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COPYRIGHT 2006 Rand, Journal of Economics
We examine the effects that passive investments in rival firms have on the incentives of firms to engage in tacit collusion. In general, these incentives depend in a complex way on the entire partial cross ownership (PCO) structure in the industry. We establish necessary and sufficient conditions for PCO arrangements to facilitate tacit collusion and also examine how tacit collusion is affected when firms' controllers make direct passive investments in rival firms.
1. Introduction
* There are many cases in which firms acquire their rivals' stock as passive investments that give them a share in the rivals' profits but not in the rivals' decision making. For example, Microsoft acquired in August 1997 approximately 7% of the nonvoting stock of Apple, its historic rival in the PC market, and in June 1999 it took a 10% stake in Inprise/Borland Corp., which is one of its main competitors in the software applications market. (1) Gillette, the international and U.S. leader in the wet shaving razor blade market, acquired 22.9% of the nonvoting stock and approximately 13.6% of the debt of Wilkinson Sword, one of its largest rivals. (2) Investments in rivals are often multilateral; examples of industries that feature complex webs of partial cross ownerships include the Japanese and the U.S. automobile industries (Alley, 1997), the global airline industry (Airline Business, 1998), the Dutch Financial Sector (Dietzenbacher, Smid, and Volkerink, 2000), the Nordic power market (Amundsen and Bergman, 2002), and the global steel industry (Gilo and Spiegel, 2003). There are also many cases in which a controller (majority or dominant shareholder) makes a passive investment in rivals. For instance, during the first half of the 1990s, National Car Rental's controller, GM, passively held a 25% stake in Avis, National's rival in the car rental industry, while Hertz's controller, Ford, had acquired 100% of the preferred nonvoting stock of Budget Rent a Car (Purohit and Staelin, 1994; Talley, 1990). (3)
While horizontal mergers are subject to substantial antitrust scrutiny and are often opposed by antitrust authorities, passive investments in rivals were either granted a de facto exemption from antitrust liability or have gone unchallenged by antitrust agencies in recent cases (Gilo, 2000). This lenient approach toward passive investment in rivals stems from the courts' interpretation of the exemption for stock acquisitions "solely for investment" included in Section 7 of the Clayton Act.
In this article we wish to examine whether this lenient approach of courts and antitrust agencies toward passive investments in rivals is justified. Like other horizontal practices (e.g., horizontal mergers), (passive) partial cross ownership (PCO) arrangements raise two main antitrust concerns: concerns about unilateral competitive effects and concerns about coordinated competitive effects. We focus on the latter and study the effect of PCO on the ability of firms to engage in tacit collusion. To this end, we consider an infinitely repeated Bertrand oligopoly model in which firms and/or their controllers acquire some of their rivals' (nonvoting) shares. This setting allows us to deal with the complexity generated by the chain effects of multilateral PCO. This complexity arises since, in general, the profit of each firm, both under collusion as well as under deviation from collusion, depends on the whole set of PCO in the industry and not only on the firm's own stake in rivals. Another advantage of this model is that PCO does not affect the equilibrium in the one-shot case. Consequently, the competitive effect of PCO comes only from its effect on the incentive of firms to engage in tacit collusion. We say that PCO arrangements facilitate tacit collusion if they expand the range of discount factors for which tacit collusion can be sustained.
It might be thought that since PCO allows firms to internalize part of the harm they impose on rivals when deviating from a collusive scheme, any increase in the level of PCO in the industry will necessarily facilitate tacit collusion. This intuition, however, ignores the fact that PCO arrangements create an infinite recursion between the profits of firms that hold each other's shares, both under collusion and following a deviation from collusion. Consequently, PCO arrangements affect the incentive of each firm to collude in a complex and subtle way.
Despite this complexity, we are able to prove that an increase in the stake of firm r in a rival firm s never hinders collusion. Moreover, we show that such an increase will surely facilitate collusion provided that (i) each firm in the industry holds a stake in at least one rival, (ii) an industry maverick firm (a firm with the strongest incentive to deviate from a collusive agreement) (4) has a direct or an indirect stake in firm r, (5) and (iii) firm s is not an industry maverick. If either one of these conditions fails, the increased stake of firm r in firm s will not affect tacit collusion. In addition, we show that a controlling shareholder (whether a person or a parent corporation) can facilitate tacit collusion further by making a direct passive investment in rival firms. Such investment particularly facilitates collusion if the controller has a relatively small stake in his own firm.
The unilateral competitive effects of PCO have already been studied in the context of static oligopoly models by Reynolds and Snapp (1986), Bolle and Guth (1992), Flath (1991, 1992), Reitman (1994), and Dietzenbacher, Smid, and Volkerink (2000). (6) Our article, by contrast, focuses on the coordinated competitive effects of PCO and examines a repeated Bertrand model. The distinction between the unilateral and coordinated competitive effects of PCO is important. In particular, PCO arrangements that may be unprofitable in static oligopoly models are shown to be profitable in our model once their coordinated effects are taken into account. For example, given that in a perfectly competitive capital market the price of the rival's shares reflects their post-acquisition value, an investing firm can gain only if its own shares increase in value. As Flath (1991) shows, this is the case only when product market competition involves strategic complements. (7) By contrast, our results show that once repeated interaction is taken into account, firms may benefit from investing in rivals even if such investments have no effect in one-shot interactions. Reitman (1994) shows that symmetric firms may not wish to invest in rivals because such investments benefit noninvesting firms more than they benefit the investing firms. In our model, there is no such free-rider problem, since when firms are symmetric, all of them need to invest in rivals to sustain tacit collusion (i.e., each firm is "pivotal").
We are aware of only one other article, Malueg (1992), that studies the coordinated effects of PCO. His work differs from ours in at least three important ways. First, Malueg considers a repeated Cournot game and finds that in general, PCO has an ambiguous effect on collusion. The ambiguity arises because in the Coumot model, PCO has two conflicting effects. On the one hand, PCO implies that firms internalize part of the losses that they inflict on rivals when they deviate. On the other hand, PCO also softens product market competition following a breakdown of the collusive scheme and hence strengthens the incentives of firms to deviate. We believe that in practice, the first effect is likely to dominate the second, otherwise firms would have no incentive to invest in rivals. The Bertrand framework that we use allows us to neutralize the negative effect of PCO on collusion and focus attention on the first positive effect. Second, Malueg considers a symmetric duopoly in which the firms hold identical stakes in one another, while we consider an n-firm oligopoly in which firms need not have similar stakes in one another. Third, Malueg effectively considers passive investments in rivals by controllers rather than by firms; consequently, his analysis does not feature the complex chain-effect interaction between the profits of rival firms that is a main focus of our article.
The rest of the article is organized as follows: In Section 2 we examine the effect of PCO on the ability of firms to achieve the fully collusive outcome in the context of an infinitely repeated Bertrand model with symmetric firms. Section 3 shows that PCO by firms' controllers may further facilitate collusion. We conclude in Section 4. All proofs are in the Appendix.
2. Partial cross ownership (PCO) by firms
In this section we examine the coordinated competitive effects of PCO in the context of the familiar infinitely repeated Bertrand oligopoly model with n [greater than or equal to] 2 identical firms that produce a homogeneous product at a constant marginal cost c. In every period, the n firms simultaneously choose prices and the lowest-price firm captures the entire market. In case of a tie, the set of lowest-price firms gets equal shares of the total sales. Using Q(p) to denote the demand function, the monopoly price is defined by
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.].
and the monopoly profit is
[[pi].sup.m] [equivalent to] Q([p.sup.m])([p.sup.m] - c).
As is well known (e.g., Tirole, 1988, Ch. 6.3.2.1), the fully collusive outcome in which all firms charge [p.sup.m] and each firm gets an equal share in the monopoly profit, [[pi].sup.m] can be sustained as a subgame-perfect equilibrium of the infinitely repeated game provided that the intertemporal discount factor, [delta], is sufficiently high:
(1) [delta] [greater than or equal to] [delta] = 1 - 1/n.
Taking condition (1) as a benchmark, we shall examine the competitive effects of PCO by looking at its effect on the critical discount factor, [delta], above which the fully collusive outcome can be sustained. In other words, [delta] will be our measure of the ease of collusion. (8) We will say that PCO arrangements facilitate tacit collusion if they lower [delta] and thereby widen the set of discount factors for which the fully collusive scheme can be sustained. Conversely, we will say that PCO arrangements hinder tacit collusion if they raise [delta].
[] Accounting profits under PCO. Let [[alpha].sub.ij] be firm i's ownership stake in firm j. We assume that the pricing decisions of each firm are effectively made by its controller (i.e., a controlling shareholder). Now, suppose that all controllers adopt the same trigger strategy whereby each firm charges the monopoly price, [p.sup.m], in every period unless at least one firm has charged a different price in any previous period; from that point onward, all firms use marginal cost pricing and make zero profits in every period. (9) To write the condition that ensures that this trigger strategy can support the fully collusive scheme as a subgame-perfect equilibrium, we first need to express the profit of each firm under collusion and following a deviation from the fully collusive scheme.
If all firms charge the monopoly price, then each firm earns [[pi].sup.m]/n directly. (10) In addition, each firm gets a share in its rivals' profits due to its ownership stake in these firms. The profit of firm i is therefore [[pi].sub.i] = [[pi].sup.m]/n + [[summation].sub.k[not equal to]i][[alpha].sub.ik][[pi].sub.k]. The vector of collusive profits in the industry, [pi] = ([[pi].sub.1], [[pi].sub.2], ..., [[pi].sub.n])', is therefore given by the solution of the equation
(2) [pi] = [pi] + A[pi],
where [pi] = ([[pi].sup.m]/n, ..., [[pi].sup.m]/n)' is an n-dimensional vector and
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.].
is an n x n PCO matrix whose ith row specifies firm i's ownership stakes in its n - 1 rivals (the diagonal terms in A are all zero because firms do not hold direct stakes in themselves).
However, if firm i deviates from the fully collusive scheme and slightly undercuts the monopoly price, then the direct profit of all firms but i (excluding their share in the rivals' profits) is zero, while firm i's direct profit is arbitrarily close to [[pi].sup.m]; to simplify matters, we write it as [[pi].sup.m]. After taking into account the shares that firms have in their rivals' profits, the profit of the deviant firm i is [[pi].sub.i] = [[pi].sup.m] [[summation].sub.k[not equal to]i][[alpha].sub.ik][[pi].sub.k] and the profit of each nondeviant firm j is [[pi].sub.j] = [[summation].sub.k[not equal to]i][[alpha].sub.ik][[pi].sub.k]. Consequently, the vector of firms' profits in the period in which firm i's controller deviates, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.], is given by the solution of the equation
(3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.],
where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] is an n-dimentional vector with [[pi].sup.m] in the ith entry and zeros in all other entries. In all subsequent periods following a deviation from the fully collusive scheme, all firms use marginal cost pricing and make zero profits.
Equations...
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