Shorting Your Rivals: Negative Ownership As an Antitrust Remedy

The merger of rivals often raises the concern that lost competition will result in higher prices or other harms. In anticipation of a government antitrust lawsuit seeking to block such a deal, the merging parties typically offer a solution that avoids the anticipated anticompetitive effects. The goal is to restore competition to the level that would exist absent the merger. 1 A standard regulatory response is divestiture: to require merging firms, as a condition of merger approval, to sell assets within the areas of competitive overlap. 2 For example, suppose that two grocery chains propose to merge, and that competition is highly localized. The parties might offer to sell every store of firm 2 that is located within two miles of a store of firm 1. The animating idea is to eliminate the competitive concern-or at least to reduce it enough to discourage the government's suit-without also destroying any procompetitive rationale for the deal. 3 Divestiture is not the only merger remedy, 4 but the attempted because there is no workable divestiture strategy. As a consequence, potentially important efficiencies are never achieved. In still other mergers, antitrust authorities have chosen to accept the bitter (some upward price pressure) alongside the sweet (procompetitive benefits) and allow potentially harmful mergers to proceed. In all of these instances we ought to prefer an alternative that achieves the potential efficiency benefits with less public harm.

In this article, we propose the use of an alternative remedy: for the merged firm to take negative ownership positions in its remaining rivals. The simplest form of negative ownership is for the firm to take a short position. For example, as a condition for JetBlue's merger with Spirit, the combined firm might be obliged to take a short position in American, United, and Delta Airlines. 10 The negative ownership remedy does not require taking a short position. As we explain, there are various ways to implement the remedy. For example, the managers of a merged JetBlue/Spirit might have been required, as a precondition of merger approval, to be paid under a new compensation scheme keyed to the merged firm's performance relative to that of its major rivals. Negative ownership can alternatively be implemented through the sale of derivatives or bespoke contracts that have other attractive features, alongside serious implementation challenges, as we explore in greater detail below.

The negative ownership approach represents a different kind of divestiture. Instead of requiring merging firms to divest themselves of their interest in Regarding AT&T Inc.'s Abandonment of Its Proposed Acquisition of T-Mobile USA Inc. (Dec. 19, 2011), www.justice.gov/opa/pr/justice-department-issues-statements-regarding-att-incsabandonment-its-proposed-acquisition; Anthem, Inc ., 855 F.3d at 349 (affirming district court order blocking merger); Press Release, Fed. Trade Comm'n, Following Sysco's Abandonment of Proposed Merger with US Foods, FTC Closes Case (July 1, 2015), www.ftc.gov/news-events/ news/press-releases/2015/07/following-syscos-abandonment-proposed-merger-us-foods-ftccloses-case; Press Release, Fed. Trade Comm'n, After Staples and Office Depot Abandon Proposed Merger FTC Dismisses Case from Administrative Trial Process (May 19, 2016), www. ftc.gov/news-events/news/press-releases/2016/05/after-staples-office-depot-abandon-proposedmerger-ftc-dismisses-case-administrative-trial-process. But see United States v. US Airways Grp., Inc., 38 F. Supp. 3d 69 (D.D.C. 2014) (approving settlement of DOJ challenge to merger of US Airways and American Airlines, subject to various conditions, including divestiture of gates and slots at several airports). 10 The district court blocked the merger on concerns about unilateral effects-that is, the loss of head-to-head competition between the merging firms. The court did not credit the government's argument that the merger would also increase the risk of collusion, in part because JetBlue employees testified that "coordinating actions were against JetBlue policy." JetBlue Airways, 712 F. Supp. 3d at 142 n.38. However, coordinated effects were an important premise for the government's decision to challenge the merger, see Complaint ¶ 5, JetBlue Airways, 712 F. Supp. 3d 109 (No. 23-cv-10511), and collusion is well documented in the airline industry. See, e .g ., Gaurab Aryal et al., Coordinated Capacity Reductions and Public Communication in the Airline Industry, 89 Rev. Econ. Stud. 3055 (2022). Below, we consider how a negative ownership remedy may have assuaged the government's concerns about both unilateral and coordinated effects. overlapping assets, our proposal would require merging firms to divest themselves of what would otherwise be an economic interest in raising their profits in a manner that also increases the profits of their unmerged rivals. Instead of requiring long selling of certain assets, our proposal would require short selling of other assets.

Our approach produces both ex ante and ex post benefits. The ex post benefits are straightforward. The remedy increases the firm's prosocial incentives to compete. As a result, customers benefit from lower prices and other anticipated consequences from increased competition, including higher quality and more innovation. 11 This benefit is compared to the world without the remedy. In its basic implementation, the pre-merger incentive to compete is preserved; customers are placed in the same position as before the merger. We also analyze an alternative, more ambitious implementation in which the remedy results in lower prices compared to the pre-merger period. 12 The remedy increases the incentive to compete by altering the firm's profitmaximization decision. To see why, note that when JetBlue sets its price, it ordinarily trades the benefit of a higher price-higher profit per unit-against the lost sales to consumers who no longer buy the product at the higher price. If JetBlue merges with Spirit, some of JetBlue's lost sales from a higher price are recaptured by Spirit, making a higher price optimal. Now suppose that JetBlue, in addition to owning Spirit, has a short position in American Airlines. If JetBlue raises its price, not only does it profit from the increased sales that Spirit experiences as a result, but it loses from the increased sales that American receives as a result of JetBlue's higher price. (As American's profits increase, its stock price increases, which then results in losses for JetBlue due to its short position.) That new incentive offsets, in whole or in part, the anticompetitive tendency to raise prices. In the jargon of antitrust, the negative ownership position is a source of downward price pressure that offsets the upward price pressure arising from the merger.

The size of this effect can be calibrated by altering the size of the short position. As we show in the Appendix, it is feasible to fully counteract the upward price pressure with an offsetting downward pressure arising from the negative ownership remedy. If merging parties are required-or volunteer-to take a negative ownership position as a condition of merger clearance, they may achieve the procompetitive elements of the deal without the anticompetitive effect.

The ex ante benefits are more subtle but equally important. Signaling and screening benefits result from conditioning regulatory approval on the merged firm contractually committing to reduced profits if its unmerged rivals' stock prices increase. These benefits arise when the merging parties have private information about the likely impacts of the merger. 13 For example, the merging firms are likely to have private information about their true motivation for merging. Merging firms operating with a negative ownership position will be less profitable if the merger's hidden goal is to reduce competition than if the merger's goal is to enhance competition and should ceteris paribus be less motivated to seek merger approval. Indeed, regulators might even ask why the merging firms hadn't already taken short positions in their rivals before publicly announcing the merger. If the likely impact of the merger is to enhance market competition (say, by reducing costs), selling rivals short should have been a profitable strategy at the rivals' pre-merger stock price. 14 These benefits are illustrative of a more general point. The current approach of antitrust authorities fails to leverage the existence of contractible information in constructing preconditions for merger approval. To be contractible, the information does not need to exist or be known to the parties at the time of contracting. It just needs to be verifiable to a court if it comes to be later known by the contractors. 15 In the merger context, the antitrust authorities often will not be able to accurately predict the competitive impact of a merger. But the stock prices (as well as the prices of the products or services sold) of unmerged rivals will often be observable to the regulators and verifiable to courts. Ex post information that a rival's stock price had excess returns may be credible evidence that a merger failed to enhance competition.

Conditioning merger approval on negative ownership can also provide tailoring benefits for antitrust authorities. Instead of making the all-or-nothing decision to approve or oppose a merger, regulators can make more nuanced 13 For analyses of merger remedies as a signaling device, see Markus Dertwinkel-Kalt & Christian Wey, Structural Remedies as a Signaling Device, 35 Info. Econ. & Pol'y 1, 2 (2016); Andreea Cosnita-Langlais & Jean-Philippe Tropeano, Do Remedies Affect the Efficiency Defense? An Optimal Merger-Control Analysis, 30 Int'l J. Indus. Org. 58, 59, 61 (2012). 14 The stock price movement of rivals on the date a merger is announced can provide evidence, when properly analyzed, of the merger's likely competitive impact. See Robert H. Mc-Guckin, Fredrick R. Warren-Boulton & Peter Waldstein, The Use of Stock Market Returns in Antitrust Analysis of Mergers, 7 Rev. Indus. Org. 1 (1992). 15 For example, in a standard principal-agent game, the parties can contract on the size of output but not on the agent's effort (which is assumed to be unverifiable). See Deniz Kattwinkel & Jan Knoepfle, Costless Information and Costly Verification: A Case for Transparency, 131 J. Pol. Econ. 504, 505 (2023) (explaining that obtaining knowledge about an agent's "type" can be difficult). decisions. For example, consider the famous "Williamson tradeoff." 16 A merger that eliminates head-to-head competition or increases concentration may lead to less price competition, and thus a predicted price increase, while also giving rise to cost savings. 17 The tradeoff is that the merger results in deadweight loss-worse allocative efficiency-due to the price increase but also increased productive efficiency thanks to the cost savings.

Without the negative ownership tool, under the current consumer welfare standard used in most of the world, a regulator or court is forced to forgo the efficiency benefits whenever they are not large enough to reduce prices-even if the merger increases total welfare. Under a total welfare standard, the regulator or court should also forgo efficiency benefits unless the cost savings are so large that total surplus increases. In that event, the transaction would likely be allowed: the deadweight loss would be accepted in order to harvest the cost savings, and the merger could make consumers worse off.

The negative ownership remedy sidesteps this tradeoff. By mandating varying degrees of negative ownership, regulators can have the best of both worlds, approving mergers with synergies without also accepting less price competition. Indeed, as we show in the Appendix, in our stylized model, mergers with even arbitrarily small cost savings can be approved with sufficiently substantial countervailing requirements to hold short positions in unmerged rivals. This result applies beyond the Williamson tradeoff setting in which the merger results in a price increase. It also applies where the increased efficiency takes the form of marginal cost savings that are sufficiently large and passed through to a sufficient degree that any price increase is prevented. Even here, regulators can have the best of both worlds, approving mergers with synergies without also accepting the tradeoff of less price competition. The result is a merger with saved costs and lower prices.

The negative ownership tool also allows regulators to rely less on asset divestitures, which can themselves undermine the cost-saving synergies of business combinations. And this tool holds promise as a way to improve the net benefits of a merger even where effective divestiture is feasible, and it does not necessitate a trading off of cost-saving efficiencies.

As we explain, the negative ownership approach has application beyond horizontal mergers to a wide variety of contexts in which the concern is weak competition among rivals. 18 Consider, for example, cartels. After a cartel is uncovered, collusion often persists. A simple injunction to "stop colluding" is unlikely to be effective. Here, a negative ownership remedy can be used to restore the former cartelists' incentive to compete. More generally, our approach is of interest whenever rivalry is weakened in a manner that an injunction is unable to restore.

The negative ownership remedy compares favorably to alternative remedies, such as price caps and licensing, that are sometimes proposed yet rarely implemented. However, it is no panacea. As part of our analysis, we consider a variety of objections to and limitations of the approach. One potential concern is that a negative ownership position might induce merging firms to engage in predatory or exclusionary practices that will allow them to profit from a fall in their rivals' stock prices. This concern is elevated if negative ownership is deployed in a highly aggressive fashion.

The tradeoff between deterring collusion and inadvertently encouraging predation is a familiar issue in antitrust, with courts generally erring on the side of preventing collusion. Our basic remedy, however, is designed to maintain the pre-merger pricing incentive, not to sharpen it. Thus, the predation incentive should remain unchanged compared to the pre-merger status quo. In addition, because our remedy works best when there are at least a few remaining competitors, it is effective precisely when predation is least likely.

Moreover, we show that we can reduce predation concerns (where they arise), while maintaining competitive incentives, through our choice of implementation. In particular, by requiring the merging firm to write (i.e., sell) at-the-money call options, we provide the desired procompetitive incentive without allowing the merging firm to profit from declines in the rivals' firm value; unlike a short position, holding such contingent liabilities are costly if rivals become more profitable but generate no gain if the rival's profit falls. 19 Another obvious concern is that in some settings, the required negative ownership position is impractically large. Here and elsewhere, we stress that our remedy is likely to function more effectively in some industries and less well in others.

Our proposal builds on previous work that has noticed that requiring managers' compensation to be tied in part to the profits of their rivals can sharpen competitive instincts. The earliest mention we are aware of is a 1984 paper by David Donaldson and Hugh Leary, which makes the point in the context of government-owned firms. 20 The most developed existing treatment we know of is a 1996 paper by Carl Lundgren, which proposes managerial compensation based on relative performance as a means to curb collusion. 21 A 1998 paper by Ian Ayres and Stephen Ross makes a related proposal in the context of mergers. 22 Our contributions in this article are fourfold. First, we identify a broader set of benefits from a negative ownership remedy-in particular, signaling, tailoring, and compensating, in addition to a sharpened incentive to compete. Second, we offer new means of implementation with attractive properties-in particular, shorts, selling calls, and bespoke contracts, in addition to relativeperformance evaluation. Third, we broaden the contexts in which a negative ownership remedy might be applied-including as a post-cartel remedy. 23 Finally, we offer a more extensive account of possible objections to the remedy, particularly with respect to possible perverse incentives to engage in various forms of exclusionary behavior. This Article proceeds in three parts. Part I describes the proposal, connects it to related literature, and identifies alternative means of implementation. Part II applies our approach to mergers, cartels, and other competitive problems. Part III examines various complications and limitations that may arise. 2020), notes in the common-ownership context that if a fund is overweight in one firm and underweight in the firm's rivals, cares about its performance relative to other investors, and is able to alter the firm's decision-making, then it will induce the firm to compete more aggressively. Being underweight in the rivals is analogous to holding a negative ownership position. Our idea is also in a somewhat similar spirit to Jonathan Macey's suggestion that whistleblowers be allowed to profit by shorting the targeted companies rather than by receiving a fraction of the fines levied. See Jonathan Macey, Getting the Word Out About Fraud: A Theoretical Analysis of Whistleblowing and Insider Trading, 105 Mich. L. Rev. 1899, 1920 (2007). 23 See infra Part II.B (discussing post-cartel collusion, continued coordination after a monopoly breakup, common ownership, and joint ventures that pose anticompetitive concerns).

Here is a simple illustration of the negative ownership remedy, based on a highly stylized model of the JetBlue/Spirit merger that was challenged by the DOJ and blocked by a district court in early 2024. 24 Suppose that the merging firms compete within a market that contains four other firms: American, Delta, United, and Southwest. For simplicity, imagine each airline sells a single product at a single price.

Further suppose that the firms are identical. That is, they all have the same costs and customer appeal; their services are all equally competitive. The assumption of symmetry simplifies the analysis and illustrates the remedy most clearly but is not necessary for the remedy to work. In the Appendix, we analyze the asymmetric case. Each firm's profit is a function of its own price and the price of all its rivals. Thus, JetBlue's profit 1 π is a function of its own price 1 p , Spirit's price 2 p , and the prices of the four other firms. 25 Likewise, Spirit's profit 2 π is a function of its own price 2 p , JetBlue's price 1 p , and the prices of the four other firms. Since the firms are symmetric, in equilibrium each has the same pre-merger price, sales, and profits.

If JetBlue and Spirit merge, the combined firm will have the profit function 1 2 π π + . 26 In determining the profit-maximizing price for the first product, 1 p , the merged firm now considers the effect of 1 p on 2 π . 27 Sales and profits increase when the price of a substitute increases. Thus, increasing 1 p raises 2 π , which gives the combined firm an incentive to increase 1 p . Similarly, when determining the profit-maximizing price for the second product, 2 p , the merged firm has a new incentive to raise price given the positive effect on 1 π . The resulting increases in 1 p and 2 p would also likely lead to increased prices (and profit) for the other remaining firms in the market.

The negative ownership remedy works by counteracting these extra terms in the merged profit function. Suppose that as a condition of this merger, the merged firm is required to short 25% of the stock of each of the four other 24 See generally United States v . JetBlue Airways Corp ., 712 F. Supp. 3d 109 (D. Mass. 2024). 25 Each firm i has a profit function of the form ( , ) π p p i i i , where p i is the price of the firm's own product and - p i is the set of prices of its rivals. Since the firms are symmetric, it doesn't matter how we order the rivals, and they all charge the same price pre-merger. 26 Expressed as a function of the underlying prices, the combined firm's profit is: The addition of these negative terms in the merged firm's profit function causes it to behave, in setting the prices under its control ( 1 p and 2 p ), as though the merger never occurred, because the incentive to increase Spirit's profit is exactly offset by the incentive to decrease the profits of the four remaining rivals. 29 Thus, in choosing the profit-maximizing level of 1 p , the merged firm chooses the same level as JetBlue pre-merger. That is, it acts as though it were simply maximizing 1 π . Similarly, maximizing this profit function leads it to select the same level of 2 p as it would in maximizing 2 π , Spirit's pre-merger profit function. In light of the fact that 1 p and 2 p are at their pre-merger levels, the other firms' prices are unchanged as well.

The negative ownership remedy balances out the merged firm's incentive to increase the profit of its other product or service with an equal incentive to reduce the profits of its rival's products or services. The precise negative ownership remedy in this example relies on the fact that the profit functions are symmetric. 30 However, the special case of symmetry is just a simple example that is useful for explaining how the remedy works. In Part III and the Appendix, we explain that our analysis readily extends to asymmetries of various kinds.

The negative ownership remedy is strongly supported by the economic literature on cross-ownership. Cross-ownership arises when a firm has an ownership stake in its rival. A substantial economic literature focuses on how the cross-ownership alters a firm's incentive to compete. Such a stake weakens the firm's incentive to compete due to the effect on the other firm. For example, 28 The merged firm's profit function becomes: a price cut steals sales and increases profits at the expense of the rival, but the net effect is less positive due to the reduced value of the ownership stake in the rival. 32 Negative ownership is simply the opposite of cross-ownership-or, more precisely, a special case in which cross-ownership is negative rather than positive. Instead of weakening the incentive to compete, the negative ownership position strengthens the incentive. It does so in a manner that is precisely analogous to its operation in positive cross-ownership. If having a positive stake in a rival weakens competition, leading to anticompetitive effects, then a negative stake should do the opposite.

The connection to cross-ownership also provides insight into a theoretical ambiguity in the implementation of a negative ownership remedy. In the airline illustration in Part I.A, the focus was lost head-to-head competition between the merging firms, what is often termed "unilateral" effects. A further issue is how negative ownership might alter the ability of the remaining rivals to collude by means of dynamic oligopoly in a repeated game. This issue is relevant in considering so-called "coordinated" effects from a merger or as a remedy for certain forms of cartel-like collusive behavior. Here, the theoretical effects are more complex. 33 32 Cross-ownership has a further potential effect. The firm might also use its ownership to gain a measure of control over the competitor. That effect has no close analogue to the negative ownership proposal. 33 Negative ownership increases the incentive to compete by increasing the short-run payoff from undercutting rivals. At the same time, the punishment for cheating is also more severethe competitive equilibrium to which the colluders revert is more competitive. This latter effect discourages cheating, and as a matter of theory, it is unclear which effect is larger.

A similar theoretical ambiguity arises in cross-ownership. On the one hand, cross-ownership increases the incentive to collude because the short-run payoff from cheating and stealing business from its rival decreases when the firm shares in the rival's profits. On the other hand, the punishment for cheating is less severe: if collusion collapses, the fallback equilibrium is not so intensely competitive. In resolving the ambiguity, one potential source of evidence is the emerging empirical literature about common ownership. See, e .g ., Martin C. Schmalz, Recent Studies on Common Ownership, Firm Behavior, and Market Outcomes, 66 Antitrust Bull. 12 (2021); Hemphill & Kahan, supra note 22. As discussed immediately below, one understanding of common ownership is the inverse of our negative ownership remedy. Under this understanding, the firm is induced to maximize a weighted average of its own profits and competitor profits. Empirical evidence that common ownership enhances coordinated effects might suggest that the reduced benefit of cheating is more important than the reduced punishment, and in turn suggest that negative ownership suppresses coordinated effects.

The caveat "might" is necessary because the relevance of common ownership depends on a conception of its effects in which the firm places a positive weight on its rival's profits. This conception has a readily analogue to negative ownership. Other mechanisms of common ownership-for example, a common owner's facilitation of information sharing among the firms-have no ready analogue in negative ownership. To the extent that these other mechanisms may explain observed effects, empirical evidence about common ownership is not relevant for Negative ownership is also closely connected with so-called "common ownership." 34 A common owner is an investor that holds stakes in multiple, competing firms. Antitrust theorists have long argued that such an investor has interests that differ from-and indeed, conflict with-the interests of managers and other owners. Such a common owner might be able to induce a firm in which it holds a stake to further the interests of the common owner. As a consequence, the firm might be induced to compete less, to the benefit of the common owner's other holdings.

The posited effects of common ownership, in its most developed theoretical form, are an extension of cross-ownership. Instead of one firm directly holding a stake in a rival, an investor holds stakes in competing firms. The investor induces the firm to behave as though it had a passive ownership stake in the rival. This is directly reflected in economic models wherein, depending on its ownership structure, a firm in a noncompetitive industry maximizes a weighted average of its own and its competitors' profits. 35 Specifically, greater common ownership induces a firm to place a greater weight on competitor profits. 36 Recent empirical work finds that, consistent with the theory, increased level of common ownership is associated with anticompetitive effects. 37 Other papers find no effect. 38 Negative ownership has opposite effects to the posited effects of common ownership. 39 This is an unsurprising result, once it is recognized that common ownership, in its most developed formulation, is itself an extension of cross-ownership.

The conceptually simplest way to implement negative ownership is to take a short position in rivals. However, there is a menu of alternative means of implementation, each with distinctive strengths and limitations. In this section, we describe three: compensation based on relative performance, derivative contracts, and bespoke contracts between the merged firm and the antitrust authorities. 40

One option is to set executive compensation contracts in the merged firm to make use of relative-performance evaluation.

That is, even if the firm's profits are not directly tied to the profits of a rival, the payment to the managers who make the decisions could be. As long as the managers who make or control the pricing decisions have compensation that is appropriately decreasing in the profits or stock price of their rivals, they will have an incentive to keep prices low post-merger. 41 A large literature considers the economic effects of "pay for performance" and, in particular, relativeperformance evaluation. That literature supports the conclusion that this is a feasible tool for implementing a negative ownership remedy.

the merged firm takes a short position of z j in each remaining competitor j, the net MHHIΔ would be:

For example, in a symmetric four-to-three merger, which raises HHI by 1250, a short position of 50% of each of the two remaining rivals would bring the MHHIΔ back to zero. Each position would reduce MHHI by 50% x 50 x 25 = 625. We are not endorsing MHHI as the way to evaluate the competitive effects of the merger. Here we simply note how our approach can fit within that framework, enabling the assessment of negative ownership as a means to reduce the MHHIΔ arising from a merger. 40 Yet another possibility, useful in relatively narrow settings, is to take a long position in a customer or supplier. A long position in the stock of a customer (and possibly the customers of unmerged rivals) would lead the merged firm to experience a loss if the post-merger product price increases-thus reducing the incentives for unilateral and coordinated reductions in competition. A long position in a supplier might analogously reduce the incentive to engage in monopsonistic behavior, as driving down the price of the supplied product would reduce the value of the long position. Contracts which penalized merged firms for driving down the wages of their workers might also similarly disincentivize anticompetitive employer behavior. For further discussion of anticompetitive effects arising from the acquisition of monopsony power, see generally Suresh Naidu, Eric A. Posner & Glen Weyl, Antitrust Remedies for Labor Market Power, 132 Harv. L. Rev. 536 (2018). 41 Use of this type of relative performance evaluation may also be necessary to motivate managers. One of us previously showed that sometimes this may limit the anticompetitive effects of mergers even without government-imposed relative performance evaluation. See Abraham L. Wickelgren, Managerial Incentives and the Price Effects of Mergers, 53 J. Indus. Econ. 327, 347 (2005).

Relative-performance evaluation was first suggested in the corporate-governance literature as an effective tool to manage the risk-incentive tradeoff. 42 Because a firm's performance is not completely under the control of the manager, incentive-based compensation that depends on firm performance makes the manager's compensation riskier. If the manager is risk averse, the manager will require higher expected compensation in order to accept the risk. One way to reduce this risk while still maintaining incentives is to make the manager's pay not only positively related to own-firm performance but negatively related to the performance of other firms in the industry. This can filter out common shocks that affect the profits of all firms in the industry but whose effects do not reflect the quality of managerial performance. 43 This reduces the risk associated with incentive-based compensation, making it more desirable.

Relative-performance evaluation not only confers an incentive to increase firm profits but also creates an incentive to lower the profits of one's rivals. One way to do that is through more aggressive competition. 44 Managers have incentives to compete more aggressively (lower prices, higher output, more advertising) than the level that maximizes the firm's profit.

Thus, stronger relative-performance evaluation, just like a short position, can counter the reduced incentives that managers in imperfectly competitive markets have to compete. That is because the manager's pay is negatively correlated to rival profit even if the owner's payoff is not. 45 There is empirical support for the theoretical prediction that stronger relative-performance evaluation induces more aggressive competition. For example, Guojin Gong and coauthors find an inverse relationship between concentration and relative-performance-based compensation. 46 This suggests that owners avoid providing managers with an excessive incentive to compete-excessive from the standpoint of maximizing profits-in 42 Fin. 1999, 2008 (1999). 45 Wickelgren, supra note 41, at 328-29, notes that the need to motivate managers and the inability to perfectly contract on prices might sometimes attenuate the incentives of merged firms to raise prices. Relative performance evaluation as part of a merger settlement implements these results without relying on incomplete contracting. 46

Shorting Your Rivals concentrated industries. 47 An article by Christoph Feichter and coauthors provides even more compelling support. 48 They show that greater use of relative-performance evaluation directly correlates with measures of competitive aggressiveness. But, because one might be concerned that the use of relativeperformance evaluation is not exogenous, they also exploit a change in rivals' use of relative-performance evaluation. They find that when a rival adds the focal firm to its peer group for relative-performance evaluation, that focal firm competes more aggressively. Because the rival's decision to add the firm to its peer group is unlikely to depend on the desire to have the focal firm compete more, this variation is plausibly exogenous. Not only does this provide empirical support for the proposition that relative-performance evaluation induces managers to behave more competitively, it also directly shows that these effects extend to firm's rivals, which further strengthens competition in the market.

More recently, Matthew Bloomfield and coauthors examined the question from a different angle. They report evidence that firms in already established cartels use relative-performance evaluation more than those who are not. 49 They also report that firms accused of engaging in cartel behavior reduce the use of relative-performance evaluation after such behavior is challenged. More specifically, they find that a firm subject to a cartel enforcement action is much more likely to drop relative-performance evaluation for their executives. 50 This tendency increases as concentration increases.

The authors' interpretation of their results is that when a firm is in a cartel, the cartel prevents relative-performance evaluation from inducing intense competition. Once the cartel has been discovered, the fact that relative-performance evaluation induces more competitive behavior can reduce overall profitability, thus firms shy away from it. As for causality, the authors show that current cartel membership predicts future use, but not past use, of relative-performance evaluation. This supports the conclusion that cartel membership drives the use of relative-performance evaluation, rather than the other way around. Consistent with their interpretation, they find that among non-cartel firms, relativeperformance evaluation is associated with more aggressive product-market competition, but strikingly, this association does not hold for cartel firms. 51 The use of relative-performance compensation as a source of intensified competition is also supported by the common-ownership literature. This result is the flip side of the idea that managerial compensation is a means by which cross-ownership or common ownership results in reduced competition. For example, some commentators argue that common ownership causes firms to implement less-performance-sensitive forms of compensation, which in turn causes managers to compete less aggressively. 52 In one such model used by these commentators, incentive pay encourages the firm to invest in marginal-cost reductions, which increase the profits of the firm and, by reducing prices, lower the profits of the firm's competitors. This model gives rise to a prediction that under common ownership, managers will receive less performance-sensitive pay in order to blunt this competition. To the extent that the empirical evidence bears out this prediction, it suggests that performance pay does indeed have an effect on competition. 53

An alternative is to synthesize the negative ownership position by means of a derivative contract. In particular, the merged firm would sell at-the-money call options in its rival. The seller (writer) of a call option to buy stock is paid to take on a contingent liability requiring the writer to sell the stock at the option price if the option holder decides to exercise the option. This will occur if the underlying stock value rises above the exercise price. Thus, the writer of at-the-money calls has an incentive to prevent rivals' stock price from rising, because increased rival values would turn the short call position into a liability.

A natural place to set the exercise price is the pre-merger stock price of the rival. At this price, the merged firm would maintain its pre-merger pricing incentives. 54 One concern in implementing negative ownership by means of a derivative is that a rival's stock price might increase for a variety of systemic reasons not having to do with the degree of competition in the industry. One response is for the merged firm to implement the negative ownership position using a 52 See, e .g ., Antón et al., supra note 34, at 1297. 53 An absence of an observed effect would not necessarily suggest the opposite. Even if common ownership had no real-world effect on compensation mechanisms, it could still be true that compensation mechanisms have a real-world effect on competition. 54 The equivalence of synthetic stock can be proved with what financial economists refer to as "put-call parity." See Richard Brealey, Stewart Myers & Franklin Allen, Principles of Corporate Finance 549-50 (13th ed. 2020). Synthetics might also be produced via the Black-Scholes formula to maintain certain leveraged fractional interests in rivals' securities. See id . at 573-80.

Shorting Your Rivals so-called Margrabe option. 55 Such options have an exercise price that fluctuates with the value of some benchmark index (or security), rather than a fixed exercise price. Margrabe options respond to the concern that a rival's stock price might increase not because of decreased market competition, but simply because the stock market value has generally increased. An implementation with a Margrabe exercise price would only penalize the call writer if the rival's stock price exhibits abnormal returns relative to the stock market generally. 56

Another way to enhance the competitive incentives of the merged firm is with a bespoke contract that includes a liquidated damages provision payable to the firm's customers if rivals' stock prices exhibit abnormal returns after the merger. The customer effectively has a long position in the rivals' stock. A liquidated damages provision of this kind represents a kind of competition insurance. It can produce a similar incentive effect as our other implementations, but if the incentives fail to maintain competition at the pre-merger level, customers would be at least partially compensated for their loss of consumer surplus.

Our core implementation of selling rivals' stock short requires the merging firm to place an actuarially fair bet by taking a short position before the merger is publicly announced. The merging firm has the chance to gain or lose on its short position. Indeed, as suggested in the Introduction, the merging firms might even expect to profit from their short position as increased competition reduces their rivals' equity value. In contrast, implementing a negative position through a liquidated damages provision benefitting customers is uncompensated. Unlike short selling, it is a condition that can never benefit the merging firms (except by securing regulatory approval). 57 56 A requirement that the merging firm sell at-the-money Margrabe calls with an exercise price that varies with a broad market index can be implemented by a specialized auction or bespoke contracting. 57 Regulators might choose to trigger compensation only if there is some minimum level of abnormally positive returns to avoid "taxing" procompetitive mergers. Note that a competitively neutral merger can be expected to leave the returns of rivals unchanged; thus, an increase or decrease is equally likely. By contrast, a marginally procompetitive merger shifts the returns of rivals in a slightly negative direction, which leaves a substantial probability of positive abnormal returns. That said, the uncompensated aspect of bespoke liquidated damages may strengthen the screening benefits of negative ownership requirements because liquidated damage provisions will be more expensive in expectation than short selling for mergers that have more uncertain competitive impacts.

Antitrust Law Journal [Vol. 86 be viewed as an automated remedy for mergers that in retrospect should not have been approved. 58 Implementing consumer compensation in most cases will pose daunting challenges. Most generally, compensation might be not only to consumers who continued to purchase but pay higher post-merger prices, but also to consumers who have forgone purchasing because of the higher prices. 59 It will often be infeasible to identify consumers and how much they would have purchased in the absence of the post-merger price hike, much less determine how to distribute liquidated damages among the class. 60 Bespoke contracting offers certain advantages-including allowing regulators to condition merger approval on a portfolio of contractible proxies for the level of competition 61but except in rare instances, we imagine that negative ownership will be more feasibly implemented by other means.

The negative ownership remedy holds promise in a variety of settings. Our principal focus is horizontal mergers. In Part I, we presented an illustration drawn from the airline industry. Here, we offer several further examples, which also illustrate the complications that can arise. Sugar refining . In 2021, the DOJ sued to block a merger of two major sugar refiners, U.S. Sugar and Imperial Sugar, alleging that what it viewed as a threeto-two deal would raise prices, in part by enabling coordination between the merged firm and American Sugar, the other remaining refiner. 62 The merging 58 Mergers typically require the approval of the target board and a majority of target shareholders. See Matteo Gatti, Reconsidering the Merger Process: Approval Patterns, Timeline, and Shareholders' Roles, 69 Hastings L.J. 835, 843-47 (2018). But one might consider involving customers in the approval process. If the merger is truly expected to enhance net market competition, customers should not be opposed to the corporate combination. Indeed, one might notionally tie regulatory approval to conditions (including liquidated damages insurance) that were sufficient to secure support from a majority of consumers. 59 In terms of the classic antitrust overcharge graph, liquidated damages would ideally compensate for not only the rectangle of supracompetitive profits but also the triangle of deadweight loss. 60 Consumer compensation via bespoke contracts will also often be more difficult for consumer goods than for intermediate goods due to the larger number of consumers and cumbersome nature of class notification. 61 In the text, we focus on a liquated damages provision conditioned on rivals' stock price. Alternatives include the merged firm's stock price and the price and quantity of upstream inputs and downstream outputs. 62 See Press Release, U.S. Dep't of Just., Justice Department Sues to Block U.S. Sugar's Proposed Acquisition of Imperial Sugar (Nov. 23, 2021), www.justice.gov/opa/pr/ justice-department-sues-block-us-sugar-s-proposed-acquisition-imperial-sugar.

Shorting Your Rivals parties countered that the merger would benefit customers and the merging parties by enabling various synergies. 63 The district court rejected the DOJ's challenge, crediting competition from additional firms beyond American. 64 We take no position on the accuracy of these contending claims. However, it is certainly possible that both claims are true. For example, the transaction might reduce marginal costs, while also tending to raise price due to the removal from the market of an important competitor. It is unlikely that a divestiture could preserve the synergies while eliminating the anticompetitive effects.

In such a situation, where an effective divestiture is infeasible, a negative ownership solution offers the prospect of the best of both worlds. If the merged firm had a negative ownership position in American, this would help ensure that consumers obtain much of the benefit from any merger-induced cost reductions. Were U.S. Sugar to increase its price after the merger, it would now face two conflicting effects. The standard merger effect would make that price increase more profitable because U.S. Sugar no longer would lose profits when customers switched to buying Imperial Sugar. Meanwhile, the negative ownership position would have an opposite effect. Any sales that U.S. Sugar lost to American as a result of increasing prices now would cost U.S. Sugar both directly in terms of lost profits and indirectly in that the greater profits of American would make the short position less valuable. Such a solution might be more attractive to both the DOJ and the merging firms compared to the risk of a loss in court.

This example points out a significant potential complication. In our stylized airline example, the size of the negative ownership position needed to prevent a price rise is relatively small. By contrast, with only two sugar refiners remaining, the size of the negative ownership position must be larger. To see this, suppose for the moment that the merger results in no cost-reducing efficiencies and that there is only one competitor after the merger. If American is symmetrically situated to the merging parties, then for U.S. Sugar to have the same profit-maximizing price post-merger as it had pre-merger, it would need to be short the entire market capitalization of American.

Relaxing these restrictive assumptions improves the feasibility of the negative ownership remedy. First, if there are significant efficiencies, the size of 63 See Jeff Gelski, U .S . Sugar to Buy Imperial Sugar, Food Bus. News (Mar. 25, 2021), www. foodbusinessnews.net/articles/18240-us-sugar-to-buy-imperial-sugar ("[T]he move will create production, logistics and supply chain synergies and efficiencies that will benefit both companies and our customers . . . ."). 64 the required negative ownership position is much smaller. Note that this is the case of interest; if there are no such efficiencies, then the right course is likely to simply the block merger rather than seek a middle ground. The role of efficiencies in reducing the required position is further explained in Part III.

Second, to the extent that other firms beyond American would provide a competitive constraint for the merged firm, as the district court found, the required negative ownership position would be smaller. Third, to the extent that the merged firm is smaller as a fraction of total market capitalization, the required negative ownership position (as a percentage of the other firms' capitalization) is smaller. 65 Finally, and as also discussed in Part III, implementation of a large position is likely easier if it takes the form of relative-performance-based compensation or derivative contracts rather than an actual short. 66 Insurance brokers . In 2020, insurance brokers Aon and Willis Towers Watson agreed to merge. The merging parties were allegedly the second-and third-largest brokers offering health, retirement, and business-risk insurance to other firms. 67 The DOJ sued to block the deal, alleging that it would reduce competition in various ways. The parties argued that the merger would combine complementary expertise and thereby enable the merged firm to improve product quality and better serve its clients. 68 The DOJ sought divestitures of large clients, which Aon resisted on the ground that they would impair the efficiency of its operations. 69 The parties abandoned the deal shortly after the DOJ filed suit. 70 65 American is larger than either of the other two firms. See Who We Are, ASR Group, asr-group.com/about-us (last visited Nov. 11, 2024) (describing itself as "the world's largest refiner . . . of cane sugar"). This suggests that the required negative ownership position in American would be less than its market capitalization. Confirming the size, however, would require additional information about cross-elasticities of demand. The size of the position would be reduced further by the presence of expected efficiencies, as discussed herein. 66 As to the latter, derivative contracts are frequently written with notional values far greater than the value of outstanding shares. See Suhail Malik, The Ontology of Finance: Price, Power, and the Arkhéderivative, in VIII Collapse 629, 629 (Robin Mackay ed., 2014) (citation omitted) (reporting that the "notional total value of derivatives market at the end of 2012 was $694.

Shorting Your Rivals Interestingly, the European Commission approved the deal subject to less significant divestitures to a smaller rival. 71 If the divestitures had an effect on competition for U.S. customers, this might suggest that the balance of efficiencies and anticompetitive effects, at least in the deal as modified by the Commission, was a close call. If so, then the DOJ's incremental concerns might have been satisfied with a negative ownership solution in addition to the Commission's required divestitures. Moreover, since the parties were willing to do the deal under these agreed-upon divestitures, this suggests they still felt there were substantial synergies to be had, even taking the divestitures into account. Thus, this deal might have been a good candidate for adding our additional incentive-based remedy to the existing remedial package. Further, note that because the approval of the European Commission suggests that the remaining net anticompetitive effects that concerned the agency might not be that large, the size of the necessary short position or the magnitude of the relative-performance evaluation might not be that large. This indicates that our remedy would likely have been feasible in this case.

Book publishers . In November 2021, the DOJ challenged the merger of Penguin Random House (the largest book publishing company) and Simon & Schuster (the fourth largest). The DOJ alleged that the combination would reduce the number of competitors who are capable bidders for best-selling authors from five to four and eliminate substantial head-to-head competition between the two firms. That loss of competition, the DOJ argued, would reduce royalties to the authors. 72 The merging parties countered that the merger would create robust efficiencies that would benefit all authors, especially smaller ones, 73 including by allowing Simon & Schuster's authors to benefit from Penguin Random House's superior distribution capacity and distribution networks. 74 DOJ challenged and successfully blocked the deal. 75 The efficiencies argument was ultimately not considered at trial. 76 76 Id . at 55 ("The Court, however, precluded the defendants' evidence of efficiencies, after determining that the defendants had failed to verify the evidence, as required by law. Efficiencies therefore play no role in the instant analysis." (citation omitted)). then a negative ownership remedy could ensure that these benefits would be passed on to authors. If the merged firm held a negative ownership position in the other three major publishers, then it would have an incentive to increase its offers to top authors because doing so either would keep such authors away from these rivals or increase the amount that the rivals would have to pay for their books. Either way, this would reduce the profits of the rivals, enhancing the value of the short position. Furthermore, to the extent that the merged firm would have a more efficient distribution system, this would reduce the direct cost of bidding more in the event it was the high bidder. Moreover, if these efficiencies were substantial, then the merged parties should be willing to agree to a short position that eliminated any market power benefits from the merger because they would still obtain the benefits from the efficiencies. Moreover, because three other large publishers would have remained after the merger, the size of the short position in each one would not have to be all that large, making implementation of this remedy easier than in cases with fewer remaining competitors.

As noted in the Introduction, negative ownership positions provide three kinds of benefits: ex ante signaling (or screening), tailoring, and the provision of ex post incentives. The sugar, insurance, and publishing examples discussed above illustrate the tailoring and ex post incentive benefits of the negative ownership approach, which is to enable potentially procompetitive transactions that would otherwise be anticompetitive and blocked. This is particularly true when there are significant benefits and no way to divest in a way that both preserves those benefits and eliminates the anticompetitive effects. The approach is particularly useful where, as may have been true of the insurance example, a small modification could make all the difference. The approach works best when the negative ownership position is in multiple firms (as in the publishing example) rather than a single firm (as in the sugar example).

Our approach can function as a remedy imposed by the court. If an enforcer establishes to the court that the deal is anticompetitive, it could seek to impose a negative ownership position on the merged firm rather than blocking the deal outright, using one of the mechanisms that we have described. As for the size of the position, one obvious answer is that it should be sufficient to eliminate the anticipated anticompetitive effects of the deal. If that is infeasibly large, a smaller position would still be valuable in order to reduce (though not eliminate) the bad effects to the point that the procompetitive benefits outweigh those lingering anticompetitive effects.

More interestingly, the merging parties can propose this type of remedy. In so doing, the parties would credibly signal to regulators that the merging firms believe the combination will not harm competition. A common strategy

Shorting Your Rivals in merger clearance is for the merging firms to proactively offer commitments to the enforcement agency that, if accepted, would reduce or eliminate the anticompetitive consequences of the deal. One such commitment can now be a promise to implement a negative ownership solution in an effort to ensure that the deal would not have anticompetitive effects overall. Unlike other "fix-it-first" commitments, the negative ownership promise demonstrates that the merger is competitively harmless, because if the parties believed the main benefit was the ability to increase prices due to reduced competition, such a commitment would not be profitable.

If the enforcer refuses the commitment as insufficient, the proposed remedy could also play an important role in subsequent litigation. A commitment proposed by the merging parties is often relevant in litigation as a heightened baseline for the enforcer to overcome. 77 For example, if the parties commit not to raise prices, the enforcer might then seek to show that prices would fall in any event, and that they would fall even more in the but-for world. 78 The heightened baseline could be important in practice. If the parties propose a negative ownership commitment as part of their deal, the enforcer would need to persuade the court that the transaction, even as modified by the commitment, is worse for competition than abandoning the transaction. The court would take into account the distinctive incentive to compete set up by the negative ownership position, just as in other contexts it takes account of managers' particularized disincentive to raise prices. 79 Whether proactively offered as a signal or demanded by regulators and functioning as a screening device, the decision to offer or accept a negative ownership commitment is a source of inference about the competitive consequences of the transaction. Because the short position decreases the profitability of a merger that also raises rivals' profits, a decision to offer a commitment is a credible signal that the transaction lacks an anticompetitive effect. On the other hand, the absence of a negative ownership commitment is a basis for a negative inference.

Put another way, the availability of a commitment (once established) can be expected to give rise to a separating equilibrium of better and worse transactions. The separation is imperfect because the merging parties might undertake the commitment as a costly (false) signal that their transaction does not 77 harm competition. 80 Doing so reduces the inferential value of the signal for the transactions where the merging parties find the false signal to be worthwhile-likely the least bad transactions (since these are where the signal will be less costly). At the same time, the effort spent to generate the signal is directly beneficial to consumers because it takes the form of more aggressive competition, which brings various benefits.

Adopting a negative ownership commitment does not necessarily signal that the transaction has significant efficiencies or benefits for consumers. A merger might be premised on, say, tax savings or empire building that leave rivals' profits unchanged. Nor does it signal that the efficiencies, if any, will be passed through to consumers. As discussed next, however, the negative ownership commitment provides a way to indirectly pass on efficiency benefits to consumers.

In addition to these ex ante benefits, the negative ownership remedy beneficially enhances the incentives of the merged firm to price aggressively. The availability of negative ownership as a tool for augmenting competition also prompts fresh consideration of just how beneficial a transaction must be in order to pass muster. One obvious baseline is that the transaction overall must leave consumers no worse off. However, negative ownership also enables authorities to increase the likelihood that consumers share in the benefits of merger synergies.

For example, regulators might implement the remedy with sufficient intensity to leave post-merger prices unchanged even in the absence of possible merger-induced cost-saving. In that case, any impact of the merger in lowering the merged firm's marginal costs would put pressure to reduce price below its pre-merger level. This remedy would completely remove the harm while preserving the benefit from the cost-saving efficiencies, which would be shared between the merging parties and consumers. 81 In the Appendix, we work through an explicit model that illustrates many of these benefits. For example, without the negative ownership remedy, antitrust authorities should only approve mergers if the synergistic efficiencies exceed some critical value. But the Appendix shows that negative ownership positions relax this constraint and can allow authorities to approve mergers with 80

A Progress Report, 29 Int'l J. Indus. Org. 356 (2011) (deriving a partial pooling equilibrium in which merging firms with moderate upward pricing pressure, anticipating ex post antitrust review, pool with harmless transactions in order to avoid ex post undoing of the merger); Marco Ottaviani & Abraham Wickelgren, Approval Regulation and Learning, with Application to Timing of Merger Control, 40 J.L. Econ. & Org. 597 (2024). 81 An even more aggressive use of the tool would push the parties to pass through to consumers a larger fraction of the benefits from the marginal cost reduction.

Shorting Your Rivals smaller synergies without sacrificing consumer surplus. The Appendix also shows that negative ownership interventions can do more than maintain premerger pricing. More substantial negative ownership requirements can induce rivals to price more competitively than they had before the merger. In one of our examples, a negative ownership position of 13% is sufficient to induce pre-merger price levels, while larger positions reduce the price further and pass through more benefits of the merger to consumers. A negative ownership position of 35% is sufficient to induce a competitive equilibrium that passes through to consumers all of the merger's benefits.

Our approach also provides a means to refine and improve a provocative proposal offered by Eric Posner to strengthen merger enforcement. 82 Posner argues that the Clayton Act, properly understood, requires that any merger that widens margins must be condemned under Section 7. 83 In its simplest form, the proposal would sweep quite broadly, condemning even mergers that merely lower marginal cost or improve products. Our friendly amendment is to note that such a merger could still pass muster under Posner's approach, provided that enough of the merger's resulting benefit is passed through to consumers. Our proposal provides a means to commit to increase the degree of pass-through.

The potential utility of the negative ownership approach extends beyond mergers to a wide variety of contexts in which the concern is weak competition among rivals. For example, consider cartels. Even after a cartel is uncovered, collusion often persists for years thereafter. Classic examples include the graphite electrodes, lysine, and citric acid cartels. 84 Persistent collusion might well be present, post-cartel, due to the firms having learned or established the "rules of the game" during the cartel period. After all, a big part of why express communication is more effective than tacit collusion is that express communication is helpful in coordinating the terms of the arrangement as an initial matter. The usefulness of that arrangement may persist thereafter. 85 These persistent effects are causally attributable to the earlier cartel period, and thus fair game for a court seeking to restore competitive conditions. Thus, 82 See Eric A. Posner, Market Power, Not Consumer Welfare: A Return to the Foundations of Merger Law, 86 Antitrust L.J. 205 (2024).

83 Id . at 249. 84 See Joseph E. Harrington, Jr., Post-Cartel Pricing During Litigation, 52 J. Indus. Econ. 517 (2004). 85 A further reason for firms to keep post-cartel prices high is that this price is often used as an input in the calculation of cartel damages. A higher post-cartel price might be taken as evidence of a higher but-for price during the cartel period and thus lower damages. Id .

to restore the but-for competitive price, a court could require each cartel conspirator to take a negative position in its rivals large enough to implement that price. 86 Just as in our discussion of mergers, the goal is to implement the competitive status quo.

Just as with mergers, moreover, the remedy can be calibrated instead to achieve an even lower price. It is feasible to compensate purchasers who were harmed during the cartel period by ratcheting up competition above the precartel level, and thereby reducing prices below the pre-cartel level. 87 This could be implemented for a defined period in order to compensate purchasers, through lower prices, for the previous harm from higher prices. Even if not implemented as a conscious remedy, the compensatory attribute of the negative ownership approach offers a partial response to concerns that the remedy might "overshoot" and intensify competition beyond the pre-cartel point rather than merely restore the status quo. The social costs of such imprecision are less troubling once it is recognized that doing so brings a compensatory benefit.

Using negative ownership as a means of compensation is an indirect, second-best form of compensation. Like other indirect remedies, such as a temporary discount or price cap, the benefit accrues to future purchasers rather than past purchasers. 88 One advantage, from an economist's standpoint, is to compensate not only overcharged purchasers but also the deadweight-loss victims of the cartel-that is, those priced out of the market during the cartel period. 89 The main advantage of using negative ownership rather than a price cap in this setting is that the negative ownership remedy automatically adjusts to changing market conditions. For example, if input prices fell during the recovery period, a fixed price cap might not be binding and therefore not provide any additional compensation. By contrast, because negative ownership 86 This price is determined in the same fashion as in a cartel damages case, where economic testimony is typically important in order to determine the relevant price and degree of competitive intensity. The pre-cartel price is one obvious candidate, but changes in demand or costs may necessitate an upward or downward adjustment, just as in a cartel damages case. 87 For expositional simplicity, here we focus on prices, but the point extends to other terms of trade. 88 89 See supra note 59 and accompanying text. Moreover, the benefits flow through to indirect purchasers without the customary challenges of compensating such purchasers. There would be no need to allocate by purchaser type, deny indirect purchaser recovery, or risk overcompensation.

Shorting Your Rivals changes the incentives to compete, for any given market condition, it would automatically produce even lower prices when input prices fell. 90 It bears note that the use of an indirect remedy-a so-called "fluid recovery"-has had a mixed reception by courts. 91 The main basis for skepticism is the mismatch between those harmed by the cartel and those benefited by the remedy. Ideally, each purchaser receiving a benefit would establish that they were actually harmed, and each victim of the cartel would have an opportunity to recover. 92 By contrast, a fluid recovery typically fails to benefit some of the harmed purchasers, while benefiting some purchasers who were not harmed. These concerns are lessened, and a fluid recovery is accordingly more palatable to the courts, where the set of future purchasers overlaps heavily with past purchasers. 93

A negative ownership solution has further application in a wide variety of contexts where there are legal and policy bases to demand strong competitive incentives and reason to expect that actual incentives fall short.

Continued coordination after the breakup of a monopoly. We have already discussed post-cartel coordination. An analogous problem may arise when a monopoly is broken up but the firms continue to coordinate after divestiture, as apparently occurred in the tobacco industry and other industries. 94 90 One question of implementation is whether to achieve the predetermined benefit by imposing a deep price cut for a short period, a shallower price cut for a longer period, or something in between. A shallower cut is easier to implement, particularly if the remedy takes the form of a short, given the complications that ensue as the short grows large. A shallower cut also avoids any risk of mistakenly dropping price below marginal cost, an action that introduces a harmful distortion. For discussion of this issue, see A. 94 See generally, e .g ., Fed. Trade Comm'n, Competition and the Financial Impact of the Proposed Tobacco Industry Settlement (1997), www.ftc.gov/sites/default/files/ documents/reports/competition-and-financial-impact-proposed-tobacco-industry-settlement/ ndoc95_0.pdf.

In addition to divestiture, a court could sharpen the incentive to compete, postbreakup, by means of a negative ownership remedy.

Reduced competition due to common ownership. As noted in Part I, negative ownership bears a close theoretical relationship to common ownership. This close connection has a further implication. If common ownership is a problem because it alters the profit maximization of the firm, then a negative ownership position is a precise solution that exactly counteracts the effects of common ownership. Put another way, common ownership (in its most developed formulation) is associated with a positive weight on the profits of other firms. A negative ownership position does the opposite.

A negative ownership solution could also be a remedy or part of settlements in Section 1 rule of reason cases. As with mergers, such cases often implicate a balancing of anticompetitive and procompetitive effects of an agreement between firms. The negative ownership remedy has the same benefits in such cases. It can preserve the procompetitive aspects of the agreement while counterbalancing any tendency towards softening competition or facilitating collusion. Here, instead of asking the defendants to take a short position in other firms in their market, they would take a short position in each other. Once again, this could be proposed by the agencies or it could be part of the original agreement of the firms so as to forestall antitrust concern.

Oligopolistic price elevation, unaccompanied by express communication, is often regarded by lower courts to be beyond the reach of Section 1 of the Sherman Act. 95 The wisdom of this limitation is hotly debated, given that the adverse welfare effects of tacit collusion are so similar to (actionable) express collusion. Nevertheless, taking legal action against tacit collusion (or, nearly equivalently, "conscious parallelism") is thought to give rise to both legal and practical difficulties.

One might readily imagine a regime in which the legal impediments are removed. For example, the Supreme Court could broadly interpret existing dicta about the applicability of Section 1 to reach tacit collusion. 96 Alternatively, Section 5 of the FTC Act, which prohibits "unfair or deceptive acts or practices . . . affecting commerce," 97 could be read to reach harmful tacit collusion. 98 One source of reluctance has been the difficulty of implementing a solution. What is a court supposed to do once it has identified the tacit collusion? The firms are accustomed to strategic thinking and making decisions in light of mutually recognized interdependence. Ordering them to stop pricing interdependently may seem to be impractical or impossible to monitor. As Richard Posner posed the question: "[I]f tacit collusion is forbidden, how does a seller in a market in which conditions . . . favor convergence by the sellers on a joint maximizing price, and adherence to that price, decide what price to charge?" 99 The negative ownership remedy provides a practical solution to this problem. Compared to monitoring a firm for interdependence, the remedy requires relatively little judicial supervision. Even without new law or an expansive reading of existing law, as discussed above, there is an important subset of tacit collusion that can already be reached by judicial action. This is tacit collusion that persists after the end of a cartel.

The remedy also provides a way forward for other possible interventions that attack oligopoly. For example, in the United Kingdom, the Competition and Markets Authority (CMA) performs in-depth investigations of the competitiveness of particular markets, with a view to implementing an ex ante also notes that later dicta in American Tobacco Co . v . United States likewise defines the agreement element of a Section 1 claim broadly:

It is not the form of the combination or the particular means used but the result to be achieved that the statute condemns . . . . No formal agreement is necessary to constitute an unlawful conspiracy . . . . The essential combination or conspiracy in violation of the Sherman Act may be found in a course of dealings or other circumstances as well as in any exchange of words. . . . Where the circumstances are such as to warrant a jury in finding that the conspirators had a unity of purpose or a common design and understanding, or a meeting of minds in an unlawful arrangement, the conclusion that a conspiracy is established is justified. remedy in response to identified industry-wide market failures. 100 We see negative ownership as a good fit for the CMA's broad remedial authority. 101 A simpler (albeit more adventurous) implementation would be to trigger negative ownership whenever price-cost margins reach a certain level. 102 This shares some features with legislative proposals from the 1970s that would have imposed automatic remedies based on concentration. One required deconcentration of industries with a four-firm concentration ratio exceeding 70%. 103 Another proposed deconcentration in industries with high concentration, high profits (after-tax earnings regularly exceeding 15% of net worth), or a lack of "substantial price competition" over three consecutive years. 104 The negative ownership remedy offers a way to update these proposals by replacing the difficulties of deconcentration with a more modest, yet potent, intervention.

It is easy to overstate the actual automaticity of deconcentration proposals. Defining a market in order to evaluate concentration and thereby infer market power is heavily contested and fraught. 105 Even using a more directly meaningful measure such as price-cost margins still requires imperfect, and almost certainly contested, estimation of those margins. Nonetheless, if policymakers decide to take action against market power generally, negative ownership provides a remedy that avoids many of the pitfalls of other proposals.

The negative ownership remedy is theoretically quite simple, but in practice, there are various potential real-world complications to consider. Part III.A addresses the concern that negative ownership might induce predatory or exclusionary behavior. Part III.B considers the risk that negative ownership might harm the incentive to innovate. Part III.C takes up issues and problems related to the necessary size of the negative ownership position. Part III.D examines complications that might arise from heterogeneity among firms. Part III.E assesses the prospects of evasion, by a firm or its managers, of its obligations to faithfully implement the remedy. Part III.F addresses the possible concern that implementing the remedy might expose the firm to liability for violating a duty to shareholders. Part III.G defends shareholder returns as an appropriate tool and target for our proposals.

One might be concerned that a negative ownership remedy would increase a firm's incentive to engage in predatory or exclusionary behavior in order to induce exit. As noted above, attention to the tradeoff between deterring collusive behavior and encouraging predation pervades many areas of antitrust. One of the main reasons some commentators are skeptical about aggressive predatory pricing enforcement is concern that this would facilitate collusion. 106 The literature has long recognized the potential for costly sabotage as a possible downside in the use of relative-performance evaluation. 107 For example, Bloomfield et al. present evidence that firms that compensate CEOs based on relative share value use corporate disclosures to harm the share price of their rivals. 108 To the extent that such disclosure distorts the relative fundamental stock price of firms in the industry, one might see this as welfaredecreasing. 109 On the other hand, if these are truthful disclosures about rivals, arguably these disclosures could also be providing more accurate information to capital markets, improving capital allocation.

Negative ownership, however accomplished, would be more problematic if it prompted competitive behavior that was excessive even from the social point of view. Most obviously, if a manager's compensation is negatively related to the profit of their rival, then predatory pricing becomes individually rational in a broader set of circumstances. The firm need not fully recoup its profit losses in the future if the manager's (or shareholders') cost of predation is lessened due to the benefit from competitors' losses.

Beyond predatory pricing, one might be concerned that a negative ownership remedy could make other predatory or exclusionary practices more profitable. Actions that raise rivals' costs would not only indirectly benefit the firm or manager by inducing the rival to price higher or reduce output, they would also provide a direct benefit in the form of lower rival profits. 110 Similarly, exclusive dealing contracts that limit rivals' access to markets become more attractive because of the direct benefit from reducing rivals' profit.

Note, however, that in our basic approach, the size of the short position is set to maintain pre-merger competitive incentives. If the remedy does that accurately, then the short-run incentive for predation relative to the pre-merger state should not change. If the merger has created efficiencies, however, then one might think that the opportunity for successful predation would increase. But recall that the magnitude of the remedy considers the efficiencies and aims to keep prices constant after the merger. This suggests that when efficiencies are present, a smaller short position is necessary to preserve the premerger status quo because the merger creates less incentive to raise price. Again, if static equilibrium pricing incentives are unchanged, then the rival firms' incentive to ride out temporary losses due to predation is unchanged relative to the pre-merger state.

The merger might increase the incentive to predate by a second pathway, namely by reducing by one the number of firms with which post-predation gains must be shared. While this concern might be significant in a three-to-two merger, recall that this is not the type of merger in which, for other reasons, we think this remedy is most useful. Instead, our remedy is a viable option in mergers with numerous remaining competitors. As the number of remaining firms increases, the predation concern is significantly attenuated. 111 This point is particularly salient in an environment of relatively aggressive merger enforcement, in which there is significant interest in scrutinizing mergers with a relatively large set of remaining competitors.

Where the predation concern is significant, we can significantly limit the incentive by implementing the remedy using an at-the-money call in its rivals instead of requiring short selling. Unlike the holder of a short position, the writer of at-the-money calls, which have an exercise price set equal to the pre-merger stock price of the rival, has no additional incentive to predate or engage in acts of exclusionary conduct to lower rivals' stock value below its pre-merger value. As long as the rivals' stock price does not increase, the call option has no value. So, a drop in the rivals' stock price creates no additional value for the writer of the call option.

As discussed in Part I, implementation by means of a call option can take the form of a Margrabe option, which responds to the concern that a rival's stock price might increase because the stock market value has generally increased. Of course, there could be other exogenous reasons why the rivals' stock price might increase independent of general market appreciation. But those reasons also make predation less likely to successfully induce exit. For example, if the industry itself expands, then the rival can operate profitably even with reduced demand due to lower prices by the merged firm. Thus, the use of call options should greatly reduce concerns of predatory conduct where they might otherwise arise.

Finally, to the extent that there are still remaining predation or exclusion concerns, these concerns can be considered by antitrust enforcers without ruling out the usefulness of the remedy. First, there may be many situations where the possibility or effectiveness of predatory or exclusionary strategies is limited. Second, since the antitrust enforcer has imposed the remedy itself, it is directly aware of the danger and can monitor the firms' behavior to ensure that they do not engage in anticompetitive exclusion in response to the remedy. This heightened attention should also provide additional deterrence. While one might be concerned that courts are reluctant to scrutinize such unilateral conduct, that concern is likely much smaller in this case. This reluctance largely stems from sympathy with the Chicago School position that markets are self-correcting. When the source of the incentive is a governmentimposed remedy, however, it should be easier to overcome a judge's reluctance to recognize anticompetitive effects where they exist. Moreover, the negative ownership remedy (however structured) could be combined with a limit on the use of exclusive dealing or other exclusionary strategies as part of the total remedy in the case. Finally, to the extent that these solutions do not completely alleviate the concern, the antitrust authority can reduce the use of negative ownership, accepting an imperfect remedy as a second-best solution. 112 The discussion thus far has focused on mergers. It is worth noting that predatory concerns are much less of an issue when using negative ownership as a collusion remedy than it might be as a merger remedy. In the case of a horizontal merger, if the merger creates substantial efficiencies as well as anticompetitive effects, the merged firm might have a cost advantage over its rivals. If the firm has few rivals, it might be more likely to think that predatory pricing could be successful. The additional incentive provided by a required short position or relative-performance evaluation could then have a nontrivial effect on predation incentives. The discussion above is a response to this potential concern.

By contrast, collusion typically features relatively equal competitors, given the difficulty of sustaining collusion in the face of asymmetry, and competitors that are financially stable. Under these conditions, it is less likely that one firm could expect to gain future monopoly power by using predatory pricing to successfully cause its competitors to exit the market.

In some industries, innovation is an important source of profitability. The economic incentive to innovate depends upon an innovator's ability to capture part of the resulting social benefits as profits. This capture may be achieved by means of a patent, a first-mover advantage, or superior distribution, among other instruments. The degree of capture is typically imperfect. One source of leakage is that, to a greater or lesser degree, the innovation is diffused to rivals. Other firms copy or otherwise free ride on the innovation and thereby earn profits as well.

Negative ownership alters the profitability of innovation. It increases the benefit of stealing business from rivals, which is good for innovationindeed, this is a socially productive version of the incentive to exclude discussed above. At the same time, negative ownership increases the downside of spillovers, which in theory might suppress innovation. Which effect predominates is theoretically ambiguous and will depend on the size of the spillovers, the cross-elasticity of the products of the merged firm with its remaining rivals, and the marginal cost of the merged firm relative to its rivals. How these factors play out in any particular industry is an empirical question. In recent work, Miguel Antón and coauthors present empirical evidence (in the context of common ownership) that the business-stealing effect predominates where the firms are in relatively close competition. 113 This is the setting where the negative ownership proposal is likely to be of most interest. Overall, we expect negative ownership to generally be neutral or positive for innovation, while recognizing that exceptions might sometimes arise.

It is straightforward to derive the formulas for the short positions needed to recreate pre-merger incentives, and we have done so in the Appendix for the stylized airline merger example. However, the antitrust agencies would still need to determine the values for parameters that go into those formulas. These parameters are the degree of substitution between the products of the merging firms with each other and the other firms in the market, as well as the margins of each firm.

These parameters can be difficult to estimate. But agencies already commonly estimate these parameters when they evaluate whether a merger presents the risk of unilateral effects. The main focus for determining anticompetitive effects is the degree of substitution between the two merging firms and their profit margins. The same techniques can be used to estimate these parameters for the other firms in the industry. When the agencies do merger simulation, they typically use an estimate of the entire demand system in the market. 114 Thus, while the exact level of the required negative ownership position will be measured with error, it should not be any different from the error inherent in any merger review. Moreover, because the remedy is not discrete, a small error in estimating the correct short position would only lead to a small increase or decrease in competition relative to the pre-merger situation.

Another approach for setting the size of the short position would be to harness the market's beliefs about future competitiveness. Imagine that antitrust authorities approved a merger conditional on the merging firm increasing the size of its short position in its rivals each day until the index-adjusted value of rivals' stock price dropped below its pre-merger level. 115 The value of rivals' stock would only dip below the pre-merger values when the size of the short position was sufficient to ensure that the pre-merger level of competition was maintained. 116 If the market reaction to the initial short position were a substantial fall in rival stock value, the mechanism might also allow the merging firm to reduce its short position as long as the index-adjusted value of rivals' stock remained below the pre-merger level. 117 The market reaction would also provide evidence about competitive effects. If the merging parties included in the merger announcement a commitment 114 See generally Oliver Budzinski & Isabel Ruhmer, Merger Simulation in Competition Policy: A Survey, 6 J. Competition L. & Econ. 277 (2010). 115 The index-adjusted stock price would be the price adjusted for general changes in the value of the stock market.

116 This approach is an example of a "topping off" mechanism. See Barry E. Adler & Ian Ayres, A Dilution Mechanism for Valuing Corporations in Bankruptcy, 111 Yale L.J. 83, 96-99 (2001) (applying the idea to valuing corporations in bankruptcy and discussing other existing applications). 117 This mechanism could also afford the merging firm more flexibility in choosing among the various short implementations. For example, the antitrust authority could grant the merging firm freedom to choose any combination of short stock, managerial pay incentives, and derivative positions, so long as the combination is priced by the market as maintaining pre-merger competitive levels.

to short a defined set of rival firms, then if the stock market reaction to the merger was that the price of those rival firms fell, this would be credible evidence to the antitrust agencies that the merger (as modified by the negative ownership commitment) would not lead to higher market prices.

One potential issue, illustrated by the sugar merger in Part II, is the size of the position (short or long) needed to completely restore pre-merger competitive incentives. In our stylized airline example in the Appendix, a short position of only about 13% restores pre-merger prices with relatively small efficiencies. But on other facts, a larger position would be necessary. This need for a large position arises when there is very little difference in the relative substitutability of the merged firm's products with the other products in the market (the symmetry case is one extreme example of this). At a practical level, however, this should be a minor hurdle for two reasons.

First, this remedy is not a cure-all for mergers with very large anticompetitive effects and only minor efficiencies. If the substitutability between the merged firm's products is much greater than between those products and the other products in the market, a merger is unlikely to be salvaged with any remedy (whether by divestiture or negative ownership). However, the impossibility of salvaging the most extreme anticompetitive transactions says nothing about the broad range of transactions whose competitive effects can be improved through a negative ownership remedy. As such, the cases where the negative ownership remedy is likely most attractive are precisely those where the size of the negative ownership position is not too large.

Second, it may often be easier to replicate the incentive of large negative ownership positions by other means, rather than through directly shorting one's rival. Take, for example, relative-performance compensation. An executive's pay is generally only somewhat sensitive to the performance of their own firm. Given this, it should be possible to suppress the incentive of an executive team to raise prices with a relatively small performance sensitivity to a rival's performance.

In any event, even if it were the case that a negative ownership remedy is feasible in only a handful of merger cases, we would regard that as a substantial success, as it would still generate substantial social value in those cases.

As discussed above, the necessary size of the negative ownership position varies with the circumstances. For larger positions, it might not be possible for the merging parties to borrow enough shares, at a reasonable premium, to 2024] Shorting Your Rivals accomplish a short sale. In such a case, one could recreate the short through a derivative contract.

We expect that if demand for such contracts exists (due to it being an essential part of merger approval), financial firms would have an incentive to offer them. It is possible that due to the long duration and possible illiquidity of these contracts, counterparty demand might be limited. This could lead merging parties to pay a premium for them in some cases. If this proves to be a problem, the government could also be the counterparty to these contracts. Such a contract could either entirely replace or be used alongside a traditional short position. To the extent the government wants to limit its long position in the market, it might try to require as much of a short sale or private derivative contract as is possible without a significant premium and then offer its own derivative contract only as a last resort. 118 On the other hand, there is a risk that a private counterparty could collude with the merging parties to undo the incentives of the short position. Because the short position is designed to restore pre-merger pricing incentives, higher prices will benefit the counterparty more than they will harm the merging parties. Thus, there is the risk of a side deal between the two to induce the merging parties to increase prices above pre-merger levels. If this risk is significant, then there would be an advantage to having the government as the counterparty.

These concerns favor an executive compensation-based remedy over a short position. That is, even if the firm's profits are not directly tied to the profits of a rival, the payment to the managers who make the decisions could be. As long as the managers who make or control the pricing decisions have compensation that is appropriately decreasing in the profits or stock price of their rivals, they have an incentive to keep prices low post-merger.

A related concern is the duration of the short requirement. The short position must stay open for long enough to deter the merging parties from raising prices. The exact duration should probably be based on expectations about entry in the market. The parties could also have the ability to appeal to the agency to exit their short if there are unexpected increases in the 118 Having the government take a position in particular firms in the economy could be problematic, which is why we suggest using short sales and private derivative contracts first. That said, both the public nature of the position and the fact that in almost all cases the size of the government's position would be trivial relative to its overall budget means that it is unlikely to pose any significant risks of bias except in the most extreme cases. Moreover, those extreme cases would tend to occur in markets with very highly valued firms, which are exactly the markets in which it might be easier for the merging parties to take on large short positions without paying a large premium. Nonetheless, this is certainly a concern that should limit the use of governmentprovided derivative contracts as a substitute for the short position. competitiveness of the market. Lastly, the government would have to monitor the merged firm to make sure that the firm did not hedge its short position with some other investment. If the merged firm is publicly traded, that should be straightforward to do from SEC filings. If the punishment for such hedging were large enough, then even with imperfect enforcement, the vast majority of firms would likely be deterred from undoing the short position via hedging.

Degree of substitution. The symmetric example introduced in Part I is just a simple example that is useful for explaining how the remedy works. It can be adapted to asymmetric cases as well. In fact, when we relax the symmetry assumption, there is a unique position in each rival firm that recreates the pre-merger pricing incentives. 119 Further details are deferred to the Appendix, where our simple formal model of the JetBlue/Spirit merger features significant heterogeneity: two small merging firms, plus four large firms providing a higher-value service.

Privately held firms. The negative ownership remedy is easiest to implement in industries, such as airlines, where the competitors are publicly traded. There, it is straightforward for one firm to take a short position in another. Taking a short position in a privately held firm, by contrast, is difficult or impossible. Relative-performance compensation may still be feasible, provided that there is sufficient knowledge of the operations of the privately held firm. A further possibility is to create a derivative security based on the profit of the private firm.

Multiple products. Another potential issue arises when one or more firms are in multiple, heterogeneous lines of business. In that case, the rival's stock price will not depend solely, or in some cases even primarily, on the line of business that competes with the products of the merging firms that compete with each other.

While this multi-product problem is far from trivial, and explored further below, notice that this is also the case in which the divestiture remedy works the best. One can divest assets within the product overlap while still retaining many of benefits of the merger. The negative ownership remedy is most important when there are no assets that can be easily divested without eliminating much of the reason for the merger. 119 In the four-firm case, let z i be the size of the short position that the merged firm must take in firm i=3,4. Then we have ( ) = --z q q m q q m q q q q m and ( ) = --z q q m q q m q q q q m where q ij measures the change in demand for product i when the price of j changes and m i is the gross profit margin of firm i.

To see the issue, let us suppose that the merging firms are supermarkets. Perhaps firms 1 and 2 both have stores in many of the same cities in the Midwest, but not elsewhere. Firms 3 and 4 might also have stores in those cities, but they also have a presence in other parts of the country. If firms 1 and 2 are not present in those areas, then the fact that firms 3 and 4 have other stores will mean that the latter firms' stock price will move for reasons other than their competition with firms 1 and 2.

That said, this will only add noise and will not affect the optimal pricing decisions for the stores of firms 1 and 2. If the merging parties' managers are risk averse, they might find that the added risk makes the merger less desirable to them.

So far, we have implicitly assumed that firms 3 and 4's stores compete with those of firm 1 and 2 to the same degree in each locality. That assumption is unrealistic. Because it is infeasible to have a separate financial position in each store, this means we can only replicate the pre-merger incentives on the average. The more heterogeneity there is in the degree of competition, the more the merger, as altered by the remedy, will intensify competition (relative to the pre-merger state) in some areas and weaken competition in others.

A more important problem occurs if firms 3 and 4 have stores that are in competition with either firm 1 or 2's stores, but not both. Now, the negative ownership remedy will intensify competition in these areas in which firms 1 and 2 do not overlap. If we want to keep average pricing and profitability for the merged firm the same, we will end up with less competition in the regions in which the merging parties compete and more competition in the regions in which they compete with the other firms in the industry. At one level, this shouldn't be a major issue if we have no particular reason to prioritize competition in one region over another. However, antitrust law typically does not allow, as a defense of anticompetitive conduct in one market, that it intensifies competition in another. Although cross-market balancing may satisfy an enforcement agency and persuade it not to challenge a transaction, a court (if the matter proceeds to litigation) might take a more skeptical view.

If negative ownership is implemented through managerial compensation, there is a potential conflict with shareholders, who prefer that the manager simply maximize profits and therefore ignore the incremental incentive to compete. (This "wedge" does not arise in other implementations, given that the firm itself holds the negative ownership position.) For example, an influential shareholder, perhaps working through a compliant board of directors, might offer to reward a manager who simply maximizes firm profits rather than acting on negative ownership, perhaps through future raises that are not observable at the outset. 120 Alternatively, a manager might be threatened with a penalty or even termination for failing to "play ball."

To safeguard the remedy against evasion, we anticipate that a court implementing this remedy would require the firm and its managers not to attempt to circumvent the remedy in this fashion. A merged firm offering the remedy in advance would make a similar commitment. Under these circumstances, attempted evasion would be contrary to the commitment and unlawful interference with a judicial decree. Moreover, an agreement between an investor and manager to harm competition in this fashion would also likely violate Section 1 in its own right. Evasion under these circumstances seems unlikely to be attempted or to succeed, especially if it carried potential criminal penalties for the manager or investor.

A second evasion concern involves common ownership. It arises from the (contested) proposition that common owners are effective in causing a firm to place a positive profit weight on rivals. One might imagine that, in response to a negative ownership position in a rival taken by the firm, the common owner takes an offsetting long position in that rival in order to restore its desired exposure. The new position gives the common owner a new reason to steer the firm away from intense competition. Whether we should worry about this depends upon the contested proposition being true. Moreover, pressing a firm and its managers to circumvent a no-evasion commitment is risky for the same reasons discussed immediately above.

In discussing the negative ownership remedy with colleagues, we have heard concerns that its implementation might expose the firm to liability for insider trading or otherwise violating a duty to shareholders. In this Part, we explain why such concerns are misplaced.

Insider trading. Placing a trade in connection with a nonpublic merger raises the question of insider trading. However, there is no realistic prospect of liability in our setting. Insider trading rules ordinarily restrict trading on the merging parties' stocks, not the stock of a rival. Trades on the stock of a rival-so-called shadow trading-has only very rarely and recently been pursued by the Securities and Exchange Commission (SEC). 122 Enforcement is a nonstarter for the further reason that the firm, rather than an employee or other individual, is putting on the trade. 123 If, contrary to our view, the SEC possesses discretion to bring a shadow trading case against a corporation that shorts its rival, a further contribution of our article is to suggest that it should not do so in the context of a short entered into to obtain merger approval. 124 Suits against the board. A short or other negative ownership remedy creates an incentive to compete more aggressively but does not guarantee that the firm will act on this incentive. A firm with a negative ownership position in its rival might fail to compete more aggressively, thereby allowing the rival to earn high profits, resulting in lower firm profits due to the position. 125 Shareholders might well protest the firm's resulting failure to maximize profits. Such shareholders might even wish to take action against the firm's board of directors for getting them into this mess-for entering into the short in the first place, or for subsequently failing to maximize profits. Such an action, however, is doomed to failure. Under the lenient business judgment rule, a court is unlikely to second-guess an action taken to facilitate government approval of a merger or a firm's alleged failure to compete hard enough to make good on the short. Moreover, as for a failure to compete hard enough, if a court did entertain a presumably egregious failure to compete under those circumstances, we do not regard liability as a bad thing from a competition standpoint. Indeed, fear of such liability would sharpen the incentive to compete.

Our negative ownership remedy, in all its major forms, relies on incentive effects pegged to shareholder returns. One might be concerned that shareholder returns do not always closely track cash flows over any given period of time. While true, notice that neither the DOJ nor the FTC would ever accept as a defense to an otherwise-anticompetitive merger that the firm was keeping the cash flows of the two entities separate on its balance sheet. This is because, while stock prices move for many reasons other than changes in cash flows, greater profits, in expectation, will increase a firm's stock price more than (or cause it to fall less than) smaller profits.

To be more concrete, the reason stock mergers can be anticompetitive is because corporate governance is designed to minimize agency problems so that managers will make decisions (including setting prices) that maximize shareholder profits. When two competitors have the same shareholders, those shareholders will expect greater returns if the competitors increase their prices above the pre-merger level. The fact that this might not always occur or that sometimes agency problems will affect the shareholders' ability to induce higher prices does not change the fact that ordinarily the managers of the merged competitors will increase prices.

If the antitrust agencies believe, despite other influences on stock prices and managerial agency problems, that joint (positive) ownership of competitors is likely to lead to higher prices, then that same belief should also lead them to believe that negative ownership of other competitors should likely counteract that effect, reducing or eliminating the anticompetitive effect of the merger.

The negative ownership remedy holds promise as a remedial tool in antitrust enforcement. Merger enforcement relies principally on the divestiture remedy, but this remedy is often infeasible or inefficient, resulting in transactions that are blocked, never attempted, or approved on imperfect terms. Our approach offers an additional tool for both parties and enforcers. The various implementations of negative ownership remedies allow regulators to condition approval on contractible proxies for future competitiveness. It is often uncertain at the time of regulatory review whether a merger will be pro-or anticompetitive. But after the fact, the value of competitors' stock can provide important evidence of whether the merger has enhanced competition. By making a firm's future profit (or managers' future compensation) contractually contingent on this variable, regulators can restore pre-merger competitive incentives.

Our remedy allows an efficiency-enhancing merger without incurring the associated anticompetitive effects. It allows regulators to approve more mergers with smaller synergies that would not be approved without negative ownership.

It bears emphasis that this tool is not always available-a limitation that is shared by the divestiture remedy-but as we have shown, it holds promise for real-world mergers. When anticompetitive and efficiency-enhancing actions are intertwined, antitrust enforcers and antitrust counsel should seriously consider the use of negative ownership as a way to benefit from the increased efficiency without sacrificing competition.

Shorting Your Rivals Merging firms and their antitrust counsel do not have to wait until the agencies officially endorse this option on their own. Just as merging parties can "fix it first" by divesting assets to resolve competitive overlaps they expect to be problematic, they can also go to the agencies with a promise to adopt a negative ownership remedy and thereby undo any anticompetitive effect. This would force the agencies to grapple with this remedy. Moreover, such a step would also credibly signal to the agencies that the firms believe that the deal is harmless or beneficial given that they are willingly giving up on the prospect of anticompetitive profits from the deal. Notice, too, that the greater the negative ownership position the firms are willing to take, the more credible this signal becomes.

Finally, the remedy of negative ownership is so versatile that it should be considered for potential application beyond mergers. For example, negative ownership requirements might usefully supplement remedial injunctions to stop fixing prices after a finding of express collusion. But we can even imagine a world where requirements of negative ownership are triggered merely by insufficient industry competition. One of the powerful features of negative ownership is its automaticity. Firms with negative ownership positions in their rivals have an immediate incentive to act more competitively. The law need not stand idly by and accept that in concentrated markets, rivals will inevitably raise price above the competitive level. On the other hand, as we have noted, there are potential difficulties and complications associated with the remedy that make it an imperfect fit in all cases. Further study can address these issues more fully.

To keep the discussion simple, we will discuss the four-firm case, first focusing on the situation in which the only asymmetry is in the substitutability of the products.

For example, if the product of firm 1 (product 1) is a closer substitute to the product of one rival, while firm 2's product is a closer substitute for the other, then we restore pre-merger incentives by requiring a short position in both rivals. Interestingly, it turns out that while the merged firm must have a short position in at least one rival firm, it is possible that for some parameter values they need to take a long position in at least one rival in order to restore pre-merger incentives.

For example, suppose that product 2 is a weaker substitute for both product 3 and product 4 than is product 1. Then the merged firm needs to have a negative ownership position in one of its rivals and a positive ownership position in the other. The merged firm should short the firm that product 2 is a relatively closer substitute for and long the firm that product 1 is a relatively closer substitute for. 127 The reason is that to make sure the merged firm doesn't want to increase the price for product 2, the short position must be quite large in the firm that product 2 is a relatively closer substitute for in order to make up for the fact that it isn't that close a substitute for either firm. This large short position would then lead the merged firm to want to cut price for product 1 unless it has a small long position in the product it is a closer substitute for. Now, consider the effect of asymmetries in the profitability of the firms (in terms of profit margins). As firm 1 becomes more profitable, then the short position in firm 3 becomes larger if and only if product 1 is a relatively closer substitute to product 4 and product 2 is a relatively closer substitute to product 3. 128 Intuitively, if a product of the merged firm becomes more profitable, this increases the incentive of the merged firm to increase the price of its other product in order to drive more sales to the more profitable one. To counterbalance this, we need a larger short position in the firm that this other product is a closer substitute for. 127 More precisely, the merged firm is short firm 3 and long firm 4 if and only if 41 42 31 32 > q q q q whenever firm 41 42 31 32 > > q q and q q . If the second set of inequalities are both reversed, then the merged firm needs to be long firm 3 and short firm 4 if and only if the first inequality is reversed. 128 Again, to put this precisely, by this we mean 41 42 31 32 > q q q q . Analogously, as firm 2 becomes more profitable, then the short position in firm 4 becomes larger if and only if product 1 is a relatively closer substitute for product 4 and product 2 is a relatively closer substitute for product 3.

As firm 3 becomes more profitable, the magnitude of the position (long or short) in firm 3 becomes smaller. 129 This follows because as a rival's profit margin increases, it takes a smaller stake in that firm (negative or positive) to influence the merged firm's pricing decisions. B. A Six-Firm Model of the JetBlue/Spirit Merger In the U.S. airline industry, there are four large carriers (American, United, Delta, and Southwest) and two smaller ones (JetBlue and Spirit). Recently, JetBlue and Spirit proposed a merger (which was subsequently blocked and abandoned). 130 To model how the negative ownership remedy would work in this case, we developed a variant of the standard circular-city model of competition between many firms. 131 In this variant, each firm competes with the other five firms for passengers in the following way. There is a line segment of length one connecting each pair of firms-15 segments in all-and a uniform distribution of passengers on each line segment. For a passenger on a line segment at position x between airlines A and B, the passenger incurs a utility cost (often termed a transportation cost) of tx if they choose to fly on A and t(1-x) if they choose to fly on B in addition to whatever price they might pay. That is, passengers located closer to A have a relative preference for A over B (and the reverse for passengers located closer to B). This preference could be due to having status on one airline as opposed to another, an airline having more convenient times for that passenger, or anything else. These passengers could also choose to fly on any of the other four airlines, but to do so, they would incur a larger transportation cost of t(1+x) or t(2-x) because for passengers on the segment between A and B, the "distance" to any other airline requires them to "go through" A or B to reach them. If these other airlines' prices were low enough, this could happen, but in our equilibrium it will not. Thus, a passenger at position x from A on the line segment between A and B will buy from A if and only if:

In this inequality, v i is the value that flying on airline i provides to all customers, and p i is the price. Thus, the consumers that buy from A between A and B are those with:

129 Analogously, as firm 4 becomes more profitable, the magnitude of the position (long or short) in firm 4 becomes smaller. 130