Over the past two decades, private equity “has become a vastly more sizable and influential part of the economic landscape” (Lerner et al. 2012).

  • In 2012 alone, private equity firms announced 2,866 buyout deals worldwide, valued at a total of $254.6 billion (Preqin 2013).
  • This trend has contributed to an increase in the number of small minority equity purchases.

It has also fostered – in the words of John Nannes, former deputy assistant attorney general and acting assistant attorney general in the US Department of Justice Antitrust Division – “a complex web of interrelated relationships” (cross-holding). Such relationships are likely to lessen competition among the firms involved.

Competition policy and partial horizontal acquisitions

As a consequence, antitrust enforcement agencies on both sides of the Atlantic have taken an increased interest in the competitive effects of partial horizontal acquisitions. Some high-profile examples include:

  • The proposed management-led buyout of Kinder Morgan, Inc.

The former was challenged by the US Federal Trade Commission on the grounds that two private-equity firms that participated in the buyout had – through a joint venture – a partial ownership interest in a competitor of Kinder Morgan.

  • Ryanair’s partial acquisition of Aer Lingus.

The latter was filed by Aer Lingus to the European Commission, claiming that the participation of a competitor would undermine its plans for growth.

Equity purchases may involve the acquisition of a financial interest and/or of corporate control. A financial interest entitles the (partial) owner to receive the stream of profits generated by the operations and investments of the target firm, whereas corporate control entitles the (partial) owner to influence the decisions of the target firm (O’Brien and Salop 2000).

Partial horizontal acquisitions raise antitrust concerns both about unilateral effects and about coordinated effects.

  • Unilateral effects flow from the incentive to increase prices after an acquisition – an incentive that results from the internalisation of consumer substitution among products of the firms involved.

Financial interests may make the acquiring firm less aggressive when competing with its rival, whereas corporate control interests may similarly influence the behaviour of the acquired firm.

  • Coordinated effects flow from repeated interactions among firms in the market.

An agreement among firms may be supported, not by explicit negotiation, but non-cooperatively – under the credible threat that defections (deviations) from this coordinated arrangement would trigger retaliation (punishment) by rivals.

To the extent that partial horizontal acquisitions affect the price-setting incentives of acquiring and acquired firms, they affect the relevant payoffs of all firms in case of agreement, defection, or retaliation. As a consequence, they are likely to change the manner in which firms interact – affecting the strength, extent, or likelihood of coordinated conduct (see e.g. Gilo et al. 2006)

The theoretical literature on the antitrust effects of partial horizontal acquisitions makes simplifying assumptions that create difficulties for empirical applications. In an earlier paper (Brito et al. 2013a), we provide a structural methodology to empirically assess the unilateral effects of partial horizontal acquisitions; while in a more recent paper (Brito et al. 2013b) – which we discuss in more detail below – we focus on the quantification of the corresponding coordinated effects.

These approaches can be used to measure the impact of direct and indirect partial horizontal acquisitions involving only financial interests, corporate control, or both – and nests full mergers as a special case. As a consequence, they may prove to be a preferable method for analysing competition policy issues to the current indirect approaches based on the theoretical literature, which are relevant only under particular economic conditions.

Quantifying the coordinated effects of partial horizontal acquisitions

In Brito et al. (2013b), we assume a setting similar to Friedman (1971) in which oligopolistic firms in an industry interact repeatedly over time (and eventually also over markets). Firms play an infinite sequence of ordinary games with discounting, which is mathematically equivalent to assuming that each firm is uncertain about remaining in the market the following period. In our framework, each ordinary static game is modelled to account for asymmetric, multi-differentiated-product firms, with a corporate governance structure that reflects the difference between financial interest and corporate control.

We assume that firms sustain a coordinated conduct under the most basic enforcement mechanism – grim-trigger strategies. In this type of strategy, in each market and time period, firms coordinate their prices above the competitive level and trust each other to continue to do so indefinitely. Faced with this conduct, individual firms may be tempted to increase their static profits for a period or so by deviating from the arrangement. However, should any single firm in any past period choose something different, trust vanishes and each firm reverts permanently to a position in which no firm has any short-term temptation to deviate.

Under this type of strategy, a coordinated arrangement can be sustained if, for every firm in the industry, the one-shot net gain from deviating from the agreement (the difference between the static defection and agreement profits) is more than compensated by the present discounted value of the long-run benefit from maintaining coordination in all succeeding periods (the difference between the static agreement and punishment profits).

If a firm places a relatively small weight on future profits, it will most likely prefer to deviate in the present – thus obtaining some short-term benefits. If, on the other hand, a firm does not significantly discount the future, it is less likely that it will trade the long-term benefits of an agreement for the short-term gains of deviating. For each firm, it is possible to calculate the rate of time preference (discount factor) that makes it indifferent between defection and maintaining coordination. A firm is willing to sustain the latter if its actual discount factor exceeds this critical threshold.

The elements required to evaluate each firm’s critical threshold can be computed using a procedure similar to that of Davis (2006) and Davis and Huse (2010) – a procedure that simulates the firms’ counterfactual static prices and profits under the different elements of the coordination model (agreement, defection, and punishment). The impact of a partial horizontal acquisition on the likelihood of coordination can then be evaluated by examining how the acquisition affects that critical threshold value.

Illustrative empirical application

In Brito et al. (2013b), we provide an empirical application of the methodology to several acquisitions in the wet shaving industry.

On 20 December 1989, the Gillette Company – which had been the market leader for years and accounted for 50% of all razor-blade unit sales – acquired 22.9% of the nonvoting equity shares of Eemland Management Services BV (the parent company of a competitor, Wilkinson Sword). On 22 March 1993, Gillette was prompted to sell its stake in Eemland, and its competitor Warner-Lambert Company acquired 100% of Wilkinson Sword (full merger). We analyse the coordinated effects of these two acquisitions using scanner data for the disposable-razor-products subcategory.

We began by evaluating the likelihood of coordinated conduct in the pre-partial acquisition industry (before 20 December 1989). To do so, we simulated the firms’ corresponding static profits under the different elements of the coordination model. The corresponding results, which are summarised in Table 1, are consistent with the following two findings of the extant theoretical literature on the impact of firm asymmetry on the likelihood of coordination.

  • In the absence of binding capacity constraints, smaller firms tend to be maverick firms (those with the greatest incentive to deviate), since they tend to be the ones that benefit the most from disrupting a coordinating agreement.

In particular, according to our estimates, by disrupting the collusive agreement, American Safety Razor and Wilkinson Sword would obtain a gain from deviation that represents 18% and 15% of the static coordinated aggregated profits, respectively.

  • Larger firms (e.g. Gillette) will have less incentive to punish, since they tend to be the ones that benefit the most from coordination (5% of the static coordinated aggregated profits per-period).

Using these elements, we computed each firm’s critical threshold for the discount factor, and the implied maximum weighted average cost of capital. The results suggest that American Safety Razor constitutes the industry’s maverick firm – the firm with the greatest incentive to undermine coordinated behaviour.

Table 1. Pre-partial acquisition analysis

Note: WACC denotes weighted average cost of capital. Results refer solely to the disposable razor products subcategory.

In order to assess the coordinated effects of the acquisitions, we evaluated whether they changed the estimated critical thresholds. To do so, we repeated the procedure for the post-partial acquisition ownership structures of the industry (after 20 December 1989, and after 22 March 1993).

As illustrated in Table 2, the results reveal that (partial or full) acquisitions tend to decrease both the benefit from coordination and the gain from deviation. For acquiring firms, the latter dominates the former, yielding a slight decrease in the discount factor’s critical threshold. For the remaining firms, the opposite occurs, yielding a slight increase in the critical discount factor. The results suggest that American Safety Razor remains the industry’s maverick firm, although its incentive to undermine coordinated behaviour decreases slightly. This is consistent with Davis and Huse (2010)’s findings for mergers that, ceteris paribus, the incentives to collude often fall as a result of an acquisition.

Table 2. Post-partial acquisition analysis

Note: G denotes Gillette, WL denotes Warner-Lambert, and WS denotes Wilkinson Sword. Results refer solely to the disposable razor products subcategory.


Brito D, R Ribeiro and H Vasconcelos (2013a), “Measuring Unilateral Effects in Partial Acquisitions”, CEPR Discussion Paper No. 9354.

Brito D, R Ribeiro and H Vasconcelos (2013b), “Quantifying the Coordinated Effects in Partial Horizontal Acquisitions”, CEPR Discussion Paper No. 9536.

Davis, P (2006), “Coordinated Effects Merger Simulation with Linear Demands”, mimeo.

Davis, P, and C Huse (2010), “Estimating the ‘Coordinated Effects’ of Mergers”, mimeo.

Friedman, J W (1971), “A Non-cooperative Equilibrium for Supergames”, Review of Economic Studies 38: 1–12.

Gilo D, Y Moshe and Y Spiegel (2006), “Partial Cross Ownership and Tacit Collusion”, RAND Journal of Economics 37: 81–99.

Lerner, J, A Leamon, and F Hardymon (2012), Venture Capital, Private Equity, and the Financing of Entrepreneurship, New York: Wiley.

O’Brien, D P and S C Salop (2000), “Competitive Effects of Partial Ownership: Financial Interest and Corporate Control”, Antitrust Law Journal 67: 559–614.

Preqin (2013), “Private Equity-Backed Buyout Deal Flow in North America Reaches Post-Lehman High in 2012”, press release retrieved from https://www.preqin.com/docs/press/Buyout_Q4_2012.pdf.

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