Antitrust Enforcement in Private Equity: Target, Bidder, and Club Sizes Should Matter

Jon Fougner

JD Candidate, Yale Law School Class of 2014

This Comment argues that plaintiffs have painted “club deals” with a broad brush as anticompetitive, whereas applying the facts alleged plaintiffs themselves to the antitrust regulators’ measurement of market concentration—the Herfindahl-Hirschman Index—implies a more nuanced conclusion: consortium bidding can be pro-competitive for large targets, small bidders and small clubs.

“We will have to trust [K]inder and the honor among thieves.”

– Goldman Sachs internal e-mail expressing hope that Rich Kinder, CEO of buyout target Kinder Morgan, would honor an exclusivity agreement with Goldman, despite the rejection of the agreement by Kinder Morgan’s special committee1

“It is hard to imagine Henry R. Kravis, co-founder of Kohlberg Kravis, calling up David M. Rubenstein, co-founder of Carlyle, to scheme about how to keep a lid on the bidding for a particular company.”

– Andrew Ross Sorkin2

Introduction

In October 2006, The Wall Street Journal reported that the Antitrust Division of the Department of Justice was investigating whether the largest private equity (PE) firms had colluded to keep buyout prices down.3 A class action against 13 PE firms, also known as “financial sponsors,” followed in December 2007.4 Although the DOJ has backed off,5 the private plaintiffs are pressing forward. The suit alleges that the defendants’ bid-rigging and market-allocating in 17 leveraged-buyouts (LBOs) from 2003 to 2007 deprived shareholders in the target companies of competitive prices, in violation of Section 1 of the Sherman Act.6 The district court has winnowed the claims7 and defendants,8 but most of the largest names in private equity—including Blackstone, Carlyle, Goldman Sachs, KKR, and TPG—remain in court.

This Comment proceeds in three parts to analyze whether the facts alleged in the plaintiffs’ Fifth Amended Complaint (the “Complaint”) state a claim for relief under the quantitative framework set forth by the DOJ and Federal Trade Commission (FTC). While the Complaint is careless with respect to the underlying financial concepts,9 it nevertheless states a claim that should survive a motion to dismiss under the federal pleading standards established by Twombly10 and Iqbal.11

Part I of this Comment shows how the Horizontal Merger Guidelines (HMGs), which focus on behavior by sellers rather than buyers, nevertheless apply to this suit. Measuring the Herfindahl-Hirschman Index (HHI) of market concentration as instructed by the HMGs, Part II models the competitive effects of “club” formation in each of the deals challenged by the lawsuit, concluding that consortia bidding can reduce market concentration for large targets, small bidders and small clubs. Part III concludes with suggestions for further research.

I. The Horizontal Merger Guidelines Apply Literally and by Analogy

The DOJ and FTC, the federal antitrust regulators, have jointly published guidelines apprising regulated parties of how the agencies model the competitive effects of horizontal mergers.12 These guidelines also inform the agencies’ analysis of non-merger horizontal collusion, such as that alleged in the Complaint.13 The HMGs primarily address competition among sellers, not buyers.14 However, the HMGs state that market power of buyers—monopsony—“has adverse effects comparable to enhancement of market power by sellers.”15 Thus, the agencies use “an analogous framework” to analyze competitive effects of buying power.16 Accordingly, the DOJ is tasked with analyzing whether club deals resulted in buyer market power that reduced head-to-head competition for target companies.17 Taking the facts alleged in the Complaint as true, they sometimes did. TPG Founder David Bonderman admitted that “[consortia] . . . limit[] bidding” so that “[there’s] less competition for the biggest deals.”18

In particular, the HMGs instruct the DOJ to interview sellers19 (here, the target companies) about the impact of the anticompetitive behavior. Here, this may be unnecessary, as the DOJ already has comparable, but even more probative evidence in several of the deals: contemporaneous instructions by managers, directors and advisers of the target companies not to bid in groups. For example, in the auction for Philips / NXP, the target directed Bain Capital, KKR and Silver Lake not to combine into a single consortium, but those bidders allegedly defied the instructions in a secret agreement.20 Contemporaneous records such as these accomplish the same investigatory purpose as ex post interviews.

Further, the HMGs emphasize the importance of the definition of the relevant market. “Market definition focuses solely on demand substitution factors, i.e., on customers’ ability and willingness to substitute away from one product to another in response to a price increase.”21 Antitrust defendants routinely argue that customers can switch to imperfect substitutes—that is, the defendants control only a small fraction of the relevant market. Thus, the defendant PE funds in Dahl might argue that other types of investors—such as mutual, index, and hedge funds—are part of their market. Because those non-control investors22 lack the two key tools of PE buyers—operational control and capital structure replacement23—they cannot and do not pay comparable prices. In particular, the difference between the price paid for stock by non-control investors and that paid by PE buyers on average exceeds 5%, the threshold set by the agencies to trigger competition concerns.24

Thus, under the qualitative guidance set forth by the antitrust agencies and the Supreme Court, the plaintiffs in Dahl have stated a claim for relief sufficient to survive a motion to dismiss. The next part maps the quantitative guidance set forth by the HMGs onto each LBO attacked by the Complaint, revealing that, according to the agencies’ own definition of market concentration, club bidding increases competitiveness of large LBOs when individual bidders are too small to bid alone.

II. HHI Analysis in the Club Deal Context Turns on Target Size, Bidder Size and Club Size

A. Model Specification

The heart of the HMGs is an instruction to the agencies to quantify the impact of mergers via the Herfindahl-Hirschman Index (HHI). A tool created by and for the use of the agencies, the HHI also applies in private antitrust suits.25 It is a measure of market concentration calculated by summing the squares of the market shares (expressed in percentage points) of all firms in the market.26 The agencies define un-concentrated markets as having an HHI below 1,500, moderately concentrated markets as having an HHI between 1,500 and 2,500, and highly concentrated markets as having an HHI above 2,500.27 Mergers that increase concentration concern the antitrust agencies. Both the measured size of the market and the size of its biggest players have powerful effects on the HHI.

I use the HHI rubric to analyze clubbing by modeling club formation as the merger—for purposes of whichever target the particular club is eying—of the club’s members. This is a natural application of HHI both because (like merged funds) cooperating funds cease competitively bidding with one another and because (like merged funds) cooperating funds can pool their capital. Allowing clubs has two effects on HHI, the sign of the net effect of which is ambiguous. First and more obviously, allowing clubs increases the size of the biggest players, thereby increasing HHI. Second and less obviously—and indeed ignored by the plaintiffs in Dahl—allowing clubs may bring new players into the market, increasing its size and decreasing HHI. “For example, in a corporate auction involving numerous well-heeled bidders, less wealthy bidders cannot compete. By joining forces, and thus combining resources, poorer contestants can gain access to the contest, thus increasing competition.”28 The following analysis estimates which effect dominates and provides a framework for modelers using different financial assumptions—for instance, different assumptions about leverage ratio or fund diversification requirements—to do the same.

The model estimates the PE fundraising by every fund named in the Complaint for the five-year period ended on December 31, 200729 (the last year of the “Conspiratorial Era” alleged by the Complaint30). It models 100% of those funds as available for the buyouts attacked in the Complaint.31 It makes 15% of the equity capital32 of a given sponsor available to any given deal.33 From these parameters, it computes the maximum equity check that any given fund could write.

To calculate the required total equity for each target, the model takes the deal size34 from the Complaint and applies 3:1 debt-to-equity leverage.35

For each LBO, the model calculates the ‘pre-club’ HHI—i.e., the HHI of the market for that target36 under a regulatory regime where clubbing does not exist. It defines the market as every fund that (1) was either ultimately part of the purchasing consortium or was identified in the Complaint as “participating” or “interested” in the auction process, and (2) could write the entire equity check itself. The market size is the sum of the maximum equity checks of all funds satisfying both criteria.37

The model then calculates the ‘post-club’ HHI—i.e., the HHI of the market for that target under a regulatory regime where clubbing is permitted. It defines the market to include the winning club and every losing fund that (1) is identified in the Complaint as “participating” or “interested” in the auction process, and (2) could write the entire equity check itself. Intuitively, relative to the pre-club analysis, by relaxing the constraint for winning bidders that the bidder be able to afford the entire equity check on its own, the model captures the expansion of the market facilitated by resource-pooling.38 The market size is the sum of the maximum equity check of the club and that of all losing funds in the market.

Finally, the model checks whether the HHIs trip any of the three red flags raised by the HMGs. Those are, in order of increasing concern: (1) an HHI increase over 100 resulting in moderate concentration (“100+” in Table A); (2) an HHI increase between 100 and 200 resulting in high concentration (“100-200” in Table A); and (3) an HHI increase over 200 resulting in high concentration (“200+” in Table A).39

B. Results and Analysis

Table A: HHI Effects of Club Formation in LBOs Challenged in Dahl [Note: Table A has been omitted from the online version. Please refer to the PDF.]

Table A summarizes the results of the model. Under the HHI framework, and accepting the factual allegations in the Complaint as true, the DOJ would likely find the majority of the challenged LBOs to be concerning. Of the 21 LBOs analyzed, 3 trip the least serious red flag, 0 trip the moderately serious red flag, 15 trip the most serious red flag (sometimes by thousands of points), and only 3 trip no red flags at all. This result is intuitive because the accused clubs were often large—larger than would be needed to bring funds into the market, and the fund sizes peaked around the time of the Conspiratorial Era.40

As Table A shows, however, five of the 14 deals tripping the most serious red flag—HCA, Kinder Morgan, Clear Channel, TXU, and Alltel (the five biggest challenged deals)—had, according to the facts alleged by the plaintiffs, no pre-club market. There was no pre-merger market because no sponsor could afford the equity check on its own. Thus, allowing consortium bidding for these large targets did not increase market concentration and should not be viewed as tripping any HHI red flag.41

The deals that did have pre-club markets but nevertheless triggered no red flag—AMC, Harrah’s, and Sabre—exemplify circumstances where the agencies would be well-advised to stay their hand. In AMC, the winning club represented only 10% of the un-concentrated market (2 of the 10 interested firms42). Harrah’s was a highly concentrated market, but the required check was big enough that allowing consortia brought a player into the market, thereby reducing concentration. In addition, the winning club represented just 38% of the buying power in that market (2 of the 8 interested firms43). Sabre, too, was won by a club of just 2 firms (of the 10 total that were allegedly interested44), representing 18% of the market. In fact, in two of these three deals, the post-club market was less concentrated than the pre-club market. Intuitively, when clubs are small, the net effect of allowing them may be pro-competitive—even for fairly small targets.

III. Conclusion

The model and its results show that antitrust regulators (and courts) ought to consider the size of targets, funds and clubs in analyzing whether consortium bidding is anti-competitive in any given instance. In general, targets that are large relative to the funds bidding on them justify formation of clubs—especially small clubs. One size does not fit all.

Nor does one size fit all in modeling these LBOs. Additional precision could be achieved by applying deal-specific leverage ratios based on empirical data from deal databases. The across-the-board assumption of a maximum equity check size of 15% of any given fund could similarly be improved by sponsor-specific estimates based on empirical data on the accused funds—and other funds run by the same sponsors but outside the Conspiratorial Era. At the theoretical level, one could model the plaintiffs’ and/or defendants’ potential objections—some of which are outlined above45—to the underlying mechanics of the model proposed herein.

Further research should analyze the natural experiment furnished by the inception of the DOJ investigation and cessation of the club era: did post-2007 premiums rise back to pre-2003 levels? The experiment is unfortunately clouded by the collapse of the debt bubble in 2008; the narrow window of roughly spring 2007 to summer 2008 may offer the most probative data.

Also unaddressed by this Comment is the qualitative policy question is what sort of reciprocity amounts to an agreement in restraint of trade. For example, it has been shown that a winning strategy in repeated Prisoner’s Dilemma is tit-for-tat.46 If all players follow tit-for-tat, they will always cooperate, despite never having an agreement to do so. Were the defendants in Dahl just playing tit-for-tat, or were they explicitly colluding? Twombly would suggest that a bare allegation of the former, without more, does not an antitrust claim make. The Complaint seizes upon the quid pro quos exchanged by the defendants,47 but merely offering to include a third party in a project because the third party previously involved you is not necessary anticompetitive, even though it is a tit-for-tat. The better question is whether the quid pro quos entailed not competing—for instance, bidding low, bidding with the intent to withdraw, or not bidding at all.48

  1. Fifth Amended Complaint at 133-34 & n.399, Dahl v. Bain Capital Partners, LLC, No. 1:07-cv-12388-EFH (D. Mass. filed Oct. 10, 2012) [hereinafter Complaint].
  2. Andrew Ross Sorkin, Colluding or Not, Private Equity Firms Are Shaken, N.Y. Times (Oct. 22, 2006).
  3. Dennis K. Berman & Henny Sender, Private-Equity Firms Face Anticompetitive Probe, Wall St. J. (Oct. 10, 2006).
  4. Complaint, Davidson v. Bain Capital Partners, LLC, No. 1:07-cv-12388-EFH (D. Mass. filed Dec. 28, 2007).
  5. White & Case, A Recent Court Decision Revives Concern That Some Club Deals Could Violate the Antitrust Laws 1 (2009).
  6. 15 U.S.C. § 1 (2006) (“Every contract, combination in the form of trust or otherwise, or conspiracy, in restraint of trade or commerce among the several States, or with foreign nations, is declared to be illegal.”); see Complaint, supra note 2, at 1, 7-12.
  7. Dahl v. Bain Capital Partners, LLC, No. 1:07-cv-12388-EFH, 2013 WL 950992, at *15 (D. Mass. Mar. 13, 2013) (narrowing the plaintiffs’ theory to a conspiracy among the defendants to refrain from “jumping,” i.e., outbidding, each other’s announced deals).
  8. Dahl v. Bain Capital Partners, LLC, No. 1:07-cv-12388-EFH, 2013 WL 4606512 (D. Mass. Aug. 29, 2013) (dismissing THL); Dahl v. Bain Capital Partners, LLC, No. 1:07-cv-12388-EFH, 2013 WL 3802433, at *10 (D. Mass. July 18, 2013) (dismissing Apollo and Providence).
  9. See, e.g., Complaint, supra note 2, at 52 (alleging, for example, that the gain extracted by a financial sponsor in a dividend recapitalization would, in the absence of the LBO, have flowed to the shareholders, without making any showing of how the shareholders would have extracted such a gain from lenders or alternative sources).
  10. Bell Atl. Corp. v. Twombly, 550 U.S. 544, 570 (2007) (when plaintiffs “have not nudged their claims across the line from conceivable to plausible, their complaint must be dismissed.”). While Twombly has come to stand trans-substantively for a heightened pleading standard, it has particular applicability in the antitrust context: the Supreme Court held that the parallel failure by companies to enter each other’s lucrative markets, without more, did not state an antitrust claim sufficient to survive a motion to dismiss. Id. at 548-50.

    Unlike in Twombly, the Complaint in Dahl cites documentary evidence of several alleged agreements, or attempts to form agreements, by the defendants. See, e.g., Complaint, supra note 2, at 23 (e-mail from Blackstone President Tony James to KKR Founder George Roberts stating “[w]e would much rather work with you guys than against you. Together we can be unstoppable but in opposition we can cost each other a lot of money.”); id. at 27 (“KKR has agreed not to jump our deal since no one in private equity ever jumps an announced deal.”); id. at 28 (alleging coordination of bids amongst supposed competitors); id. at 142 (alleging that KKR dropped out of the Freescale auction in exchange for Blackstone’s dropping out of the HCA auction). But see Dahl, 2013 WL 950992, at *14-15 (narrowing the plaintiffs’ theory to jumping and holding that mere quid-pro-quos, without more, do not evidence an antitrust conspiracy); Jessica Jackson, Much Ado About Nothing? The Antitrust Implications of Private Equity Club Deals, 60 Fla. L. Rev. 697, 708-10 (2008) (listing shallow pockets, diversification requirements, debt fundraising, and shared expertise as reasons for consortium bidding).

  11. Ashcroft v. Iqbal, 556 U.S. 662, 679 (2009) (“[W]here the well-pleaded facts do not permit the court to infer more than the mere possibility of misconduct, the complaint has alleged—but it has not ‘show[n]’—‘that the pleader is entitled to relief.’” (second alteration in original) (quoting Fed. R. Civ. P. 8(a)(2))).
  12. U.S. Dep’t of Justice & Fed. Trade Comm’n, Horizontal Merger Guidelines (2010) [hereinafter HMGs].
  13. Complaint, supra note 2, at 15-16. See also Fed. Trade Comm’n & U.S. Dep’t of Justice, Antitrust Guidelines for Collaborations Among Competitors 5 (2000) (“The Agencies treat a competitor collaboration as a horizontal merger in a relevant market and analyze the collaboration pursuant to the Horizontal Merger Guidelines if appropriate, which ordinarily is when: (a) the participants are competitors in that relevant market; (b) the formation of the collaboration involves an efficiency-enhancing integration of economic activity in the relevant market; (c) the integration eliminates all competition among the participants in the relevant market; and (d) the collaboration does not terminate within a sufficiently limited period by its own specific and express terms.” (footnote omitted)); Jackson, supra note 11, at 712-14 (arguing for the applicability of the collaboration guidelines to Dahl and predicting that the clubs would be treated as joint ventures).
  14. See HMGs, supra note 13, at 2.
  15. Id.
  16. Id.
  17. Id. at 3.
  18. Complaint, supra note 2, at 3.
  19. HMGs, supra note 13, at 4. The HMGs, however, warn that seller interviews may suffer from defects of honesty and accuracy.
  20. Complaint, supra note 2, at 149.
  21. HMGs, supra note 13, at 7-8.
  22. Mutual funds and hedge funds generally do not own a large enough stake in a firm to control it. The summer of 2013, however, witnessed the rising power of activist hedge funds, winning board elections and concessions from management despite owning less than 20% of the firm. See, e.g., Health Management Associates, Inc., Current Report 2-3 (Form 8-K Aug. 12, 2013) (documenting written consent by sufficient shareholders to remove and replace all members of the HMA board of directors with hedge fund Glenview’s slate); Health Management Associates, Inc., Schedule 13D at 2-4 (Aug. 16, 2013) (documenting Glenview’s mere 15% stake in HMA).
  23. Defendant PE funds would also argue that strategic buyers should be considered part of the market. Strategic buyers can use operational control and capital structure replacement and do pay premiums, so they likely should be included in the market. See Complaint, supra note 2, at 196-98 (showing that strategic buyers paid premiums averaging 22%, compared to 16% for sole-sponsor LBOs and 8% for club deals).
  24. HMGs, supra note 13, at 9.
  25. E.g., Rothery Storage & Van Co. v. Atlas Van Lines, Inc., 792 F.2d 210, 219-20 (D.C. Cir. 1986).
  26. HMGs, supra note 13, at 18 & n.9. For instance, a one-firm market has an HHI of 10,000 (100 squared). A two-firm market split equally by the two firms has an HHI of 5,000 (50 squared plus 50 squared). A 100-firm market split equally by the 100 firms has an HHI of 100. A higher HHI implies greater market concentration. Like an least-squares regression, the HHI is particularly susceptible to large outliers—such as a club consisting of all or most of the biggest firms in the market.
  27. Id. at 19.
  28. Pa. Ave. Funds v. Borey, 569 F. Supp. 2d 1126, 1133 (W.D. Wash. 2008); accord In re Toys “R” Us, Inc. S’holder Litig., 877 A.2d 975, 1009 (Del. Ch. 2005) (“The ‘cooperative’ bid that First Boston permitted the KKR Group to make gave the Company a powerful bidding competitor to the Cerberus consortium . . . .”).
  29. For AlpInvest ($5.4 billion), Apax ($18.9 billion), Apollo ($13.9 billion), Bain ($17.3 billion), Blackstone ($28.4 billion), Carlyle ($32.5 billion), Cerberus ($6.1 billion), Goldman Sachs ($31.0 billion), Hellman & Friedman ($12.0 billion), KKR ($31.1 billion), Lehman Brothers ($8.5 billion), Leonard Green ($7.2 billion), Madison Dearborn ($6.5 billion), Permira ($21.5 billion), Providence ($16.4 billion), T.H. Lee ($7.5 billion), TPG ($23.5 billion), Silver Lake ($11.0 billion), and Warburg Pincus ($13.3 billion), I take the corresponding five-year total directly from Private Equity International, PEI 50 (2007). PEI 50 does not list the other sponsors or strategic buyers involved in the challenged LBOs, so as a rough proxy, their corresponding total is estimated to be equal to that of the lowest (50th) fund on the list: $3.9bn.
  30. Complaint, supra note 2, at 1.
  31. This estimate could be somewhat below or above the true figure. It could be too low because a fund’s life may be greater than five years (a common lifespan is ten years, of which, roughly five is focused on deploying capital and roughly five is focused on returning capital); a fund that closed six years ago would be incorrectly excluded from the estimate. See Steven N. Kaplan & Per Stromberg, Leveraged Buyouts and Private Equity, 23 J. Econ. Perspectives 121, 123 (2009). On the other hand, it could be too high because some sponsors—such as Carlyle—are “supermarkets” offering a variety of funds, each targeting a different geography (some outside of North America, the location of the challenged LBOs). See Gregory Zuckerman & Ryan Dezember, Carlyle’s 3 Founders Share $400 Million-Plus Payday, Wall St. J., Jan. 12, 2012 (“Carlyle has launched many more smaller buyout funds than rivals, sometimes with a narrow focus . . . .”).
  32. Equity capital is cash from the sponsor itself and its limited partners representing ownership in the fund’s portfolio companies. Acquisition financing that is not equity capital is debt: money borrowed from banks, bondholders or non-traditional lenders that generates the “leverage” in “leveraged buyout.”
  33. Buyout funds invest in a handful of companies each, so it would be incorrect to assume that an entire fund’s equity, or even the majority of it, were in the market for a given deal merely because that fund’s sponsor was a bidder. See, e.g., David Snow, Private Equity: A Brief Overview 7, PEI Media (2007) (“For example, a firm that says it specialises in doing deals that require between $25 million and $100 million in equity per deal may target $750 million for a fund to complete roughly 7 to 10 deals before needing to go back to investors for more capital.”).
  34. See Complaint, supra note 2, at 59 (PanAmSat); id. at 63 (AMC); id. at 66 (Loews); id. at 72 (Toys “R” Us); id. at 78 (SunGard); id. at 84 (Neiman Marcus); id. at 93 (Texas Genco); id. at 103 (Education Management); id. at 113 (Univision); id. at 120 (Michaels Stores); id. at 127 (HCA); id. at 134 (Aramark); id. at 142 (Kinder Morgan); id. at 150 (Freescale Semiconductor); id. at 156 (Philips Semiconductor / NXP); id. at 163 (Harrah’s); id. at 170 (Clear Channel); id. at 176 (Sabre); id. at 184 (Biomet); id. at 190 (TXU); id. at 199 (Alltel). Excluded are Nalco (data not provided), Cablecom (data not provided), Warner Music (data not provided), Susquehanna (data not provided), Vivendi (deal not consummated), and Community Health Systems (deal not consummated).
  35. That is, 25% of the purchase price is modeled as equity. While the leverage ratios varied from deal to deal, 75% debt for mega-buyouts during the 2003 – 2007 boom era is a reasonable approximation. See Kaplan & Stromberg, supra note 31, at 124 (“The buyout is typically ?nanced with 60 to 90 percent debt . . . .”). But see Ulf Axelson et al., Borrow Cheap, Buy High?: The Determinants of Leverage and Pricing in Buyouts 44 (Nat’l Bureau of Econ. Research, Working Paper No. 15952, 2010) (calculating the debt-to-enterprise-value ratio of public-to-private LBOs during the era of the transactions challenged in Dahl as averaging between 0.65 and 0.68, i.e., 2:1 debt-to-equity leverage).
  36. A separate criticism of the antitrust accusations, not explored here, is that it may not even make sense to characterize a single target as a market.
  37. For instance, suppose only one fund is interested in the target, and that that fund has $10 billion in committed equity capital. The model estimates 15%, or $1.5 billion, of the equity as available for the target.

    Now suppose the total enterprise value of the target is $8 billion. At the modeled 3:1 debt-to-equity ratio, the equity check for the LBO would be $2 billion. Since that exceeds the would-be bidder’s available equity ($1.5 billion), the fund is out of the market and the market size is $0.

    On the other hand, suppose the total enterprise value of the target is $4 billion. At the modeled 3:1 debt-to-equity ratio, the equity check for the LBO would be $1 billion. Since that does not exceed the would-be bidder’s available equity, the fund is in the market and the market size is $1.5 billion.

    Note that it is irrelevant that the market modeled is the market for equity rather than the market for total enterprise value. Intuitively, because HHI is computed from market shares (percentages) rather than absolute dollar values, it doesn’t matter where in this arithmetic the leverage is introduced.

  38. For instance, suppose a $10 billion fund and a $20 billon fund are interested in the target. The model estimates 15%, or $1.5 billion of the former fund and $3 billion of the latter fund, as available for the target. Suppose the total enterprise value of the target is $8 billion. At the modeled 3:1 debt-to-equity ratio, the equity check for the LBO would be $2 billion.

    Under a regime where clubbing is forbidden, the $10 billion fund is out of the market, so only the $20 billion fund is in. The market size is $3 billion.

    On the other hand, under a regime where clubbing is permitted, both funds are in the market. The market size is $4.5 billion.

  39. HMGs, supra note 13, at 19.
  40. The Dahl defendants would argue that the HHIs are inflated (and red flags exaggerated) by excluding from the market PE funds merely because the Complaint failed to identify those funds as interested in a given target. The defendants might also argue that the post-club HHI should use a market size including funds too small to bid alone but able to bid as clubs, even if they did not happen to be members of the winning consortium. To be sure, the defendants should be permitted to make such showings. At the motion-to-dismiss stage, however, the facts of a well-pleaded complaint are treated as true. Ashcroft v. Iqbal, 556 U.S. 662, 664 (2009).
  41. Arithmetically, this result also flows from the HHI formula itself if the pre-club HHI is interpreted as “undefined” rather than zero.
  42. Complaint, supra note 2, at 63.
  43. Id. at 163-64.
  44. Id. at 176-77.
  45. E.g., supra note 41.
  46. Robert Axelrod, The Evolution of Cooperation (1984) (describing tit-for-tat as a strategy by which you cooperate on turn n if and only if your opponent cooperated on turn n – 1); see also Berman & Sender, supra note 3 (quoting Harvard Business School Professor Josh Lerner as characterizing PE bidding as a repeat game).
  47. E.g., Complaint, supra note 2, at 72-73 (Goldman tells Silver Lake that Goldman has, in exchange for Silver Lake’s letting it into SunGard, a “quid pro quo obligation.” (emphasis added)).
  48. See, e.g., id. at 46 (alleging that Blackstone promised future deals to other bidders in exchange for dropping out).