical Contract

Efficiency in Multilateral Vertical Contracting: Bargaining and the Nature of Competition by Catherine de Fontenay and Joshua S. Gans* VERY PRELIMINARY AND INCOMPLETE First Draft: April 2001 This Version: 4th July, 2001

We study bargaining between many upstream and downstream when downstream firms compete with one another. Using new results in noncooperative bargaining we demonstrate that such bargaining results in efficient arrangements -- that is, upstream-downstream contracts are written so as to implement a monopoly outcome downstream. This result occurs despite the fact that upstream and downstream firms bargaining in a decentralised manner (i.e., bilaterally) and regardless of the number of upstream and downstream firms, the nature of downstream competition, the relative bargaining power of upstream and downstream firms and does not require all pairs of upstream and downstream firms to negotiate with one another. We demonstrate that despite being efficient, this bargaining model leads to an equilibrium division of the rents useful in analysing entry, exclusivity, integration and strategic commitment.

*

School of Economics, University of New South Wales and Melbourne Business School, University of Melbourne, respectively. We thank Stephen King, Perry Shapiro, Leslie Marx, and Greg Shaffer for useful comments. Responsibility for all errors lie with the authors. Corresponding author: Professor Joshua Gans ([email protected]). The latest version of this paper is available at www.mbs.edu/home/jgans/research.htm).

1.

Introduction Current theories of oligopoly take firms as the unit of analysis; that is, as the

agents who non-cooperatively choose their prices and quantities generating different degrees of competitive outcomes in an industry. This approach makes sense when all of the relevant agents in the industry are associated exclusively with one firm or another. In that case when bargaining over the division of profits, they will take into account the profits of that firm only. However, it is more realistic to suppose that at least some input suppliers to one firm supply to other firms in the industry. In this case, it is not as obvious what the outcome of factor-firm bargaining will be. In this paper, we consider the issue of the competitiveness of outcomes in an industry where some factors are supplied to all firms. We model firms and input suppliers as engaging in one-on-one bargaining; although production does not begin until all negotiations are complete. Thus, we take a long-run approach and allow all contracts to be subject to potential renegotiation at the behest of one party or another. Negotiations in the industry do not end until no agent has an incentive to renegotiate. Thus, our bargaining model is similar to that of Stole and Zwiebel (1996) who consider bargaining between many input suppliers and a single firm. Our bargaining game yields a striking result: in any subgame perfect equilibrium, negotiated outcomes are such that monopoly outcomes occur in the industry. This is because, in negotiating with a particular firm, a supplier anticipates the impact of any agreed upon contract on its negotiations with the other firm (as well as its impact on other contract negotiations taking place). As a result, all externalities between firms are internalised and the only stable negotiation outcomes are those consistent with the generation of industry profit maximising outcomes; that is, monopoly.

3

In sections 2 and 3, we set up our bargaining game and derive our basic efficiency result for our base case where there are fixed numbers of upstream and downstream firms. Section 4 considers applications of our basic result including the impacts of entry and exclusive arrangements.

2.

A Model of Bilateral Bargaining with Competitive Externalities We begin by specifying the bargaining game that arises between M upstream

firms (the manufacturers) who are supplying N downstream firms (the retailers) in an industry. In an abuse of notation, we will sometimes refer to M and N as the sets of manufacturers and retailers respectively. In a traditional, neoclassical model of vertical relationships each manufacturer, taking into account the derived demand from each retailer, would set input supply prices. In contrast, here we assume that each manufacturer and retailer engage in one-on-one bargaining over input supply terms. The purpose of this section is to specify the form those negotiations take and state formally our equilibrium concept. Bargaining takes place under complete information. Input supply contracts can be viewed as a pair (qmn , pmn ) constituting a supply quantity, qmn , from manufacturer, m, to retailer, n, and a lump-sum transfer, pmn , from n to m.1 Manufacturer m’s costs of supplying a vector of inputs, q m , is a function cm (q m ) that is non-decreasing and quasi-convex in all of its arguments.2 To emphasise, there is nothing technological

1

Note that it is possible that this transfer could be negative. Also, note that this contract specification is a notational simplification; our analysis would carry over to include any non-linear price contract. For a discussion of this issue see Rey and Tirole (1997). 2 We could have made c(.) also depend on the outputs of other manufacturers representing competition between them in resource markets further up the vertical chain. It will be readily apparent below that such an extension could easily be accommodated with precisely the same results.

4

preventing a manufacturer from supplying any retailer, although this specification does not rule out retailer-specific supply costs. On the retailer-side, let p n (Qn , Q - n ) be the (net) profits of retailer n, given their total output, Qn, and a vector of their rivals’ outputs, Q - n . It is assumed that Qn = Fn (q1n ,..., qMn ) . If some manufacturers cannot supply a retailer, n, we will write

Qn ( M \{m}) to denote n’s output if all manufacturers other than m supply it. Notice that this specification allows for considerable asymmetries among retailers in terms of their costs of production and also the degree of differentiation of their respective products. Note also that p n can be viewed as the outcome of a game of oligopolistic competition between the retailers that takes place given a set of input supply agreements. We will assume, however, that p n is non-increasing in the output of any other retailer. Thus, our specification encompasses all commonly assumed forms of oligopolistic competition including Bertrand, Cournot, Hotelling, Stakelberg, dominant firm, supply function and even tacit collusion. Bargaining takes place prior to any production and competition. As mentioned in the introduction, our bargaining game follows the spirit of Stole and Zwiebel (1996). That is, each manufacturer bargains bilaterally with individual retailers and agrees to price terms that split the expected surplus from their agreement. Contracts are, however, not binding and can be renegotiated at any stage. For instance, upon observing a different contract between another retailer-manufacturer pair, one party or the other can re-open negotiations and agree to a contract that splits the changed expected surplus. We look for outcomes that are stable in the sense that no single party has an incentive to renegotiate any contract terms. To see this formally, consider negotiations between manufacturer m and retailer n. As in Stole and Zwiebel, we assume that the outcome of such negotiations

5

equally splits the difference between the surplus earned from an agreement and each party’s’ disagreement payoff.3 In our notation, this requires that (qmn , pmn ) satisfies: n

Ym Fm 644744 8 6444 47444 4 8 æ æ ö ˆ ) - pˆ n = p n + p j - c(q ) - ç pˆ j - c(qˆ ) ö÷ (1) p n (Qn , Q - n ) - pmn - å pin - ç p n (Qˆ n , Q å å å m i ÷ m m m m -n i¹m i¹m j ¹n è è j ¹n 144444444 42444444444 3ø 1444444 424444444 3ø n

Net Profits from Agreement to Retailer n

Net Profits from Agreement to Manufacturer m

where each of the terms with a ‘hat’ denote the adjusted variables following contract renegotiations that take place between all pairs other than m and n taking into account the fact that m could no longer supply n. That is, all other negotiating pairs take a disagreement between m and n as permanent and irreversible. We let Fnm denote retailer n’s expected payoff following a breakdown in negotiations with m and, similarly, Y mn for m. Here we do not model the outcome of one-on-one bargaining explicitly as a non-cooperative game relying on equation (1) as a ‘black box.’4 This greatly simplifies the exposition of our model. However, we demonstrate in the appendix that this heuristic approach could be derived as the outcome of a fully specified noncooperative bargaining model such as that of Binmore, Rubinstein and Wolinsky (1986) in our structure. In the appendix we explicitly model the subgame that generated the disagreement payoffs (see Stole and Zwiebel, 1996, for example). We now turn to the definition of a contract equilibrium. Specifically, we amend the definition of Stole and Zwiebel (1996) for our purposes. Let g denote the set of negotiating pairs (m, n); this is simply the set of manufacturers and retailers that can negotiate with one another. Therefore, a contract profile is a set of price quantity pairs {(qmn , pmn )} 3

( m , n )Îg

.

The equal split assumption here is not necessary for the main results below and it will be demonstrated there that they are robust to any allocation of bargaining power between a retailer and manufacturer and allowing particular allocations to be negotiation-specific.

6

DEFINITION. A contract equilibrium for a given g is a contract profile such that for each g ¢ Í g , given the split the difference renegotiations (as in (1)), no individual manufacturer can improve upon their profits in a pairwise renegotiation with a retailer, and no retailer can improve upon their profits in a pairwise renegotiation with a retailer. Given this specification of one-on-one bargaining, a contract equilibrium is defined as a set of contracts so that (1) is satisfied for each pair (m, n) under the condition that the disagreement payoffs, Fnm and Y mn , regardless of the past history of breakdowns, are the equilibrium outcome of the subgame where all pairs other than (m, n) satisfy (1). Effectively, this requires that no manufacturer or retailer have an incentive to renegotiate their own contract with any other party anticipating the potential changes in other contracts this would trigger. This is essentially the same as the notion of stability employed by Stole and Zwiebel translated to an environment with many parties on each side of the market.5 Notice that, because there is complete information, negotiating pairs effectively take the disagreement payoffs, Fnm and Y mn , as given when negotiating over (qmn , pmn ) . As will be demonstrated below, this simplifies our analysis of this bargaining environment considerably by being able to consider the restrictions places by the bargaining equations (typified by (1)) on the set of lump-sum transfers, letting input quantity choices to be set unilaterally by either m or n as being equivalent to their joint agreement over the pair (qmn , pmn ) .

4

Jackson and Wolinsky (1996) and Wolinsky (2000) also follow this ‘black box’ approach to bargaining. 5 Notice that our contract equilibrium should be contrasted with that of Cremer and Riordan (1987) who assume that a given set of contracts is not an equilibrium when there is a joint incentive for a manufacturer-retailer pair to unilaterally negotiate their contract terms given the contract outcomes of other pairs. Here we allow an individual party to unilaterally trigger a contract renegotiation but also that in so doing the outcomes of any further renegotiations are taken into account.

7

3.

Characterising the Contract Equilibrium This section demonstrates that any contract equilibrium replicates the prices

and quantities that would arise if the industry were made up of a single, integrated monopoly. That is, the total profits in the industry are maximised if each manufacturer *

only supplies an amount, qmn , given by: N

*

qmn = arg max

{ } qmn

m =1,..., M ;n=1,..., N

åp n =1

M

n

(Qn , Q - n ) - å cm (q m )

(2)

m =1

As noted above, in traditional models of vertical relations, industry output will typically be greater than the levels implied by (2); depending on the extent of ‘double marginalisation’ along the vertical chain.6 Here, however, we demonstrate that not only does the non-linear price structure solve the ‘double marginalisation’ issue but also that it does so in a way the maximises industry profit; i.e., any contractual equilibrium is efficient for the manufacturers and retailers as a group.

3.1

The General Result Formally, this result is as follows:

PROPOSITION 1. The input supply quantities in any contract equilibrium satisfy *

qmn Î qmn .

The proof of this proposition is a simple application of de Fontenay and Gans (2001, Proposition 1) noting that because each manufacturer supplies every retailer, all agents are connected; that is, one can construct (many) paths from any given firm to any other firm (whether on one side of the market or not) through a set of bilateral negotiating pairs. This notion of connectedness is depicted in Figure 1.7

6

For a comprehensive analysis of the traditional model, see Economides and Salop (1992). Connectedness is a concept from graph theory that was first utilised in economics by Myerson (1977) to characterise the outcomes of cooperative bargaining games. 7

8

Figure 1: Complete Network M1

M2

M3

M4

M5

R1

R2

R3

R4

R5

A Monopoly Manufacturer To explain the logic of the result, it is perhaps easiest to begin with a situation where there is a single manufacturer and two retailers (n = A or B) that have symmetric technologies the products each produces are perfect substitutes for one another. In addition, suppose that for each retailer, F(.) is linear so that one unit of input is turned into one unit of output. The manufacturer bargains with each retailer bilaterally. In this situation, a contract equilibrium is characterised by two equations representing the bargaining outcomes between the manufacturer and A and B respectively. p (q A , q B ) - p A - F A 144424443

= p A + p B - c(q A + q B ) - Y A 14444244443

(3)

p (q B , q A ) - p B - F B 144424443

= p A + p B - c(q A + q B ) - Y B 14444244443

(4)

Net Profits from Agreement to Retailer A

Net Profits from Agreement to Retailer B

Net Profits from Agreement to Manufacturer

Net Profits from Agreement to Manufacturer

Proposition 1 states that in this situation, each pair would agree to an outcome so that q A = q B = 12 Q M , where QM is the output that maximises total industry profit

p (q A , q B ) + p (q B , q A ) - c(q A + q B ) . Moreover, at this point, the supply prices become: p A = 13 (p ( 12 Q M , 12 Q M ) + c(Q M ) ) - 13 ( Y B - F B ) - 32 F A + 32 Y A

(5)

9

p B = 13 (p ( 12 Q M , 12 Q M ) + c(Q M ) ) - 13 ( Y A - F A ) - 32 F B + 32 Y B

(6)

Note that, to be an equilibrium, neither the manufacturer or either retailer should wish to renegotiate their contract quantity. In particular, suppose that retailer A wishes to purchase more inputs from the manufacturer; so that q A = 12 Q M + D . In the vertical contracting literature, this incentive arises because, given the contract between the manufacturer and B, the manufacturer and A can jointly profit from an increase in A’s output. That is, holding qB and pB as given, pA becomes: p A = 13 ( 2p ( 12 Q M + D, 12 Q M ) - p ( 12 Q M , 12 Q M ) + 2c(Q M + D ) - c(Q M ) ) - 13 ( Y B - F B ) - 32 F A + 32 Y A

(7)

Here, however, an increase in A’s output and consequent adjustments to pA so that (7) is satisfied will imply that (4) no longer holds for the original contract between the manufacturer and B. Hence, there will be a change in qB and pB as well. Suppose that there is only a change in pB. Then, pA becomes: p A = 13 ( 2p ( 12 Q M + D, 12 Q M ) - p ( 12 Q M , 12 Q M + D ) + c(Q M + D ) ) - 13 ( Y B - F B ) - 32 F A + 32 Y A

(8)

but importantly, A’s profits become: p ( 12 Q M + D, 12 Q M ) - p A = 13 (p ( 12 Q M + D, 12 Q M ) + p ( 12 Q M , 12 Q M + D) - c(Q M + D ) ) + 13 ( Y B - F B ) + 23 F A - 23 Y A

(9)

By the definition of QM, this is strictly less than it would earn with the original contract. Hence, if the manufacturer and A anticipate changes to pB in their own renegotiations, it would not be in A’s interest to renegotiate its original contract quantity. Note that this outcome stands in contrast to other models of vertical relationships where either pricing is restricted (potentially resulting in double marginalisation) or agreements are binding so that outcomes are constrained by the

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possibility of ex post opportunism.8 In Rey and Tirole (1997), for example, if the upstream and one downstream firm agree to an output consistent with industry profit maximisation, the upstream firm has an incentive to negotiate further supply agreements with other downstream firms and cannot commit to doing otherwise. In our model, such ex post opportunism is not possible because any downstream firm would be able to renegotiate their own supply agreement in that event. Thus, externalities among downstream firms are always internalised.

Many Manufacturers Perhaps the most surprising implication of Proposition 1 is that it applies in situations where there are many manufacturers and retailers. To see this, suppose there are only two manufacturers (m = 1 or 2) and two retailers (n = A or B) and, as in the previous case, suppose that each firm has symmetric technologies, the products each produces are perfect substitutes for one another in their respective segments, and that for each retailer, F(.) is linear so that one unit of input is turned into one unit of output. As noted above, the traditional way of analysing outcomes in this setting would be to generate derived demand functions from the non-cooperative game generating retailer profits and having manufacturer competition take the same or an alternative non-cooperative form taking the input market demand function that arises from downstream equilibrium outcomes as given. Here, our alternative approach is to model the formation of input price functions as arising from the series of bilateral bargaining games between manufacturers and retailers and looking at the equilibrium quantities chosen by manufacturers given that equilibrium bargaining outcome. This

8

See O’Brien and Shaffer (1992) and McAfee and Schwartz (1994).

11

approach is essentially equivalent to modeling manufacturer-retailer bargaining as taking place over contracts specifying price/quantity pairs. In this simplified setting, the contract equilibrium is characterised by four bargaining equations of the form (say between manufacturer 1 and retailer A): p (q1A + q2A , q1B + q2B ) - p1A - p2A - F1A = p1A + p1B - c(q1A + q1B ) - Y1A 144444424444443 14444244443 Net Profits from Agreement to Retailer A

(10)

Net Profits from Agreement to Manufacturer 1

This can readily be transformed into the payments received by manufacturer 1 from both retailers: p1A =

1 2

p1B =

1 2

(p ( q (p ( q

A 1 B 1

+ q2A , q1B + q2B ) - p2A - p1B + c(q1A + q1B ) - F1A + Y1A ) + q2B , q1A + q2A ) - p2B - p1A + c(q1A + q1B ) - F1B + Y1B )

(11) (12)

From this we can see that the total revenue of manufacturer 1 is:

(

p1A + p1B = 13 p (q1A + q2A , q1B + q2B ) + p (q1B + q2B , q1A + q2A ) + 2c(q1A + q1B ) - ( p2A + p2B ) - ( F1A - Y 1A + F1B - Y1B )

(13)

)

and, similarly, for manufacturer 2:

(

p2A + p2B = 13 p (q1A + q2A , q1B + q2B ) + p (q1B + q2B , q1A + q2A ) + 2c(q2A + q2B ) - ( p1A + p1B ) - ( F 2A - Y 2A + F 2B - Y 2B )

(14)

)

Substituting (14) into (13), we can now write manufacturer 1’s profits as: æ p (q1A + q2A , q1B + q2B ) + p (q1B + q2B , q1A + q2A ) - c(q1A + q1B ) - c(q2A + q2B ) ö ÷ p1A + p1B - c(q1A + q1B ) = 14 ç 3 A ç - 8 ( F1 - Y1A + F1B - Y1B ) + 18 ( F 2A - Y 2A + F2B - Y 2B ) ÷ è ø

(15)

This is manufacturer 1’s profit subject to the bargaining constraint. Note that it is a weighted sum of total industry profits and the disagreement payoffs. As noted earlier, this latter set of terms is taken as given when setting contract terms. Hence, when manufacturer 1 chooses its supply quantities, it does so to maximise industry profits. The same is true for manufacturer 2 so that in any equilibrium, total industry output is its monopoly level. The implication of this outcome is striking. In contrast to the usual expectations regarding duopolistic outcomes in this type of setting, the only equilibrium outcome involves the industry behaving as an integrated monopoly. That

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is, contracts are negotiated that restrict supply of the manufacturers’ inputs to a level consistent with profit maximisation as if those two manufacturers where merged or acting collusively. As will be demonstrated in Section 3.4 below, this efficiency result is robust to any allocation of bargaining power between individual retailers. For the moment, it is important to understand the intuition behind this outcome and why it differs from neoclassical intuition. Consider the equilibrium where each retailer produces a quantity consistent with a monopoly outcome. That is, let total industry output under monopoly equal Q*. Then each retailer supplies a total of

1 2

Q* . In a neoclassical world, a retailer (say A)

would want to expand their output and hence, contract for a greater supply of inputs. Thus, holding the supply terms to retailer B as given, retailer A chooses its input quantities to maximise: p (q1A + q2A , 12 Q* ) - p1A - p2A

= 23 p (q1A + q2A , 12 Q* ) - 13 ( c( q1A + 12 Q* ) + c(q2A + 12 Q* ) - p1B - p2B - F1A + Y1A - F 2A + Y 2A )

(16)

Taking retailer B’s input supply contracts as given,9 retailer A would like to contract for a new input supply that maximises (16). So, if retailers took the contracts of other retailers as given when choosing their input supply, a monopoly outcome would not be sustained. Here, however, this is not a reasonable conjecture as manufacturers will not take the contracts with retailer B as given when renegotiating terms with retailer A. In particular, if A received a contract that maximised (16), retailer B would want to reduce their supply quantities from both manufacturers and consequently the lumpsum transfer paid to them. Given (13) and (14), this would necessarily involve a reduction in manufacturer’s expected profits causing each to want to renegotiate terms with A. Thus, it is reasonable to suppose that both retailers and manufacturers will

9

This is equivalent to McAfee and Schwartz’s (1994) passive beliefs assumption.

13

anticipate potential renegotiations that would occur if they altered any single contract. Taking this into account, the only point at which no manufacturer or retailer would not wish to renegotiate a single contract is when contracts implement an outcome that maximises total industry profits. At this point, it is important to emphasise that the monopoly outcome generated by a contract equilibrium is not the result of collusion – explicit or implicit. All market transactions are conducted bilaterally; although, in the long-run, lump-sum transfers depend on the actual realisation of input supply quantities. Nonetheless, unlike collusive results the outcome here is self-enforcing and unique. That is, this is not a folk theorem result that relies upon far-sighted supergame strategies. Instead the equilibrium relies upon the stationarity that exists in alternating offer bargaining games; hence, there is no dependence on the history of actions as would arise in the repeated game underlying models of tacit collusion.

3.2

Minimal Conditions for a Monopoly Outcome The above model demonstrates how an efficient (i.e., monopoly) outcome can

be achieved when all manufacturers negotiate and supply inputs with all retailers. In reality, some input suppliers will be tied to one firm or another – labour is the obvious example. Indeed, the above efficiency result does not hold when all manufacturerretailer relationships are specialised to one another. This is because, even if negotiations were to break down, and the manufacturers may alter their supply arrangements by switching retailers, the outcomes of these subsequent renegotiations do not impact on current supply arrangements. With no link in current arrangements, there is no mechanism by which horizontal externalities among retailers are internalised and hence, traditional duopoly outcomes will result.10

10

See de Fontenay and Gans (2000) for a discussion of the case they term ‘network duopoly.’

14

This raises the important question of whether such a complete network is necessary to generate a monopoly outcome and if not what would be the minimal network to achieve this. As will be demonstrated here the key condition is not that a network is complete but that it is connected. Connectedness is a term from graph theory. In our definition of a contract equilibrium above we defined that equilibrium with regard to a given set of negotiating pairs. Proposition 1 that assumed a complete network in that every buyer dealt with every seller did not involve a complete graph in the sense that every pair of firms negotiated; that is, firms in a particular vertical segment could not negotiate (or collude). Formally, n and m are connected by g if and only if there is a path in g that goes from n to m. Thus, connectedness does not require that a particular manufacturer and retailer negotiate directly with one another but simply that they negotiate with other parties that negotiate (directly) or are themselves connected to the other. Using this concept, we can establish that so long as all manufacturers and retailers are connected, any contract equilibrium involves a monopoly outcome. PROPOSITION 2. Take a set of negotiating parties defined by a graph g and suppose that all (n, m) Î M ´ N are connected. Then the input supply quantities in any *

contract equilibrium satisfy qmn Î qmn . Once again the proof of this proposition is a simple application of the main result of de Fontenay and Gans (2001). To demonstrate it here, let us return to our 2 x 2 example but assume that manufacturer 1 cannot supply retailer B and only supplies retailer A. In contrast, manufacturer 2 is a flexible manufacturer and can supply both retailers. Notice that this is the situation that would arise a subgame following a breakdown in negotiations between retailer B and manufacturer 1. In this case, negotiated lump-sum transfers are governed by three bargaining equations, yielding prices of:

15

p1A = p2A = p2B

1 2

(p ( q

A 1

+ q2A , q2B ) - p2A + c(q1A ) - F1A + Y1A )

(17)

(p ( q + q , q ) - p - p + c ( q + q ) - F + Y ) = (p ( q , q + q ) - p + c ( q + q ) - F + Y ) A 1

1 2

1 2

A 2

B 2

A 1

B 2

A 1

A 2

B 2

A 2

A 2

A 2

B 2

B 2

A 2

B 2

A 2

(18)

B 2

(19)

Solving these simultaneously, the profits (subject to these bargaining constraints) of manufacturers 1 and 2 become respectively: 1 4

(p (q

A 1

(

+ q2A , q2B ) + p ( q2B , q1A + q2A ) - c( q1A ) - c( q2A + q2B ) ) - 14 3 ( F1A - Y1A ) - 2 ( F 2A - Y 2A ) + F 2B - Y 2B

)

(20)

Clearly, in choosing their respective quantities, both manufacturers will consider their impact on industry profits only and a monopoly outcome will be generated. Thus, having one flexible manufacturer who supplies to both retailers (or alternatively, one retailer who purchases from both manufacturers) is sufficient for an efficient outcome to be negotiated. Thus, networks that have a mix of flexible and tied relationships (e.g., Figure 2) will generate monopoly outcomes at an industry level; although the degree of flexibility will alter each firm’s disagreement payoffs. This type of mixture is a realistic representation of supply relationships as most firms have a mix of suppliers and customers that are tied and flexible; the obvious example of flexible suppliers being providers of key inputs such as energy and telecommunications.

Figure 2: Network of Flexible and Tied Manufacturers M1

M2

M3

M4

M5

R1

R2

R3

R4

R5

16

In general, many network arrangements will support a monopoly outcome. For example, another example of a connected network is the chain in Figure 3. Notice that in terms of the number of negotiating pairs this is the same as that of Figure 2. An issue we return to below is what types of networks are efficient and whether these would arise in a setting where the graph of links arises endogenously from the choices of individual pairs of manufacturers and retailers.

Figure 3: Network Chain M1

M2

M3

M4

M5

R1

R2

R3

R4

R5

The notion of connectedness can also assist in considering the conditions under which more competitive industry outcomes may occur. In particular, consider Figure 4 that has two disjoint but otherwise connected sets of firms. In each connected set, manufacturers and retailers that will maximise the profits of their respective networks. As there are two such sets, the outcome will be duopolistic; indeed, given our contracting game, the outcome will be the same as a Cournot asymmetric duopoly (given the additional resources available to one network). Moreover, it is easy to see that as the number of disconnected sets of manufacturers and retailers grows, the more intense is competition likely to be.11 This suggests that as an empirical matter, the competitiveness of an industry will be closely related to the nature of specialised

17

supply arrangements in the industry; in particular, the disconnection between sets of input suppliers and final goods producers.12

Figure 4: Network Duopoly

3.3

M1

M2

M3

M4

M5

R1

R2

R3

R4

R5

Equilibrium Rent Distribution A natural question to ask, given the above discussion, is what the precise

distribution of monopoly rents to individual manufacturers and retailers is likely to be once the disagreement payoffs are derived from their respective subgames? In general, deriving the equilibrium rent distribution is a difficult task, even where firms on a particular vertical segment are symmetric as the disagreement payoffs will involve subgames with substantial asymmetries. For example, after a series of break downs one manufacturer could be negotiating with all retailers while another negotiations with a retailer who negotiates with only a specific set of manufacturers and while another pair of manufacturer and retailers may be disconnected from the

11

De Fontenay and Gans (2000) consider this type of network competition in more detail where each retailer has an exclusive set of supply arrangements with a set of manufacturers. 12 Notice that an industry could have a common input supply of, say, electricity and still have competitive outcomes so long as that common supplier does not negotiate individually with each firm but instead posts non-discriminatory prices, as would a neoclassical firm.

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others. This complexity has meant that to date we have been unable to find a general formula characterising equilibrium rent distribution.13 Nonetheless, when there are small numbers of firms on each side of the input market, it is possible to derive the equilibrium payoffs to each firm. As we will demonstrate throughout the remainder of this paper, even a 2 x 2 example can be useful in analysing the implications of the assumed bargaining relationships in this paper. To consider the issue of equilibrium division, in light of our efficiency result above, an important concept is the state that describes the type and numbers of negotiating parties. In particular, a state is fully described by a triple (mA , mB , mF ) consisting of the number of manufacturers negotiating with A only (mA), B only (mB),

or both A and B (mF). Thus, we begin with the state (0,0,2) and may enter states, for example, where only one manufacturer negotiates with A and B and the other negotiates with B alone (0,1,1), both manufacturers negotiate with A alone (2,0,0) or only one manufacturer remains who negotiates with B alone (0,1,0). Using this notation, there are two types of manufacturers – flexible and tied. For a flexible manufacturer, let qmn (mA , mB , mF ) be the quantity supplied by m to n in state (mA , mB , mF ) and let pmn (mA , mB , mF ) be the corresponding lump-sum transfer. For a tied manufacturer, let the corresponding supply quantity and price be denoted by qmn (mA , mB , mF ) and pmn (mA , mB , mF ) . Note that so long as mF > 0, all parties remain

connected, so that given (mA , mB , mF ) , industry profits are maximised. However, if mF = 0, equilibrium profits will reflect some oligopolistically competitive outcome.

13

An exception is the case where retailers do not compete with one another. In this situation, the equilibrium payoffs of each firm are their respective Shapley values (see de Fontenay and Gans, 2001). However, this case is not of interest to us here as we are explicitly interested in the case where there are downstream externalities between firms.

19

Given this notation, and using symmetry to focus on retailer A, the following set of equations fully describes the subgame perfect equilibrium outcomes of the bargaining game: p (0, 0, 2) - 2 pmA (0, 0, 2) - (p (0,1,1) - p-Am (0,1,1) )

= pmA (0, 0, 2) + pmB (0, 0, 2) - cm (0, 0, 2) - ( pmB (0,1,1) - cm (0,1,1) )

(21)

p (0,1,1) - pmA (0,1,1) = pmA (0,1,1) + pmB (0,1,1) - cm (0,1,1) - ( pmB (0, 2, 0) - cm (0, 2, 0) ) (22)

p (1, 0,1) - p-Am (1, 0,1) - pmA (1, 0,1) - (p (0, 0,1) - p-Am (0, 0,1) ) = pmA (1, 0,1) - cm (1, 0,1) (23) p (1, 0,1) - pmA (1, 0,1) - p-Am (1, 0,1) - (p (1,1, 0) - p-Am (1,1, 0) )

(24)

p (0, 0,1) - pmA (0, 0,1) = 2 pmA (0, 0,1) - cm (0, 0,1) - ( pmB (0,1, 0) - cm (0,1, 0) )

(25)

= pmA (1, 0,1) - cm (1, 0,1) - ( pmB (1,1, 0) - cm (1,1, 0) )

p (2, 0, 0) - 2 pmA (2, 0, 0) - (p (1, 0, 0) - pmA (1, 0, 0) ) = pmA (2, 0, 0) - cm (2, 0, 0)

(26)

p (1, 0, 0) - pmA (1, 0, 0) = pmA (1, 0, 0) - cm (1, 0, 0)

(27)

p (1,1, 0) - pmA (1,1, 0) = pmA (1,1, 0) - cm (1,1, 0)

(28)

where

(

A

A

B

B

p ( m A , m B , m F ) = p q1 ( m A , m B , m F ) + q 2 ( m A , m B , m F ), q1 ( m A , m B , m F ) + q 2 ( m A , m B , m F )

(

A

B

cm ( m A , m B , m F ) = c q m ( m A , m B , m F ) + q m ( m A , m B , m F )

(

n

cm ( m A , m B , m F ) = c q m ( m A , m B , m F )

) if m is flexible

) and

) if m is tied to retailer n.

Solving (21) to (28) simultaneously, we have: pmA (0, 0, 2) = 121 ( 3p (0, 0, 2) - 2p (0, 0,1) + p (2, 0, 0) + 3cm (0, 0, 2) + cm (0, 0,1) - 2cm (2, 0, 0) ) (29)

From this we can work out the payoff to a manufacturer and a retailer 2 pmA - c(0, 0, 2) = 16 ( 3p (0, 0, 2) - 3cm (0, 0, 2) - 2p (0, 0,1) + cm (0, 0,1) + p (2, 0, 0) - 2cm (2, 0, 0) ) p (0, 0, 2) - 2 pmA = 16 ( 3p (0, 0, 2) - 3cm (0, 0, 2) + 2p (0, 0,1) - cm (0, 0,1) - p (2, 0, 0) + 2cm (2, 0, 0) )

(30) (31)

Notice that this outcome has the intuitively appealing property that manufacturers earn most of the rents when 2p (0, 0,1) - cm (0, 0,1) > p (2, 0, 0) - 2cm (2, 0, 0) ; that is, when industry profits when a single manufacturer is available exceeds industry profits when there is a single retailer.

20

3.4

Asymmetric Bargaining Power The above model assumes that when a manufacturer and retailer negotiate,

each has equal bargaining power and hence, they negotiate a lump-sum payment that splits the surplus created from an agreement. In reality, one might be concerned about the symmetry imposed by this assumption – in particular, on the outcomes of negotiations across all retailer-manufacturer pairs. So here we suppose instead that each negotiation has associated with it a specific allocation of bargaining power as described by a term, lmn Î [0,1] , that is the fraction of the surplus appropriated by the manufacturer in that negotiation. We demonstrate that, despite this change, our efficiency result still holds. Formally, our result can be generalised as follows: COROLLARY 1. Take a set of negotiating parties defined by a graph g and suppose that all (n, m) Î M ´ N are connected and for each pair (n, m) n has bargaining power described by lmn Î [0,1] . Then the input supply quantities in any contract *

equilibrium satisfy qmn Î qmn . Once again the proof (hopefully!) follows directly from de Fontenay and Gans (2001, Proposition 1). To see its intuition and implications we again utilise the symmetric 2 x 2 case, but here we assume that in each negotiation retailers have symmetric bargaining power of l. With this assumption, the bargaining equation between, say, retailer A and manufacturer 1: l (p (q1A + q2A , q1B + q2B ) - p1A - p2A - F1A ) = (1 - l ) ( p1A + p1B - c(q1A + q1B ) - Y1A ) (32)

This can readily be transformed into the payments received by manufacturer 1 from both retailers: p1A = l (p (q1A + q2A , q1B + q2B ) - p2A - F1A ) - (1 - l ) ( p1B - c(q1A + q1B ) - Y1A ) p1B = l (p (q1B + q2B , q1A + q2A ) - p2B - F1B ) - (1 - l ) ( p1A - c(q1A + q1B ) - Y1B )

(33) (34)

21

From this we can follow the same sequence of substitutions as before to show that the profits of manufacturer 1 (subject to the bargaining constraints) becomes: (35)

p1A + p1B - c(q1A + q1B ) = 12 l (p (q1A + q2A , q1B + q2B ) + p (q1B + q2B , q1A + q2A ) - c(q1A + q1B ) - c(q2A + q2B ) ) +

1 4(1-l )

( -l + ( Y 2

A 1

+Y

B 1

) (2 - l (3 - l )) - ( Y

A 2

+Y

B 2

) l (1 - l ) - ( F

A 1

+ F ) l (2 - l ) + ( F + F B 1

A 2

B 2

)l ) 2

while the profits of a retailer are: p (q1A + q2A , q1B + q2B ) - p1A - p1B = 12 (1 - l ) (p ( q1A + q2A , q1B + q2B ) + p (q1B + q2B , q1A + q2A ) - c(q1A + q1B ) - c(q2A + q2B ) )

(

- 4(11-l ) -l 2 + ( Y1A + Y1B ) (2 - l (3 - l )) - ( Y 2A + Y 2B ) l (1 - l ) - ( F1A + F1B ) l (2 - l ) + ( F2A + F 2B ) l 2

(36)

)

In each case, profits are a weighted sum of industry profits and disagreement payoffs. Therefore, when choosing quantities, industry profits will be maximised. Notice that as l rises (i.e., manufacturers have relatively more bargaining power), their weight on industry profits increases while the weight retailers place diminishes. To gain a fuller understanding of the role of bargaining power, it is useful to solve for the equilibrium rents of manufacturers and retailers. Using our simplified notation, for a manufacturer, these are: l (p (0, 0, 2) - cm (0,0, 2) ) æ (l 2 - 1) ( 2p (0, 0,1) - cm (0, 0,1) ) ö ç ÷ l + (1+ l )(2 - l ) ç + (1 - l )(2 - l ) (p (2, 0,0) - 2cm (2, 0, 0) ) ÷ çç +2(1 - l )(2l - 1) (p (1,0,0) - cm (1, 0, 0) ) ÷÷ è ø

(37)

while a retailer earns:

(1 - l )(p (0, 0, 2) - cm (0, 0, 2) ) æ (l 2 - 1) ( 2p (0, 0,1) - cm (0,0,1) ) ö ç ÷ l - (1+ l )(2 - l ) ç + (1 - l )(2 - l ) (p (2, 0, 0) - 2cm (2, 0, 0) ) ÷ çç ÷÷ è +2(1 - l )(2l - 1) (p (1, 0, 0) - cm (1, 0, 0) ) ø

(38)

As l approaches 1, (37) becomes p (0, 0, 2) - cm (0, 0, 2) . Thus, if manufacturers (similarly, retailers) have all the bargaining power, they earn all of the industry rents. So, even in situations where one party or the other can make take it or leave it offers (as is often assumed in the contracting literature), the party with the bargaining power has an incentive to insist on input supply terms that maximise industry profits.

22

4.

Applications Having established our general result, we are now in a position to apply our

model to consider some important issues in industrial organisation. In this section, we examine how multilateral bargaining over inputs impacts upon the value of entry into a particular vertical segment, the role of exclusive dealing, incentives and inefficiencies arising from strategic commitments, and the profitability and competitive consequences of mergers (both horizontal and vertical). In each case, we demonstrate how a consideration of input bargaining either overturns or qualifies traditional conceptions regarding these issues. In analysing each of these issues, it will be useful to have regard to the equilibrium payoffs manufacturers and retailers receive in different circumstances beyond our earlier symmetric 2 x 2 case. In particular, while we will assume that all manufacturers remain symmetric, we will consider situations where retailers may be non-identical and also cases where there is a single, two or three manufacturers. Table 1 summarises the payoffs in each of these alternative situations and we draw upon particular cells of this table below. Also, to simplify notation, we drop the assumption that manufacturers have costs and assume that c(.) = 0.

Table 1: Payoffs with Identical Manufacturers and Two Non-Identical Retailers Number of Manufacturers

1

2

1 6

1 12

Manufacturer Payoff

Retailer A’s Payoff

æ 2p A (0, 0,1) + 2p B (0, 0,1) ö ç ÷ è +p A (1, 0, 0) + p B (0,1, 0) ø

æ 2p A (0, 0,1) + 2p B (0, 0,1) ö ç ÷ è -2p B (0,1, 0) + p A (1, 0, 0) ø æ 3p A (0, 0, 2) + 3p B (0, 0, 2) ö ç ÷ ç +2p A (0, 0,1) + 2p B (0, 0,1) ÷ 1 ç ÷ 12 +6p A (1,1, 0) - 6p B (1,1, 0) ç ÷ ç -4p A (1, 0, 0) + 4p B (0,1, 0) ÷ ç +p (2, 0, 0) - 3p (0, 2, 0) ÷ B è A ø

æ 3p A (0, 0, 2) + 3p B (0, 0, 2) ö ç ÷ ç -2p A (0, 0,1) - 2p B (0, 0,1) ÷ ç +p (2, 0, 0) + p (0, 2, 0) ÷ B è A ø

1 6

23

æ12p A (0, 0,3) + 12p A (0, 0,3) ö ç ÷ ç -6p A (0, 0, 2) - 6p B (0, 0, 2) ÷ ç -4p A (0, 0,1) - 4p B (0, 0,1) ÷ ç ÷ ç +p A (1,0, 0) + p B (0,1, 0) ÷ 1 ç ÷ 60 +4p A (1,1, 0) + 4p B (1,1, 0) ç ÷ ç -6p A (1, 2, 0) + 4p B (1, 2, 0) ÷ ç -3p (2, 0, 0) - 3p (0, 2, 0) ÷ A B ç ÷ ç +4p A (2,1, 0) - 6p B (2,1, 0) ÷ çç ÷÷ è +3p A (3, 0, 0) + 3p B (0,3, 0) ø

3

4.1

æ 4p A (0,0,3) + 4p B (0, 0,3) ö ç ÷ ç +3p A (0, 0, 2) + 3p B (0, 0, 2) ÷ ç +2p A (0, 0,1) + 2p B (0, 0,1) ÷ ç ÷ ç +7p A (1,0, 0) - 8p B (0,1,0) ÷ 1 ç ÷ 20 -22p A (1,1, 0) + 18p B (1,1, 0) ç ÷ ç +18p A (1, 2, 0) - 12p B (1, 2, 0) ÷ ç -6p (2, 0, 0) + 9p (0, 2, 0) ÷ A B ç ÷ ç +8p A (2,1, 0) - 12p B (2,1, 0) ÷ çç ÷÷ è +p A (3, 0, 0) - 4p B (0, 3, 0) ø

Entry Thus far, our analysis has assumed a given industry structure both in terms of

the numbers of manufacturers and retailers and also in terms of whether they are tied or flexible. We have demonstrated that, for a given industry structure, industry profits are maximised and monopoly outcomes ensue. This raises the question of how competition through entry would operate. Here we will focus on issues associated with upstream (manufacturer) entry although everything here can equally be addressed if one were to, alternatively, analyse retailer entry. A first natural question to consider is the impact of entry by manufacturers on the profits of both manufacturers and retailers. Traditional intuition suggests that increased competition on one side of the market improves payoffs of agents on the other side of the market. Consider then a change in industry structure from a single manufacturer to two manufacturers. Also, assume here that all retailers are identical. Then it is easy to show that a manufacturer’s profits changes by: 1 6

( 3p (0, 0, 2) - 6p (0, 0,1) + p (2, 0, 0) - 2p (1,0, 0) )

(39)

while a retailer’s profits changes by: 1 6

( 3p (0, 0, 2) - 2p (0, 0,1) + p (1, 0, 0) - p (2,0, 0) )

(40)

For the traditional intuition to hold, manufacturer’s profits would fall while a retailer’s would rise following the entry of another manufacturer. Certainly, the

24

incumbent manufacturer’s profits will be lower following entry if its input is a substitute to that of the entrant manufacturer either in terms of increasing overall profits when there are two retailers or when there is only a single retailer. However, it is possible that retailer profits could also fall if p (2, 0, 0) - p (1, 0, 0) is relatively large while the contribution of an additional manufacturer to overall industry profits is relatively low. That is, 3p (0, 0, 2) - 2p (0, 0,1) < p (2, 0, 0) - p (1, 0, 0)

(41) EXAMPLE. Suppose that, p (q + q , q + q ) = (a - b(q + q + q + q ))(q + q2A ) , for A, and similarly for B and that c(q + q ) = a + b (q + q ) where b > 0, and A 1

A 2

b + 2 b > 0 . Then p (0, 0, 2) = p (2,0, 0) =

B 1 A m

B 2 B m

a2 2(2 b + b )

A 1 A m

a 2 (3b + 2 b )

8( b + b )2

B 1

B 2

- 2a , p (0, 0,1) = p (1, 0, 0) =

Moreover, total surplus (consumer plus producer) is equal to are two manufacturers and

A 2 B 2 m

a 2 (3b + b )

2(2 b + b )2

A 1

a2 4( b + b )

-a .

- 2a when there

- a when there is only one. Suppose that total

surplus is maximised with two manufacturers (i.e., that a £ a H =

a 2 b (8b 2 + 9 b b + 2 b 2 ) 8( b + b ) 2 (2 b + b )2

) while

2

total profits are maximised with only one (i.e., that, a ³ a L = 4(b + ba)(2b b + b ) ). This means that the profits of manufacturer will fall if another enters. For a retailer, profits will also fall upon manufacturer entry if (41) is satisfied; that is, if 2p (0, 0, 2) < p (0, 0,1) . 2

+3 b ) This occurs if a ³ 12(ab +(2bb)(2 b + b ) . Notice that

a 2 (2 b + 3 b ) 12( b + b )(2 b + b )

> a L , however, it may be the

2

+3b ) 2 2 case that a < 12(ab +(2bb)(2 b + b ) < a H Þ 2(2b + 3 b )(b + b )(2b + b ) < 3b (8b + 9b b + 2 b )

which holds whenever a H > a L . Thus, it is possible that socially desirable entry may not be favoured by retailers. Note, that in this symmetric situation, if entry is profitable for the industry, it will also be favoured by retailers. This example demonstrates that entry by a manufacturer may actually reduce the profits of a retailer. On the one hand, that entry will increase a retailer’s bargaining power with other manufacturers as it has more options. On the other hand, each manufacturer can use the threat value of allowing other retailers to command a more dominant position in the retail market in the event that traditional oligopolistic competition arises as a means to extracting more rents from the retailer. Thus, in the sense of Segal (1999), an additional manufacturer enhances the ability of other manufacturers to exploit competitive externalities among retailers to extract more rents from them.

25

4.2

Exclusivity A considerable amount of attention in anti-trust research has been focused on

the role of exclusive arrangements that tie particular firms to one another. A quintessential case is where a retailer opts to only source supplies from a single manufacturer or, alternatively, a manufacturer opts to only supply a single retailer. These are one-sided exclusivity arrangements because they bind only a single party. This is in contrast to a mutually exclusive arrangement that would tie both parties to one another. The concern with such arrangements is that they limit competition to the detriment of overall efficiency and consumer welfare in an industry. Our bargaining framework allows us to consider both the one-sided and twosided exclusivity arrangements that are of potential concern. Given our emphasis on renegotiation, even if an exclusivity arrangement was signed, the parties to that arrangement could still agree to trade with other parties if it is efficient to do so (see Segal and Whinston, 2001). Thus, exclusivity only impacts on the bargaining connections that remain when a breakdown in bargaining occurs. For example, suppose that manufacturer 1 agrees to supply A exclusively. This prevents that manufacturer from negotiating with B directly independent of any negotiations with A. However, if A consents, it can allow manufacturer 1 to supply B if it is efficient to do so. This might occur, for instance, if the inputs supplied by the manufacturers are imperfect substitutes for retailer B. In effect, exclusivity ties the bargain between 1 and B to the bargain between 1 and A. The key issue arises, however, if there is a breakdown in supply negotiations between retailer A and manufacturer 1. In particular, we envisage a timeline similar to Segal and Whinston (2001), where retailer A and manufacturer 1 can ex ante agree to an exclusive arrangement but cannot, at that time, agree on particular pricing terms. Nonetheless, by paying manufacturer 1 upfront, retailer A can compensate them for

26

any lack of future bargaining power. So the key impact of exclusivity is to prevent manufacturer 1 from supplying retailer B without the express consent of A. Thus, for them, if negotiations breakdown, manufacturer 1 is disconnected from any further bargaining or trade. What this means is that the impact of exclusivity is wholly felt in terms of the distribution of industry rents ex post and not on the level of those rents themselves; although if individual firms take non-contractible actions, there will be an impact. For the moment, let’s consider the incentives for parties to sign one-sided exclusive arrangements. Once again, it is useful to consider our 2 x 2 symmetric case. In this situation, retailer A and manufacturer 1 will gain from 1 having an exclusive arrangement if their joint profits under the exclusive arrangement exceeds their joint profits when there is a fully connected network. Specifically, the relevant bargaining equations become: p (q1A + q2A , q1B + q2B ) - p1A - p2A - F1A = p1A + p1B - c(q1A + q1B ) p (q1A + q2A , q1B + q2B ) - p1A - p2A - F2A = p2A + p2B - c(q2A + q2B ) - Y 2A p (q1B + q2B , q1A + q2A ) - p1B - p2B - F2B = p2A + p2B - c(q2A + q2B ) - Y 2B

(42) (43) (44)

p (q1B + q2B , q1A + q2A ) - p1B - p2B - F1B = p1A + p1B - c(q1A + q1B ) - Y1B

(45)

Notice that only (42) is distinctly different than previous cases, as manufacturer 1 has no outside option given its exclusive arrangement with retailer A. Nonetheless, these equations and those comprising the disagreement payoffs can be readily solved to give the payoffs to retailers A and B and manufacturers 1 and 2, respectively: æ 3p A (0, 0, 2) + 3p B (0, 0, 2) + 2p A (0, 0,1) + 2p B (0, 0,1) ö p A (0, 0, 2) - p1A - p2A = 121 ç ÷ è -p A (1, 0, 0) - p B (0,1, 0) + 3p A (1,1, 0) - 3p B (1,1, 0) + p A (2, 0, 0) ø æ 3p A (0, 0, 2) + 3p B (0, 0, 2) + 2p A (0, 0,1) + 2p B (0, 0,1) ö p B (0, 0, 2) - p1B - p2B = 121 ç ÷ è +p A (1, 0, 0) - p B (0,1, 0) + 3p B (1,1, 0) - 3p A (1,1, 0) - 3p A (2, 0, 0) ø

(46)

æ 3p A (0, 0, 2) + 3p B (0, 0, 2) - 2p A (0, 0,1) - 2p B (0, 0,1) ö p1A + p1B = 121 ç ÷ è -3p A (1, 0, 0) + 3p B (0,1, 0) + 3p A (1,1, 0) - 3p A (1,1, 0) + p A (2, 0, 0) ø æ 3p A (0, 0, 2) + 3p B (0, 0, 2) - 2p A (0, 0,1) - 2p B (0, 0,1) ö p2A + p2B = 121 ç ÷ è +3p A (1, 0, 0) - p B (0,1, 0) + 3p B (1,1, 0) - 3p A (1,1, 0) + p A (2, 0, 0) ø

(48)

(47)

(49)

27

where we have used our simplified notation; ignoring the manufacturer cost terms. Note that, despite the exclusive arrangement, each firm still wishes to maximise total industry profits given the availability of both manufacturers to both retailers; that is, each firm’s payoffs have an additively separable term of

1 4

(p A (0, 0, 2) + p B (0, 0, 2) ) .

Note also that this same term appears in their payoff when there is no exclusive arrangement between 1 and A. The exclusive arrangement only changes the disagreement payoffs of all agents. By entering into an exclusive arrangement, the sum of payoffs to retailer A and manufacturer 1 increases by

1 6

(p B (0, 2, 0) - p B (0,1, 0) ) . Essentially, the benefit of

an exclusive arrangement is to reduce the ability of any manufacturer to use the profits B might earn if all manufacturers where tied to it as a means of improving their bargaining position with A. While signing an exclusive arrangement removes this threat value for manufacturer 1, it also removes it for manufacturer 2 and that external effect makes it jointly profitable for 1 to become exclusive to A. Hence, they have a bilateral incentive to commit to an exclusive arrangement; resolving it by some upfront transfer from retailer A to manufacturer 1. This result reinforces those of Segal and Whinston (2001) who find that when a buyer and seller can negotiate an exclusive contract prior to the arrival of another seller and, when that arrival can trigger a renegotiation of pricing terms, then the effect of exclusivity is purely to impact on the disagreement point of those subsequent renegotiation. That conclusion is preserved here even though there is an additional competing buyer (i.e., retailer) to whom both sellers (i.e., the manufacturers) can trade with. Segal and Whinston (2001) demonstrate, however, that when firms can undertake an ex ante investment that is non-contractible, exclusivity can impact on the

28

overall surplus generated. However, their main result is that this impact only occurs when investments impact on disagreement payoffs and not when they are purely internal to a relationship. While a complete analysis of this issue is beyond the scope of this paper, it is easy to demonstrate that when manufacturer 1 makes a noncontractible investment, x1, that impact upon its own costs, by moving to an exclusive arrangement with 1, its marginal benefit from that investment diminishes by: ¶ 3c1 (q1B (1,1, 0)) + c1 (q1B (0, 2, 0)) - c1 (q1B (0,1, 0)) ) ( ¶x1

(50)

terms that depend only on the costs incurred by 1 in states where it serves only B (and not A). Hence, the impact of exclusivity is solely in terms of investments that are external to the relationship between 1 and A. Note, however, that unlike Segal and Whinston (2001), here an investment need not be purely internal to the relationship between 1 and A to be neutral to exclusivity provisions. That is, an investment may change the costs of serving both A and B. It is solely in terms of its impact on purely external investments (i.e., that impacting only on the relationship between 1 and B) that there is an impact from exclusivity. Finally, our framework also allows us to consider the impact of a two-sided exclusivity arrangement; whereby neither party can trade with an external party without the consent of the other. In this case, (42) becomes: p (q1A + q2A , q1B + q2B ) - p1A - p2A = p1A + p1B - c(q1A + q1B )

(51)

but otherwise the form of the bargaining equations are unchanged. In this situation, it is relatively use to show that the joint payoff for 1 and A to enter into a two-sided arrangement is

1 6

(p A (0, 0,1) + p B (0, 0,1) + p B (0, 2, 0) - 2p B (0,1, 0) )

payoff without any exclusivity arrangement and

1 6

greater than their

(p A (0, 0,1) + p B (0,0,1) - p B (0,1, 0) )

greater than their payoff from a one-sided arrangement. Hence, the bilateral incentives

29

to enter into a two-sided exclusivity arrangement are stronger than both no arrangement and a one-sided arrangement. Of course, the above analysis only considers bilateral incentives to sign exclusive arrangements. It would be interesting to consider the full non-cooperative game and the potential equilibrium sets of exclusive arrangements that might be signed. Also, it would be interesting to consider the role of entry – especially if supported by an exclusive arrangement – in this context. These extensions are, however, left for future work.

4.3

Mergers

TO BE DONE

4.4

Strategic Commitments

TO BE DONE

30

Appendix A: Extensive Form GameHere we provide an extensive form game that has as an equilibrium outcome the contract equilibrium as described in the body of the paper. We will demonstrate this game first utilising the example of a single manufacturer and two retailers. An extension to the general setting here will be readily apparent. A retailer, i, and a manufacturer can only negotiate over their particular ( pi , qi ) . Moreover, any agreement they reach over ( pi , qi ) is unenforceable in the sense of Stole and Zwiebel. That is, any time before production takes place, the monopolist can refuse to supply the downstream firm or the downstream firm can refuse to accept and pay for input from the upstream firm. Our extensive form game is as follows. Suppose there are N retailers labeled 1, ..., N. Initially, fix an order of those firms, describing the sequence in which they engage in pairwise negotiations with the monopolist. Prior to any negotiation, each retailer announces its desired quantity. The manufacturer and each retailer negotiates over the price to be paid for that quantity. There are three possibilities that could arise – they could agree, disagree or agree to an alternative quantity. If they agree (A), bargaining proceeds to the next downstream firm in the sequence. If they do not agree (B), a fresh sequence of bargaining occurs in the same order as initially designated but without the downstream firm who was party to the broken down negotiation. If they agree to an alternative quantity (AQ), then with probability q this becomes known to all other firms, and a fresh sequence of bargaining occurs in the same order as initially designated without the downstream firm who was a party to the amended negotiation whose current agreement stands. Prior to those negotiations, retailers announce new desired quantities.14 Let G(.) denote the subgame which begins with the indicated sequence of firms. For instance, G(1, 3, ..., N) is the subgame that begins after retailer 2 has exited the game (following a breakdown) and the remaining players line up in numerical sequence to bargain with the monopolist. Let G(2, 1, 3, ..., N) be the subgame that begins if retailer 2 has amended their previously announced quantity. Figure 1 depicts this extensive form game when there are just two downstream firms. That figure implicitly assumes q = 1 (perfect observability). Note that the game is potentially without end. However, as is described next, we assume that bilateral negotiations take a Binmore, Rubinstein and Wolinsky (1986) form in which there is a positive probability, r, of a breakdown in any given negotiation. Thus, this game will end in finite time. We now turn to describe the game within each bargaining session. The bilateral negotiations stage proceeds as follows: (1) Nature chooses (with probability ½) which firm is the initial offeror; (2) the offeror makes an offer ( pi , qi ) ; (3) the offeree accepts or rejects the offer; (4) if it is accepted, there is an agreement while if 14

Alternatively, we could assume that there are two options. Either there is no agreement (B), or there is an agreement and the agreed upon contract becomes observable with probability q. In this case, if the observed quantity is different from the announced quantity, then all other firms – that is, firms that have either agreed upon contracts at their announced quantities or are yet to negotiate – renegotiate in their original sequence holding the quantities of the ‘deviator’ retailers as fixed.

31

it is rejected, then with probability r there is a breakdown and with probability (1-r), we return to (1).

Figure 1

G(1, 2) Ann. by 1 & 2

AQ

1

A

G (1, 2)

G(1, 2)

Ann. by 2

A

B

2

G(2)

G(2)

2

Ann. by 2

2

end

A

B

AQ

end

end

end

B AQ

G(1) G(1, 2)

A

B

AQ

end

end

end

PROPOSITION 2: As q approaches 1, the unique subgame perfect equilibrium involves each retailer announcing its industry profit-maximising quantity and each pair reaching an immediate agreement as to the price associated with that quantity. PROOF: We will prove this proposition for the case of one manufacturer and two retailers. Without loss in generality, suppose that the fixed of bargaining is fixed as 1 followed by 2. Suppose that each retailer announces its industry profit-maximising quantities, q1* and q2* , respectively. Working backwards, suppose retailer 2 observes the outcome of an agreement between the manufacturer and retailer 1. Then if the manufacturer and retailer 2 agree, retailer 2 will pay a price of: p2 =

1 2

(p

2

(q2* , q1* ) - p1 + (p 1 (qˆ1 , 0) - pˆ1 ) )

(52)

where the variables with hats denote the disagreement choices of the manufacturer and retailer 1. While retailer 2 does not observe p1, it can infer it by the fact that there has been an earlier agreement and the quantity agreed upon. That inferred price is determined by: p 1 (q1* , q2* ) - p1 = p1 + p2 - (p 2 (0, qˆ2 ) - pˆ 2 ) Þ p1 = 12 p 1 (q1* , q2* ) - 12 p2 + 12 (p 2 (0, qˆ2 ) - pˆ 2 ) Þ p1 = 23 p 1 (q1* , q2* ) - 13 p 2 (q2* , q1* ) - 13 (p 1 (qˆ1 , 0) - pˆ1 ) + 23 (p 2 (0, qˆ2 ) - pˆ 2 )

substituting in for p2 as in (52). Thus, by agreeing and not adjusting quantity, retailer 2 would receive: p 2 (q2* , q1* ) - p2 = 13 (p 1 (q1* , q2* ) + p 2 (q2* , q1* ) - 2 (p 1 (qˆ1 , 0) - pˆ1 ) + (p 2 (0, qˆ2 ) - pˆ 2 ) ) (53)

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Alternatively, the manufacturer and retailer 2 could agree to an alternative quantity. If this is done then, with probability q, this becomes known to retailer 1 who will renegotiate their contract. If the resulting quantities are q1R and q2R , retailer 2’s resulting payoff will be: p 2 ( q2R , q1R ) - p2 =

1 3

(p ( q

R 1

1

, q2R ) + p 2 ( q2R , q1R ) - 2 (p 1 ( qˆ1 , 0) - pˆ 1 ) + (p 2 (0, qˆ 2 ) - pˆ 2 ) ) (54)

which is strictly less than that in (53) by the definition of industry profit maximisation. On the other hand, if the adjusted quantity is not revealed to retailer 1, the negotiations end and retailer 2 will receive: 1 2

p 2 ( q2R , q1* ) + 23 ( 23 p 1 ( q1* , q2* ) - 12 p 2 ( q2* , q1* ) ) - 23 ( (p 1 ( qˆ1 , 0) - pˆ1 ) - 12 (p 2 (0, qˆ2 ) - pˆ 2 ) ) (55)

Therefore, for a given q, the expected difference in profits from an adjusted quantity and agreeing to the announced quantity will be: 1 3

(q (p (q , q ) + p (q , q )) + (1 - q ) ( R 1

1

R 2

R 2

2

R 1

- (p 1 ( q , q ) + p 2 (q , q ) ) 1 3

* 1

* 2

* 2

1 2

p 2 (q2R , q1* ) + 23 ( 32 p 1 (q1* , q2* ) - 12 p 2 ( q2* , q1* ) )

))

(56)

* 1

Notice that as q goes to 1, this necessarily becomes negative. The proof of retailer 1’s incentive to agree to the announced industry profit-maximising quantity proceeds analogously. The analysis for the manufacturer in both cases follows similarly. For uniqueness, note that for a given announcement, as q goes to 1, each player expects a payoff that is a weighted sum of industry profits and another term that is independent of announced quantities. Hence, so long as there is a unique industry profit maximising solution, each player will have an incentive to agree to quantities that are consistent with that outcome. □

It is worthwhile comparing this extensive form game with that specified by Stole and Zwiebel (1996). There game was essentially the same except that quantities could not be adjusted (they were set equal to 1 in every case). In their game, as in ours, prices were not directly observed and breakdowns were publicly observed with all agents being able to renegotiate contracts in the event of any single breakdown. This also meant that ordering was not strategically relevant in their model. Finally, they assume, as do we, that no pair can negotiate a contract once negotiations between them have broken down. In this respect, our game simply extends their to take into account the quantity dimension of negotiations. If contract quantities were never observed, then under a passive beliefs restriction on out of equilibrium beliefs, the quantities agreed upon would be consistent with a Cournot outcome (as in Rey and Tirole, 1997). Nonetheless, each player would still receive a proportion of total industry profit; it is just that this profit would be at its Cournot level. If contract quantities were observed but renegotiation based on it were not possible, then a Stackelberg-like outcome would result with initial negotiators weighing industry profits while later negotiators took into account their own profits only. This would result in a higher industry profit than the Cournot case but still below the integrated-monopoly case. Nonetheless, all firms would share in that industry profit. These outcomes are explored in more detail in de Fontenay and Gans (2001).

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In our opinion, having observable quantities that can trigger renegotiations – just as a breakdown in negotiations would – gives us a game closest in spirit to the non-binding nature of contracts as emphasised by Stole and Zwiebel. As such, we regard it as an accurate depiction of long-run equilibrium outcomes when prices adjust more frequently than industry structure.

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References Binmore, K., A. Rubinstein and A. Wolinsky (1986), “The Nash Bargaining Solution in Economic Modeling,” RAND Journal of Economics, 17, 176-188. Cremer, J. and M. Riordan (1987), RAND Journal of Economics. de Fontenay, C. and J.S Gans (1999), “Extending Market Power Through Vertical Integration,” Working Paper, No.99-02, Melbourne Business School (available at www.ssrn.com). de Fontenay, C. and J.S Gans (2001), “The Efficiency of Bilateral Negotiations in the Presence of Externalities,” mimeo., Melbourne Garvey, G. and R. Pitchford (1995) “Input Market Competition and the Make or Buy Decision,” 4 (3) Journal of Economics and Management Strategy, pp.491-508. Grossman, S. and O. Hart (1986), “The Costs and Benefits of Ownership: A Theory of Vertical and Lateral Integration,” Journal of Political Economy, 94, 691719. Hart, O. and J. Tirole (1990), “Vertical Integration and Market Foreclosure,” Brookings Papers on Economic Activity, Microeconomics, 205-285. Jackson, M.O. and A. Wolinsky (1997), Journal of Economic Theory McAfee, R.P. and M. Schwartz (1994), “Opportunism in Multilateral Vertical Contracting: Nondiscrimination, Exclusivity and Uniformity,” American Economic Review, 84 (1), 210-230. O’Brien, D.P. and G. Shaffer (1992), “Vertical Control with Bilateral Contracts,” RAND Journal of Economics, 23 (3), 299-308. Rey, P. and J. Tirole (1997), “A Primer on Foreclosure,” Handbook of Industrial Organization, Vol.III, North Holland: Amsterdam (forthcoming). Segal, I. (1999), “Contracting with Externalities,” Quarterly Journal of Economics, 114 (2), pp.337-388. Stole, L. and J. Zwiebel (1996a), “Intra-firm Bargaining under Non-binding Contracts,” Review of Economic Studies, 63 (3), 375-410. Stole, L.. and J. Zwiebel (1996b), Organizational Design and Technology Choice Under Intrafirm Bargaining,” American Economic Review, 86, 195-222. Wolinsky, A. (2000), Econometrica.