metadata: authors: 0: author: Mattoo,Aaditya
docna: 0: docna: Can no antitrust policy be better than some
            antitrust policy?
docty: Policy Research Working Paper
subtopic: Mining & Extractive Industry (Non-Energy),International Trade and Trade Rules,Competition Policy,Energy and Mining,Competitiveness and Competition Policy
teratopic: Infrastructure Economics and Finance
abstracts: cdata!: The author examines how the market
            structure is likely to evolve where there is multistage
            oligopolistic production - and what the implications of this
            are for antitrust policy. The author treats the decision to
            merge across or within stages of production as endogenous.
            He shows that when firms at a particular stage of production
            are relatively dominant, simultaneous merger decision are
            conducive to competitive vertically integrated outcomes,
            while sequential decisions are not. The persistence of
            non-integrated market structures may be explained by the
            existence of equally dominant firms that make merger
            decisions sequentially. The credible threat of retaliatory
            merger may deter both socially desirable and undesirable
            forms of merger. What implications does the author's
            findings have for antitrust policymakers? For one thing,
            partial antitrust policy may lead to less competitive market
            structures than the total absence of such policy, because
            policy barriers to horizontal mergers only at a particular
            stage of production eliminate the deterrent effect of
            retaliatory merger. For example, if the two stages of
            production are located in countries with different antitrust
            legislation, a policy that protects consumers from domestic
            mergers may ultimately hurt them by rendering foreign
            mergers more attractive. When the equilibrium market
            structure does not contain socially undesirable mergers,
            there is no need for antitrust (or competition) policy.
            Moreover, there may sometimes be a case for the government
            actually providing supplementary incentives to encourage
            particular forms of merger - as, for instance, when the
            threat of retaliatory merger deters socially desirable
            vertical mergers.
repnme: repnme: Can no antitrust policy be better than some
            antitrust policy?
display_title: Can no antitrust policy be better
            than some antitrust policy
listing_relative_url: /research/1999/09/440011/can-no-antitrust-policy-better-some-antitrust-policy
topicv3: Mining Services m1326410 1701,Trade m1326924 698,Competition Policy m1326982 406,Antitrust m1327697 2101,Iron m1503514 2931
publishtoextweb_dt: 2010-07-01T00:00:00Z
historic_topic: Infrastructure Economics and Finance
origu: Development Research Group (DECRG)
no_of_pages: 48
author_keys: 0: author_key: 429183
model_extractions: | POLICY RESEARCH WORKING PAPER 2191

# **Summary findings**

Mattoo examines how the market structure is likely to evolve where there is multistage oligopolistic production - and what the implications of this are for antitrust policy.

Mattoo treats the decision to merge across or within stages of production as endogenous. He shows that when firms at a particular stage of production are relatively dominant, simultaneous merger decisions are conducive to competitive vertically integrated outcomes, while sequential decisions are not.

The persistence of nonintegrated market structures may be explained by the existence of equally dominant firms that make merger decisions sequentially. The credible threat of retaliatory merger may deter both socially desirable and undesirable forms of merger.

What implications do Mattoo's findings have for antitrust policymakers?

For one thing, partial antitrust policy may lead to less competitive market structures than the total absence of such policy, because policy barriers to horizontal mergers only at a particular stage of production eliminate the deterrent effect of retaliatory merger. For example, if the two stages of production are located in countries with different antitrust legislation, a policy that protects consumers from domestic mergers may ultimately hurt them by rendering foreign mergers more attractive.

When the equilibrium market structure does not contain socially undesirable mergers, there is no need for antitrust (or competition) policy.

Moreover, there may sometimes be a case for the government actually providing supplementary incentives - to encourage particular forms of merger as, for instance, when the threat of retaliatory merger deters socially desirable vertical mergers.

- - This paper a product of Trade, Development Research Group is part of a larger effort in the group to examine the links between trade and regulatory policy. Copies of the paper are available free from the World Bank, 1818 H Street NW, Washington, DC 20433. Please contact Lili Tabada, room MC3-333, telephone 202-473-6896, fax 202-522-1159, Internet address Itabada@worldbank.org. Policy Research Working Papers are also posted on the Web at http:// www.worldbank.org/html/dec/Publications/Workpapers/home.html. The author may be contacted at amattoo @worldbank.org. September 1999. (39 pages)

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings_ **_out_** _quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represen_ **_t_** _he view of the World Bank, its Executive Directors, or the countries they represent._ Produced by the Policy Research Dissemination Center
**Can no anti-trust policy be better than some anti-trust policy?**

_By Aaditya Mattoo*_ _Key words:_ oligopoly, vertical merger, horizontal merger, antitrust policy _JEL:_ L13, L40, L41, L42

* World Bank, 1818 H Street NW, Washington, D.C. 20433.

E-mail: amattoo@worldbank.org The views expressed in the paper are those of the author and should not be attributed to the World Bank. The paper has benefited from the comments of Henrik Horn, Abhinay Muthoo, Bob Rowthom, Arvind Subramanian, David Ulph and especially, David Newbery. The comments of two anonymous referees and, in particular, an editor of this Journal have helped greatly to improve the paper.
**Can no anti-trust policy be better than some anti-trust policy?**

It has for long been recognised that modelling the merger decision as endogenous is likely to be fruitful. As Salant, et al. (1983, p. 374), wrote, "This...approach is exciting because it would permit predictions about which mergers are contained in the set of equilibria and which mergers will never occur. Antitrust authorities need not concern themselves with blocking mergers outside the equilibrium set, since market forces would prevent their occurrence; for the same reason, the government could not cause such mergers to occur (without using supplementary incentives) even if they would be socially desirable. Finally, such models may ultimately help us understand the evolution of industry structure over time as coalitions form and regroup." Much of the existing literature on horizontal and vertical merger reveals two inadequacies. Merger is usually treated as an exogenous change in the market structure, and each form of merger is treated as the outcome of an independent decision.I While there have been several recent attempts to treat the decision to merge as endogenous, there has so far been no analysis of multistage oligopolistic production where both horizontal and vertical merger are options. This paper seeks, not only to _endogenise_ the decision to merge, but to examine which, if any, of the two forms of merger will take place when _both_ are possible.

Allowing for the possibility of both horizontal and vertical mergers enables us to pose the following question: is one form of merger universally more likely to occur in the absence of restraining legislation, or does the result depend on factors such as the initial market structure and the manner in which various participants move? This is of particular interest because there is a general presumption that horizontal integration leads to an anti-competitive outcome (in the absence of significant economies of scale), while vertical integration is likely to be procompetitive (unless there is significant vertical foreclosure).

1
These issues have wider significance since they relate to the more general problem of coalition formation, relevant, for instance, to multinational enterprises (MNEs) operating in the extractive industries. Thus while there is evidence of NINEs forming joint ventures and colluding with each other - witness the cartels of raw material and oil producers - there is also considerable evidence of MNE's in oligopolistic situations resorting to vertical integration either as a device for pre-empting a rival or for punishing a rival for a similar move undertaken elsewhere (see Caves (1996) for a survey of this literature). As noted, for instance by Scherer (1980, p. 90): "When vertical integration induced by fewness of supply sources thins the market further, other buyers may be stampeded into integrating as well despite appreciable scale economy sacrifices. Dynamics of this sort can be observed in the histories of the U.S. and European refrigerator-freezer industries, the U.S. automobile industry, and the movement by American steel makers into iron ore mining."<sup>13</sup> The observed variations in behaviour - from collusion at a particular stage of production to successive vertical integration of oligopolists at different stages of production - have prompted several different explanations. These include technological features, the importance of transactions costs at different stages of production, and the manner in which agents can best respond to the riskiness of an environment characterised by uncertain demand or input supplies. This paper focuses purely on the interdependence of oligopolistic producers operating at each stage of production.

The importance of two features in determining the emergent market structures is highlighted: first, whether or not firms at a particular stage of production are relatively dominant, and, second, whether firms move simultaneously or sequentially. Firms at a particular stage of production are _relatively dominant_ when they have the option of merging with each other and firms at the other stage of production do not. Empirically, relative dominance may be 2
observed where firms at a particular stage are situated in a country or sector where anti-trust policy does not pose impediments to merger.

Merger moves can be regarded as _simultaneous_ or as _sequential._ The former implies that all firms must make an offer of merger, including its terms, at the same time. In the latter case, firms move in alternate sequence over one or more rounds of moves. The appropriate solution concepts in the two cases are, respectively, the Nash equilibrium and the sub-game perfect equilibrium. Empirically, simultaneity may be a way of depicting the situation in markets in which _if_ there were first movers in the merger game, they would gain significantly at the expense of others.

The basic results can be summarised as follows:

1. When firms at one stage of production are relatively dominant, whether the equilibrium market structure is pro-competitive (i.e. vertically integrated) or anti-competitive (horizontally integrated) depends on whether the dominant firms act simultaneously or sequentially. Simultaneous behaviour is conducive to competitive outcomes. The result arises because the payoffs of the relatively dominant firms have a "prisoners' dilemma" structure: in the simultaneous move merger game, there is a dominant strategy Nash equilibrium in which each firm independently chooses vertical integration, and the integrated units compete fiercely against each other. This outcome is strictly inferior for the relatively dominant firms than horizontal merger with each other, but the latter outcome only emerges as a sub-game perfect equilibrium in a sequential move merger in which each firm can base its decision on the choices of the other.

2. When all firms are equally dominant, and merger moves are sequential, the most likely outcome is no merger at all. Even though each merger is in itself profitable, ceteris paribus, the credible threat of retaliatory merger creates sufficient disincentives to initiating either form of
merger. Horizontal merger of firms at one stage is deterred because it would optimally provoke a merger also of firms at the other stage, leading to a situation of successive monopoly, which results in a decline in industry profits because it is highly inefficient. Vertical merger between two firms is deterred because it would optimally provoke a vertical merger also of the other two firms, leading to a situation of low cost duopoly, which also results in a decline in industry profits because it is highly competitive.

The most striking implication for policy is that partial anti-trust policy may lead to less competitive market-structures than the total absence of such policy . The reason is that a policy which creates barriers to horizontal merger only at a particular stage of production, eliminates the deterrent effect of retaliatory merger. In particular, if stages are located in countries with differing anti-trust legislation, a policy which protects consumers from domestic mergers may actually hurt them by rendering foreign mergers more attractive.

It is also noteworthy that there may sometimes be a case for the government actually providing supplementary incentives to encourage particular forms of merger. This would be the case when the threat of retaliatory merger deters socially desirable vertical mergers.

In the next section the basic assumptions of the model are described. Section II contains a discussion of the appropriate solution concept, after which the alternative market structure equilibria are examined in Section III. Section IV discusses some implications of the analysis.

# 1. THE MODEL

There are two stages of production - the first can be thought of as 'mining' and the second as 'refining' of a mineral. There can be three kinds of firms: 'mines' which produce crude, 4
'refineries' which produce the final good, and those which do both, vertically integrated firms (VIFs). The following symbols are used:

|Final good producers (refineries)|_RI, R2_|
|---|---|
|Intermediate good producers (mines)|_M1, M2_|
|Vertical integration (VI)|_(Al+RO), (M2+R2)_|
|Horizontalintegration (HI)|_(M1+M2), (R+R2)_|

The incentive to integrate vertically arises from the desire to circumvent the mark-up over variable cost charged in the intermediate good market. By eliminating the inefficiency arising from double-marginalization, the VIF effectively gains a competitive edge in the final good market, so that the constituent firms together gain at the expense of the rest of the industry.<sup>2</sup> The incentive to integrate horizontally at either stage of production arises from the increase in the monopoly power that such integration involves.<sup>3</sup> Through integration, Cournot duopolists gain by internalizing the inframarginal losses that they impart to each other when they decide on output levels independently.

There are several choices to be made regarding the depiction of the merger process. The whole process is viewed as a two stage game: first, a stage in which various forms of merger are considered and accomplished, described by assumptions (A6) to (A10); second, the market stage, where the game is played according to Cournot rules between firms at the same stage of production, while firms at the earlier stage of production are price leaders vis-a-vis those at a later stage of production, described by assumptions (Al) to (A5).

First, regarding the demand conditions it is assumed that: 5
- Al. The final demand function is linear. The inverse demand function is of the form p = 1 - _Y,_ where p is the price of the final good and _Y_ the total output of the final good.<sup>4</sup>

As work by Seade (1985), Bulow, et al. (1985) and others has shown, linearity does impose a significant restriction in oligopolistic situations. The assumption is used here to obtain explicit solutions for profits of the firms under different market structures.

# Regarding the production conditions it is assumed:

- A2. The production function can be written (through appropriate choice of units) in the form y x, where y is a refinery's output of the final good and x the input of crude. Mines produce the intermediate good, "crude", costlessly. Refining uses solely the input from the mine. Hence, the marginal cost of an unintegrated refinery is the price of crude charged by the mine, while the marginal cost of a vertically integrated firm is zero.

Note that the total production costs in both the vertically integrated and the unintegrated case are zero - i.e., the mine mark-up in the latter case is not a cost of production, but only a transfer from the refinery to the mine. There is no significant loss in generality in assuming away costs of production when there are no economies of merger. The assumption of fixed coefficients technology makes it simple to obtain the derived demand for crude - although it does impose a significant restriction compared to allowing for variable proportions (see Waterson (1982) for a more general treatment). Given this assumption, the existence of other inputs can be ignored without further loss of generality, provided they are supplied competitively and produced using constant returns to scale technology.

6
- A3. There is a single period (one-shot) homogeneous good Cournot duopoly at each stage of production. There is complete information regarding the demand function and the cost functions of all firms, and this is common knowledge.

- A4. Refineries exercise market power only vis-a-vis consumers and not vis-a-vis the mines, whose price they take as parametrically given; i.e. mines act as "price leaders" vis-a-vis the unintegrated refineries.

This assumption is needed to render the non-merger situation determinate and thus provide a clear reference point for establishing the nature of outside options. There is as yet no satisfactory theory of how intermediate good prices are determined in situations of successive monopoly or oligopoly. Assumption (A2) is frequently made in the literature and is reasonable if the decisions of the intermediate good producers precede those of the final good producers (see Lewis et al. (1986) and Salinger (1988)).5

- _A5._ VIFs make the Cournot conjecture about the behaviour of rival final good producers; the VIFs do not buy or sell the intermediate good.

These assumptions are made to simplify the analysis. Assuming that the VIF withdraws from the intermediate good market is in conformity with results obtained in the literature.<sup>6</sup> Given our assumptions, it is possible to show that a VIF makes greater profits by processing any single unit of the input itself and selling the resultant output on the final good market than by selling the unit of input to rivals.<sup>7</sup> Strangely, it turns out to be more difficult to show that a VIF would not buy the input in order to raise rivals costs even though it can produce it more cheaply itself. However, this possibility raises complex issues about the nature of firms' conjectures from which we choose to abstract in this paper.<sup>8</sup> 7
- A6. The decision to merge involves only two firms, is irreversible and involves a binding commitment to maximise the joint profits of the constituent firms.<sup>9</sup>

The utilities of the owners of firms are identical to the profits of the firms, which can be distributed freely within a merged unit - i.e. utility is transferable. The distribution of profits post-merger is decided between participating firms before the merger, and it is possible to write binding contracts to enforce this. Both the negotiations preceding the merger and the writing of contracts are accomplished costlessly.

Note that the merged entity behaves essentially like a multi-plant firm under the control of a particular player in a non-cooperative game. Firms have available the options of forming alternative mergers when bargaining over the profits from a particular merger. Whether they have the time to use these options will depend on which of the following is assumed:

- A7(a). The merger stage is a one shot simultaneous move game, followed by a one shot game in the market stage.

- or (b). The merger stage is a sequential move game, followed by a one shot game in the market stage. Firms move alternately in the merger stage playing one or more rounds of moves, and enter the market stage either (i) when two firms have merged, and the other two have had an opportunity to react by merging or not merging, or (ii) when each firm has had an opportunity to react to the decision of the other firms not to merge.

How these alternative assumptions influence the nature of options available to firms will be discussed later. But note that assuming the firms move simultaneously in the one-shot merger stage implies that if they fail to agree on the terms of a merger, they only have the option of remaining unmerged. When the merger stage is a sequential move game, Assumption (A7b) ensures that merger is not a precondition for entry into the market stage.

8
Regarding the costs of merger itself, the following weak assumption is made:

- A8. If a particular merger and staying unmerged offer the same payoffs to a firm, it prefers to stay unmerged.

If a particular merger A (horizontal or vertical) offers a firm even slightly (s) greater profits than staying unmerged, UI, or another merger B (horizontal or vertical), the firm prefers A to UI and B.

This assumption implies that the price at which a firm will accept to merge must be **6** above the alternative, and this turns out to be an important tie-breaking rule (an alternative would be simply to assume that the transactions costs of implementing a merger are £).

In the sequential move merger games, only the following weak assumption is made regarding the time preference of firms and the termination of the merger stage:

- A9. Between two identical outcomes at different points of time, the firm prefers the earlier one. The firms do not want to delay indefinitely the market stage in which the payoffs are obtained.

This "negligible" time preference simply means, in the sequential case, that firms would prefer that any specific eventual equilibrium be reached after a minimum number of offerresponse rounds.

The numerals 1 and 2 are used to distinguish between the two mines and the two refineries, and the following simplifying assumption is made: 9
Al0. Mine 1 and refinery 1 consider vertical merger (VI) only with each other, as do mine 2 refinery 2, i.e. diagonal mergers are ruled out.

The crucial issue is as to how the payoffs _within_ the merged unit are decided. To begin with, the profits accruing to various units under the different market structures can be calculated and are depicted in Table 1 (note that we suppress the negligible cost of delay, if any, from our computed profits). Given assumptions (Al) to (A5) it is straightforward to obtain these values from the standard Cournot duopoly model and the mathematical detail has been relegated to the Appendix.

# **[TABLE 11**

The initial situation, with no integration, is depicted in row (4). To see the intuition for the levels of profits and prices associated with different outcomes, we can identify two types of externalities that arise between firms in this model: a horizontal externality between firms at the same stage of production, and a vertical externality between firms at different stages of production. The horizontal externality is that any decision by a mine (or refinery) to expand output, leads to a decline in prices which reduces the profit of the other mine (or refinery). However, Cournot duopolists, which maximize their own profits, do not take their rivals' incremental profits into account, and therefore tend to overproduce relative to the joint-profit maximizing level of output. The vertical externality is, first, that any decision made by a refinery that increases demand for the intermediate good generates increased profit for mines. Similarly, any decision by a mine to expand output, reduces crude prices and increases the profits of refineries. However, neither the refineries nor the mines, which maximize their own profits, take into account the incremental profits of firms at the other stage of production, and therefore tend to make decisions which lead to underproduction relative to joint-profit maximizing levels of output.

10
HI between two mines (or two refineries) benefits participants (for any given structure of the rest of the industry) because they internalise the inframarginal losses that they impart to each other when they decide on output levels independently, so that the merged unit produces the monopoly level of output. But the merger hurts firms at the other stage because the resultant price increase worsens the negative spillover on them.<sup>1</sup> I VI between a mine and a refinery benefits participants (for any given structure of the rest of the industry) because it eliminates one of the two successive mark-ups (or double-marginalization) and leads to an expansion of output to the efficient level. But it hurts rivals because it worsens the negative effect that they suffer through the reduction in prices caused by increased output.

It is well known that with fixed factor proportions and successive monopoly (rather than successive duopoly), double marginalization leads to a price in excess of the monopoly price that would occur with VI (Tirole, 1989), lowering both profits and consumer surplus. And this is what we in fact see in the first outcome in Table 1: if the horizontally integrated firms were permitted to then vertically merge into a monopoly industry, price would be _0.5,_ a price between that in outcomes 4 and 5.

For the industry as a whole, fragmentation (outcome 4) serves to dampen competition and raise prices above those that would be charged by a vertically integrated Cournot duopoly (outcome 7), toward the monopoly price. Indeed, the price with fragmentation is a little bit higher than the monopoly price.

As expected, final good price is highest in outcome (1), i.e. HI at both stages, and diminishes (or stays unchanged) down through the rows, being least in outcome (7), i.e. VI of successive duopolists. It is straightforward to show that social welfare, measured as the unweighted sum of consumers surplus and firms profits, is least for outcome (1) and increases through to outcome 11
(7). This confirms, in the context of the model, that vertical integration is socially more desirable than horizontal integration. Profits are maximized by complete integration, but attention is restricted to single mergers.

# 11. SOLUTION CONCEPTS

For a merger to be consummated, we need only to specify that for the two firms involved the opportunities on the merger frontier exceed those from, ceteris paribus, the alternatives (not merging or selecting an alternative merger). Then they would merge and share the gains of moving to the frontier in some fashion which is Pareto superior relative to both neither merging nor selecting an alternative merger. For concreteness, we wish to show the profits of each firm, to demonstrate the gains from merger. To implement a functional form for the profit sharing rule, we use a particular interpretation of the well-known Nash bargaining solution to the problem (qualitative results are insensitive to this formulation). "I This solution concept will be seen to imply, in the present context, a simple sharing rule: profits from each merger are divided equally between the participants, unless either party can obtain more from an alternative merger or by staying unmerged.

The Nash bargaining solution to the two-player/one-cake problem involves maximising: _- (ii si)(rj_ Si) subject to **7ci** + _crj_ = **_7r_** _Y_ and **_Ti >_** _s 1 , j > sj, rr i 1_ **> roi, j >** 'oj where:

**_7it_** are the total profits of the merged firm,

12
ni, 7cj are the payoffs to individual firms within the merged unit,

**_si,_** _sj_ are the status quo points,

**7C,j** **_,_** Tj are the outside options.

It is necessary to establish the nature of (a) the 'status quo' point which fixes the origin with respect to which the maximisation exercise is carried out, and (b) the 'outside options' which fix the minimum profits acceptable to the two parties, and are only relevant if the unconstrained Nash solution were to allocate profits to one party below this level. Here, as in Birnmore (1985), the distinction lies in that the outside option is something to which the firm can voluntarily withdraw while the status quo is the payoff which the firm earns if the bargaining process continues unsuccessfully for an indefinite period, i.e. the 'disagreement point'. Since the situation has been depicted as a two stage game, and the market stage is only entered after the negotiation stage, the firms are not operating as such until the bargaining has been concluded. So it is appropriate to regard the firms as earning nothing while the bargaining process continues inconclusively, therefore I put _si = sj_ = 0.

The outside options, **7rj,** _7ro._ are the profits earned either if the firm stays unmerged or if it enters into alternative mergers, depending on whether the latter option is open to it when it is bargaining. This will depend on the specification of the merger process, and for each of the following situations an appropriate definition will be suggested.

The crucial issue is how outside options, i.e. the possibility of forming alternative mergers or staying unmerged, affect the payoffs within the merged unit. There is an obvious interdependence here, in that a firm's potential profits from one merger are an outside option for it in another merger and vice versa. The next section is devoted to the solution of this problem.

13
## III. ALTERNATIVE MARKET STRUCTURE EQUILIBRIA

In this section, I establish the nature of market structure equilibria under alternative assumptions about the temporal structure of the model, i.e. variants of assumption (A7). This is done in two stages. First, a two-person non-cooperative game between the mines is studied. This is done by assuming that the input producers or mines, Ml and M2, are _relatively dominant,_ i.e. they have the option of merging horizontally while the final good producers or refineries, _R1_ and R2 do not. It will also be convenient to assume that it is the relatively dominant mines which can initiate integration with the refineries, and that the latter are 'passive'. After this we present a more general case, in which all firms are equally dominant. This marks a shift from the earlier "two-person game" to a "four-person game." In this case, for simplicity, attention will be restricted to the situation where merger moves are sequential.

# _A. Relatively dominant mines, passive refineries: simultaneous moves_

In this section, the consequences of assumptions (Al) to (Al0) including (A7a) are examined: relatively dominant mines, _M1_ and M2 move simultaneously in the one shot merger stage of the game, after which there is a one-shot market stage.

Each mine can do one of three things: (i) remain unintegrated, UI, (ii) merge with a final good producer, VI, - it is assumed that Ml considers merger with _RI,_ and **M2** with R2, or (iii) offer to merge with the other mine - the offer is represented by the notation "HI?". Each mine simultaneously makes an offer of merger, including its terms, to one other firm. If the offers match both in the choice of firm and the terms, they merge, otherwise they stay unmerged. There is no possibility of switching to another firn: the only outside option is to stay unmerged. The matching offers, which are also the payoffs from successful merger, are calculated using the Nash bargaining solution: as if they were the outcome of actual bargaining with only non-merger 14
profits as outside options.1<sup>2</sup> In effect the four-person/four cake problem has been broken into four two-person/one-cake problems.

If _Ml_ chooses VI, then while it is bargaining with _R,,_ it only has an outside option of staying unmerged, given the one shot nature of the game. There are two possibilities: either M2 and R2 do not merge, i.e. outcome 5, or they also merge, i.e. outcome 7. In the former case the profits to be divided are 0.1837, and the outside options for _Ml_ and RI, i.e. their profits from staying unmerged, are 0.0494 and 0.0741, respectively (see outcome 4). These are strictly less than the shares determined by the unconstrained Nash bargaining solution, 0.0918 to each. In the case of outcome 7, the profits to be divided are 0.1111, and the outside options for _Ml_ and RI are 0.0204 and 0.0408, respectively (see outcome 6), which are also strictly less than the shares determined by the unconstrained Nash bargaining solution, 0.0555 to each. The payoffs to M2 and R2 from outcomes 6 and 7 can be similarly calculated. Table 2 depicts the payoffs to Ml and M2 from each of their different actions.

# **[TABLE 21**

The parenthetical terms in Table 2 refer to the outcomes as presented in Table 1. The first item in each box is the payoff to Ml and the second the payoff to M2. These payoffs, anticipated by the firms in their merger decisions, have a "prisoners' dilemma" structure: there is a dominant strategy Nash equilibrium: outcome 7 _(MlI+R,_ M2+R2), i.e. both _M1_ and M2 integrate forward into the final stage, and compete more fiercely against each other. This is strictly inferior for them than outcome 2 _(M1+M2 , RI, R2),_ i.e. horizontal merger, and even outcome 4, i.e. no merger, but neither can risk offering HI? or choosing UI in a one shot simultaneous move game. Hence: 15
PROPOSITION 1: _Given assumptions (Al) to (A.10) including (A7a) (i.e. simultaneous moves), with relatively dominant mines and passive refineries, the unique Nash equilibrium involves vertical integration of each intermediate good producer with a final good producer._ The realism of modelling merger decisions as a one-shot simultaneous move game may be questioned since it is almost always possible for other firms to retaliate. However, retaliation may take time. The distinction made in the paper between simultaneous and sequential move games is based on the relative lengths of time of the merger and market stages. In some cases, first movers in the merger stage of a game can make significant gains in the product market before others are able to conclude negotiations on a retaliatory merger. Thus no one can afford to wait for others to move first, so firms may be stampeded into merging - even though multiple mergers may lead to lower profits for everyone.

# _B. Relatively dominant mines, passive refineries. sequential moves_

All the assumptions of the previous section are retained except (A7a), which is replaced by (A7b). The merger stage is now assumed to be a sequential (alternating) move game of possibly several rounds played once, which continues till market structure equilibrium (if it exists) is reached. The decision to merge is irreversible, while the decision not to merge is reversible until the merger stage is terminated. Each mine has one additional element in its choice set: it can _accept_ an offer from the other mine to merge horizontally - denoted by "HI!".

To see how the game proceeds, assume Ml moves first. As in the previous game, it can do one of three things: (i) remain unintegrated, UI; (ii) merge with a final good producer, VI; or (iii) offer to merge with the other mine, HI?. If _Ml_ has chosen UI, then M2 has available to it the same three options: UI, VI, HI?. If, however, Ml has chosen VI, then M2 can choose between 16
only Ul and VI, and the merger stage concludes once it has chosen either option (see A7(b)(i)). If _Ml_ has chosen HI?, then M2 again has three options open to it: UJ, VI, HI!. If it chooses HI!, the merger stage concludes. Except in the three conclusion scenarios, (VI,UI), (VI,VI), (HI?, HI!), after M2 's move Ml has an opportunity to move again. If the previous choices of both had been UI, and if Ml chooses Ul again, then the merger stage concludes - since each firm has had an opportunity to react to the decision of the other firm not to merge (A7(b)(ii)). The other possible paths down the game tree can be worked out similarly.

In this game, as distinct from the simultaneous one, a mine, when bargaining over the terms of a particular merger, may have the _outside option offorming an alternative merger,_ in addition to the one of staying unmerged. In particular, _MI,_ by virtue of moving first, has the outside option of offering HI to M2 when it is considering VI with RI. But if Ml has chosen VI, M2 no longer has the outside option of HI with _M1_ when considering VI with _R2._ First note that outcomes (5) and (6) will never be observed as equilibrium market structures, unless there are partial barriers to VI. If either Ml or M2 chooses VI, it is in the best interests of the other to do the same. E.g. compare from the point of view of M2 and R2, outcomes 5 and 7, in which Ml and RI have _already_ merged; they can earn 0.0204 and 0.0408 respectively if they stay unmerged (5) and 0.0555 each if they too VI (7). The latter is obtained from the distribution of 0.1111 from VI, _given_ the merger of Ml and _R1_ (with outside options of 0.0408 for M2 and 0.0204 for R2 if they stay unmerged). Clearly VI is preferable to staying urnerged. Thus outcome 7 _(M1 +R1, M2+R2)_ is a Nash equilibrium, in which the total expected payoff to each vertically integrated unit is equal to 0.1111.

Now consider outcomes (2) and (7), which must be treated differently from Section IIIB.

The most _Ml_ can obtain from VI with RI is (0.0833-6). To see this note that the least _RI_ is 17
assured of is 0.0278, which are its profits from staying unmerged given that the mines have merged (outcome 2). By assumption (A8), regarding the costs of merger, RI will want at least e more to induce it to accept VI rather than stay unmerged. The size of the cake obtainable from VI is 0. 1111, as shown above. Hence, the most Ml can get is 0. 111 1-(0.0278+6), which gives the above expression.

If _Ml_ offers HI? to M2, the latter can accept HI!, choose Ul or initiate VI with R2. At this stage, with Ml unmerged, the most M2 would get from VI is also (0.0833-c) (which is greater than the most available from Ul, i.e.0.0741). After taking into account their maximum possible outside options, the Nash bargaining solution divides the profits from HI, 0.1666, equally between Ml and M2 , i.e. each gets 0.0833 from outcome 2. The second mover status means that M2 gets less than Ml if the latter chooses VI, but does not affect the sharing of profits from HI.

# **[TABLE 31**

Given the payoffs from outcome 2, the payoffs to the two mines from outcomes (5), (6) and (7) can be similarly calculated and are presented in Table 3. The choices by _Ml_ in period 3 that do not have a final outcome as the end, lead either to previously achievable outcomes in later periods or indefinite delay in the attainment of market structure equilibrium and entry into the market stage. These are ruled out by the assumption of weak time preference (A9).

Outcome 7 _(MI +R]j,_ M2+R2) continues to be a Nash equilibrium (albeit, as we shall see, not sub-game perfect) in this game as well, as noted above. If either mine chooses VI, it will expect the other to do the same, since it is in the latter's best interest to do so. But this involves less 18
profits for the mines than outcome 2 _(MI+M2 , RI,_ R2). Given the assumption of weak time preference (A9), Ml will straightaway offer HI? and M2 will accept HI!. Hence: PROPOSITION 2: _Given assumptions (Al) to (A.10) including (A7b) (i.e. sequential moves), with relatively dominant mines and passive refineries, the unique sub-game perfect equilibrium involves horizontal merger of the mines._ It is evident that if the option of VI is not open to a particular mine, then the other mine will choose VI, e.g. Ml prefers _(5)_ to (2). Without the threat of retaliatory VI, the gains from VI outweigh those from HI.

# _C. Mines and refineries are equally dominant: sequential moves_

In this general situation, each firm can offer the relevant other firm HI? or VI?, accept an offer HI! or VI!, or choose UI. The merger stage is again assumed to be a sequential (alternating) move game of possibly several rounds played once, which continues till market structure equilibrium (if it exists) is reached, after which there is a one-shot market stage. The important difference from the previous section is that now the refineries can offer and accept HI as well. The similarity is that the firms can base their decisions on the choices of other firms. There are several different ways of describing this game, for instance by specifying a precise order in which players move. However, the object here is to obtain fairly general results so that little specific structure is provided. The first thing to be established is that: LEMMA 1: _The threat of retaliatory merger is credible, i.e. if any two firms merge, it is in the best interests of the other two firms to do the same._ 19
For example, say Ml and M2 have merged. If RI and R2 stay unmerged they earn 0.0278 each (Table 1: outcome 2). If they merge (outcome 1) the Nash bargaining solution gives them each 0.0313, greater than their identical outside options of staying unmerged. This can be established for each of the other forms of merger. It emerges that outcome 1 _(M1 +M2, R1+R2)_ and outcome 7 _(MK+Rl,_ M2+R2) are two of the Nash equilibria in this game, which implies that the threat of retaliatory merger is credible. Asymmetric outcomes, like outcome 2 _(M1+M2 , RI,_ R2) and outcome 6 _(MI, RI, M2+R2),_ etc. will never be observed as market equilibria.

It has been established that outcomes (2), (3), (5) and (6), involving partial merger, cannot be final equilibrium outcomes, while (1) and (7) are both Nash equilibria. However, it is possible to show that the maximum payoff for each firm is from outcome (4), i.e. no merger at all - an outcome which also maximises industry profits (given the available choices). On this basis, we seek to establish that:

# LEMMA 2: _The credible threat of retaliatory merger deters all mergers._

We need to demonstrate that each firm prefers to stay unmerged, provided no other firms merge, to merger given that other firms will also merge. Consider Ml. The most it could get from merger with M2 is 0.0695. This is the difference between 0.1250, the total profits from merger (outcome 1), and 0.0555, the profits M2 can be sure of even if _Ml_ has already merged with RI (see Section IIIC).

The best possible outside option for MK, when it is bargaining with RI, is therefore 0.0695. Since the profts that MI and RI would obtain from merger are 0.1111 (outcome 7), the outside option constraint is binding for Ml, so it can expect to get 0.0695. Thus Ml would get less from 20
merger with either K!2 or RI than what it could get from staying unmerged if no one else merges, 0.0741 (outcome 4).

Similar reasoning establishes that _M2, R1_ and R2 can each do better by staying unmerged provided no one else merges. So the optimal strategy for each firm is simply to refrain from merger provided no one else merges, and to participate in a retaliatory merger the moment someone else merges. Thus, each firm in its turn will choose UI, and given Assumption (A7b), they will enter the market stage once each has had an opportunity to react to the decision of the others not to merge. If any two firms were to merge, Assumption (A7b) would ensure that the merger stage would continue until the other firms had a chance to react. In sum, the threat of retaliatory merger will be a credible and effective deterrent to any merger.

PROPOSITION 3: _Given assumptions (Al) to (A.10) including (A7b) (i.e. the firms move sequentially), with both mines and refineries equally dominant, the unique subgame perfect equilibrium involves no merger at all._ Comparing this with the previous section, it is evident how _potential countervailing power_ can lead to relatively pro-competitive outcomes, i.e. it is an effective deterrent to the anticompetitive horizontal merger. It is the fear of the unprofitable successive monopoly situation which deters merger, because the gains from reducing competition within a stage are more than offset by the losses from increased prices at the other stage. But there is also a deterrent to the pro-competitive vertical merger. Here it is the fear of highly competitive low-cost duopoly situation that deters merger. The gains from eliminating the mark-up over marginal costs are more than offset by the expansion in the rival's output.

It is also possible to establish: 21
PROPOSITION 4: _Given assumptions (Al) to (A10) including (A7b), i.e. firms move sequentially, if two specific firms are prohibitedfrom merging with each other, but all other two firm combinations are permitted, then there is one unique merger which will occur, and it involves the merger of the other two firms._ From an examination of situations where two firms cannot merge with each other, it emerges that in each case the symmetric merger is most attractive, i.e. if vertical merger between two firms is not possible, the vertical merger of the other two firms will occur, and not horizontal merger at each stage. And, as seen in Section IIIC, if horizontal merger at one stage is not possible, the horizontal merger of the other two firms will occur, not vertical mergers across stages. Thus the firms which cannot merge with one another will be left out of any merger. This is a consequence of the feature that retaliatory merger is most damaging, and the firms will choose the strategy which leaves no possibility of its happening.

# IV. IMPLICATIONS OF THE RESULTS

This paper treated the decision to merge as endogenous in a simple model of two-stage duopolistic production. In the process, it demonstrated how equilibrium market structures depend on whether firms move simultaneously or sequentially, and whether firms at a particular stage of production are relatively dominant. Section IIIA showed that loss-making mergers could occur when firms have to take merger decisions _as if they were simultaneous._ This may be a reasonable depiction of circumstances in which the first mover in a merger game would reap significant benefits, so that no one can afford to wait for the others to move first. It is the prisoner's dilemma structure of payoffs which makes multiple merger. difficult to prevent despite their negative impact on each firm's profits. McBride (1983), in a study of the U.S. cement industry, found evidence of multiple VI which led to a decline in industry profits.

22
Some situations are better approximated by depicting the firms as moving sequentially, so that they can base their decisions on the actual and rationally expected decisions of other firms. In these situations, I suggest, it is the relative dominance of some firms, or the absence of it, which will determine the outcome. Horizontal merger, or the formation of collusive oligopolies, is likely when the firms at one stage are relatively dominant and have no fear of the firms at another stage indulging in retaliatory merger - as in Section IIIB.

Vickers (1984) identified the possible strategic advantage to be had from non-integration. The results of Section IIIC, i.e. the equilibrium with no merger, point to a similar possibility. Firms refrain from VI which would commit them to competing fiercely against each other and hence lead to a decline in collective profits. They also refrain from HI because of the unattractiveness of successive monopoly. (The important assumption here is that successive monopoly will involve the highly inefficient double marginalisation and not a cooperative equilibrium between the monopolists at different stages.) The threat of retaliatory mergers is crucial. Since such mergers are Nash equilibria in the merger game, they constitute credible threats, and effectively deter any merger. This may explain both the persistence of nonintegrated market structures in some situations and why firms do not proceed with ostensibly profitable mergers.

The implications for policy are significant. When the equilibrium market structure does not contain socially undesirable mergers, there is no need for anti-trust (or competition) policy. Furthermore, partial anti-trust policy, which creates barriers to horizontal merger only at a particular stage of production, may lead to less competitive market-structures than the total absence of such policy . For instance, if the two stages of production are located in countries with differing anti-trust legislation, a policy which protects consumers from domestic mergers may nevertheless hurt them by rendering foreign mergers more attractive.<sup>14</sup> 23
The threat of retaliatory merger does not always play a benign role. It can also deter socially desirable vertical mergers. In this case, it may be desirable for the government to provide supplementary incentives to encourage particular forms of merger.

# FOOTNOTES

IE.g. Salant, Switzer and Reynolds (1983), Perry and Porter (1985), Farrell and Shapiro (1990), Kamien and Zang (1990, 1993) and Bloch (1995) are articles on horizontal merger in oligopolistic situations similar to the one dealt with here, while Greenhut and Ohta (1979), Salinger (1988,1989), Hart and Tirole (1990), Ordover, et al. (1990) and Innes and Sexton (1994) are concerned with vertical merger. Most of the work since 1990 has modeled the merger decision as endogenous. More general work on these lines can also be found in a new strand of the literature analyzing the formation of coalitions in non-cooperative games with spillovers (see Chatterjee et al. (1993) for an introduction to this literature, Bloch (1997) for a recent survey and Horn and Persson (1997) for an application of this approach to the study of mergers).

- 2 The inefficiency could also be eliminated by the use of two-part rather than linear-price contracts (see Tirole (1989), p. 176). Vertical integration is defined here to include the possibility of implementing such two-part tariffs.

- 3 An added incentive for such integration is that it may lead to synergies but this possibility will not be considered.

- 4 Setting the slope and the intercept of the demand function equal to I does not lead to any loss of generality. The intercept matters only in relation to marginal cost, and no comparative statics are performed on either. Setting the slope equal to I only involves changing units.

- 5 The assumption of successive market power gives input sellers an advantage over output sellers, leading to an asymmetric distribution of profits in non-integrated situations. It is possible to show that the results of this paper also hold for more symmetric assumptions about price determination - for instance, in a situation of mutually related market power where each of two complementary inputs is produced by a duopoly.

24
- 6Salinger (1988) concludes, on the basis of certain assumptions about the conjectures that the VIF makes, that the VIF does not participate in the intermediate good market. Ordover, et al. (1990) find that vertical foreclosure may be an equilibrium outcome when the final good is differentiated and firms compete in prices; they arrive at a conclusion similar to the above assumption for the case of homogeneous good Coumot duopoly. However, the question of how the VIF is likely to behave in the intermediate good market remains to be adequately answered (see Tirole, 1989, p. 195).

- 7A VIF earns price p from a unit sale in the final good market and a price q from a unit sale in the input market. The VIF makes the Cournot conjecture in the input market, i.e. it believes that other mines will not change their output in response to changes in its output. So it expects a unit of input sale to translate into an additional unit of final good sales by its rival refineries, and a unit reduction in crude sales to lead to a unit reduction of final good sales by its rival refineries. Thus shifting one unit of crude from sales on the crude market to its own refimery's final good sales is not expected to change the total output of the final good, the final good price or the revenue from inframarginal sales. From such a shift the VIF makes a net gain of p - q. This is positive, since for it to be profitable for an unintegrated refinery to operate, it is necessary that p - q > 0.

- 8 While in the case of the VIF entering the input market as a seller there is a well-defined derived demand from the non-integrated refineries, it is difficult to define the appropriate conjectures that the VIF makes as a buyer. These issues are examined in detail in Mattoo (1990). See also Salop and Sheffman (1983) and Krattenmaker and Salop (1986).

- 9 Most recent mergers have involved only two firms at any point of time. For instance, Scherer and Ross (1990, p. 153) find that "multifirm consolidations have been extremely rare in the United States since World War I.'

- I<sup>0</sup> Mathewson and Winter (1997) present a similar argument in their analysis of buyer groups in a differentiated good model.

- 11 The interpretation of the Nash bargaining solution used here follows Binmore (1985). The Nash solution has several appealing features. It has been given a rigorous non-cooperative game-theoretic justification (see e.g. Rubinstein, 1982), to complement the earlier behavioural (Harsanyi, 1956) and axiomatic (Nash, 1950) justifications. It is also fairly tractable, as compared to, for instance, the solution due to Kalai and Smorodinsky (1975). Finally, it has the attraction of ensuring that the bargain is efficient.

25
- '<sup>2</sup> For there to be a successful horizontal merger, both firms should choose HI?, while a mine can proceed with vertical merger unilaterally, subject to the requirement that it offers the firm being taken over adequate payoffs. E.g. if one firm chooses HI? and the other chooses Ul, both remain unmerged, while if one firm chooses HI? and the other VI, the former remains unmerged and the latter merges forward. Since the refineries are passive, a 'takeover' may be a more accurate depiction of VI than a more symmetric merger. A firm taking over must pay the shareholders of the firm being taken over a share of the anticipated gain determined by the Nash solution. Even though the final good producers are passive, they can resist takeovers and choose to stay unmerged if the Nash equilibrium terms of the takeover are not suitable.

- 1<sup>3</sup> See Bolton and Whinston (1993) for an examination of supply assurance concerns, which arise when several downstream firms compete for inputs in limited supply, in the context of a transactions costs model of vertical integration.

- 140ther inferences can be drawn for the design of competition policy in the international context by specifying which firms and what proportion of consumer demand fall within a particular regulatory jurisdiction. The model then enables us to identify the effects on welfare of domestic and foreign mergers. A similar idea is explored in Head and Ries (1997).

26