Partial cross ownership and tacit collusion.

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.