Eur J Law Econ DOI 10.1007/s10657-012-9330-7
Merger settlement as a screening device Juwon Kwak
Springer Science+Business Media, LLC 2012
Abstract This article presents an economic model of judicial settlement in an asymmetric information setting to analyze the merger settlement between merging firms and a competition authority. The model analyzes how the competition authority may use the settlement process to screen out efficient mergers from inefficient ones. Because of the self-selection among merging firms, efficient mergers may be litigated in court, whereas inefficient mergers may be settled before going to trial. We further analyze the role and the effect of the second request in a merger settlement. Keywords Merger settlement Hart–Scott–Rodino Act Merger Regulation 4064/89 Second request JEL Classification
L41 K21 K41 K42
1 Introduction Most merger disputes between merging firms and the competition authority are solved by merger settlements. In the European Union, under Merger Regulation 4064/89 Art. 8(2), the European Commission ‘‘may attach to its decision conditions and obligations intended to ensure … the commitments.’’ In 2010, out of 18 challenges made by the European commission, 14 were settled (compatible with commitments) in the first phase and two were settled during the second phase (European Commission, Statistics 2010).1 In the United States, under the 1
Out of 274 cases notified, 253 cases were determined to be Art 6.1(b) compatible. Fourteen cases were determined to be compatible with Art. 6.1(b) in conjunction with Art. 6.2 (compatible with
J. Kwak (&) 26 Jang gun maeul 3 gil, Gwacheon-si, Gyenggi-do, Juam-dong, South Korea e-mail:
[email protected]
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Hart–Scott–Rodino Act 15 U.S.C. § 18a, the Department of Justice (DOJ) and the Federal Trade Commission (FTC) practically have the authority to settle consent decrees with merging firms. Out of 37 challenges made either by the DOJ or the FTC in 2008, 34 were solved either by consent decree or by restructuring (Federal Trade Commission 2008).2 In this respect, for the competition authority, merger settlement is the key regulatory instrument concerning merger control. Despite the importance of merger control, only a limited number of studies have focused on the economic implication of merger settlements. Moreover, most of the prior works simply attempted to defend either side of the dichotomy between lenient and strict merger control. For example, Sims and McFalls (2001) argue that negotiated merger remedies are too intrusive and that the principle of minimal intrusion must be observed, whereas Frankel (2008) argues that the current merger control is too lenient. Many empirical studies have focused on the economic effects of merger control. The results of these studies are inconclusive, and some of the results seem shockingly different from our basic intuition. For example, Crandall and Winston (2003) show that mergers that have been challenged by the competition authority but allowed by the court decreased price-cost margins in US manufacturing industries, whereas mergers settled by consent decrees increased it. From this empirical result, they argue that a merger settlement may change efficient mergers to inefficient ones. This work uses the screening model in an asymmetric information setting to analyze the merger settlement process and indicates how selfselection can explain this empirical puzzle.3 This article is most closely related to Cosnita and Tropeano (2009) and Gonzalez (2008). Cosnita and Tropeano (2009) attempts to find a revelation mechanism combining divestures with two additional tools, which are the regulation of the disvestures sale price and merger fee. Gonzalez (2008) proposes a revelation mechanism in two markets setting. The biggest difference between this article and these former works is that the former works try to find a revelation mechanism, where as this article does not. However, this article tries to analyze the economic impacts of various preexisting policies, such as the role of the court and the second request, which have never been analyzed before.
Footnote 1 continued commitments). Four cases went to the Second Phase and two were determined to be Art. 8.2 compatible with commitments. 2
The difference between restructuring and consent decree is not significant. Restructuring means a settlement that was agreed upon before a complaint was filed, and a consent decree means a settlement made during the litigation proceeding.
3
This paper uses settlement models developed in law and economics to analyze the merger settlement process. There are two types of settlement models: one is the differentiated belief model and the other is the screening model. The former assumes that neither plaintiff nor defendant have superior information but only different information, leading to different beliefs about the outcome of the litigation. In contrast, the screening model assumes asymmetric information. See Gould (1978), Landes (1971), and Cooter (1989) for the differentiated belief model. See Bebchuk (1984) and Nalebuff (1987) for the screening model.
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Section 2 introduces the model. Section 3 analyzes the settlement process where there is no second request, and Sect. 4 inserts the second request process into the model. Section 5 presents the conclusion.
2 Model Imagine a situation in which the Competition Authority (CA) has received an application for the approval of a merger. The CA has three choices. First, it can enjoin the merger. Second, it can allow the merger. Third, it can propose a remedy settlement. When the CA enjoins the merger, the merging firms (MFs) can either challenge the denial in the court, or give up the merger. If the CA proposes a settlement remedy, then the MFs can accept the settlement proposal, challenge it in the court, or abort the merger. The CA and the MFs will make their decisions based on the characteristics of the merger in question. Let x be the characteristic of the merger, which denotes the gain in market power by the MFs due to the merger. Although there can be other variables that affect the characteristic of the merger, we assume that the market power is the most important factor. Furthermore, we assume that the profit gained by the merger is PðxÞ ¼ x. Therefore, x is the gain of market power normalized to the gain of the MFs’ profit. We call this variable x, the Structure of Merger. We further assume that MFs can freely structure the merger so that they can fully control the value of x. The assumption that PðxÞ ¼ x implies that the profit is independent of the type of the merger (PL ðxÞ ¼ PH ðLÞ, where subscript L and H denote the type of the merger and it is defined below), but one may argue that this assumption is unrealistic. In Appendix 1, we assume PL ðxÞ 6¼ PH ðxÞ and show how the result may change qualitatively in few cases. Let us assume that the value of x is common knowledge to the CA and MFs, but the welfare effect of the merger Wi(x), where i 2 fL; Hg, is only known to the MFs and is hidden from the CA. We call MFs with i = L, L-type MFs and those with i = H, H-type MFs. Let WH(x) [ WL(x) for every x. Hence, L-type mergers produce less social welfare than do H-type mergers. Let us further assume that Wi is a decreasing function of x so that as market power increases, social welfare decreases. One may justifiably argue that MFs do not have more information concerning the welfare effect compared to the CA. However, there exists some justification for the information asymmetry assumption. Controversies over merger control typically are about two issues. First, many issues in merger control cases are about the market power to be gained through the merger. Because the nature of the issue involves market structure analysis, MFs and the CA have no more information about the nature of the merger than the other. This factor is why we have assumed that x is a variable that is observable by both parties. However, MFs generally have more information about the efficiency effect of the merger. 4 For this reason, we assume that the MFs has more information than the CA. 4 Note that Federal Trade Commission (2010) explicitly acknowledges that ‘‘ … much of the information relating to efficiencies is uniquely in the possession of the merging fimrs.’’ This is why the burden of
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Although the CA cannot observe i, they know the ex-ante distribution of i. Let r be the probability that the merger is an L-type, and 1 - r be the probability that the merger is an H-type. If the merger is litigated, the court can discern an H-type from an L-type with the probability P 2 ð1=2; 1Þ. A trial will cost CA for the CA and C for the MFs. CA maximizes the aggregate social welfare minus the litigation cost. However, we assume that CA cannot ask MFs to change a competitively neutral merger to a procompetitive merger. We further assume that the court adjudicates based on an initial merger proposal by the MFs rather than on the settlement offer by the CA. A merger settlement proceeds in the following order: •
•
•
Stage 1: Initial proposal The MFs apply for the approval of the merger. We call this the Initial Proposal. Let y be the value of x that is initially proposed by the MFs. Stage 2: Merger settlement offer Let xi be the value of x that satisfies Wi(xi) = 0. As we assumed earlier, for any given x, WH(x) [ WL(x) and Wi is a decreasing function of x. Therefore, xH [ xL. Let us call xi the Competitively Neutral Level of Market Power. Suppose the initial proposal results in the market power, y B xL. The merger is either competitively neutral or procompetitive. As we assumed, the CA allows the merger and the process stops here. If y [ xH, then it is certain that the merger is anticompetitive; hence, we assume that the CA enjoins the merger without proposing a settlement remedy. One may argue that the CA may ask MFs to engage in procompetitive mergers when y B xL, or propose a merger settlement when y [ xH. Although such possibility might be true, these assumptions are only introduced to simplify the analysis and to focus on the range of y that is most interesting. The result of the model does not differ qualitatively without these assumptions. When y 2 ðxL ; xH , the welfare of the merger is unknown to the CA. If it is an H-type merger, then the merger is procompetitive, but if it is an L-type merger, then it is anticompetitive. In this case, the CA has three choices: it can enjoin the merger, allow it or propose a merger settlement to divest some of the asset so that market power (x) decreases from y to z. Let us call z the Settlement Proposal. As we assumed earlier, CA cannot knowingly ask MFs to change a competitively neutral merger to procompetitive merger: if CA knows i = H, then it cannot offer z \ xH, or if i = L then z \ xL. Stage 3: Offer acceptance or rejection If a merger settlement is proposed at Stage 2, then the MFs must decide whether to accept the offer, reject it or give up the merger. If the merger is enjoined, then they must decide whether to challenge it or abort the merger.
Footnote 4 continued proving the efficiency effect falls upon the MFs rather than the CA. FTC v. University Health, 938 F.2d 1206, 1222 (11th Cir. 1991). Also note that many previous literature also assumed that MFs have more information than CA (Cosnita and Tropeano 2009; Lagerlo¨f and Heidhues 2005).
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•
Stage 4: Court decision If the MFs challenge the CA’s decision at Stage 3, the court adjudicates on the initial offer, y. The probability that the court identifies the true type of the merger is P; thus, if the merger is an H-type, then the court will identify the merger as an H-type with probability of P, and if the merger is an L-type, then the court will identify the merger as an H-type with probability of 1 - P.
3 Merger settlement without a second request The merger settlement process presented in the previous section is a finite dynamic game. In this section, we derive the Nash equilibrium of the game through backward induction and analyze the economic implication of the equilibrium. Stage 4: Court decision If the initial proposal by the MFs, y, satisfies y B xL, then the court will allow the merger with probability 1 because regardless of the type of merger, the merger will be at least competitively neutral. If y [ xH, then the court will enjoin the merger with probability 1 because it is anticompetitive. When xL \ y B xH, the court must determine the type of the merger. If the court determines that the merger is an H-type, then the merger will be allowed, and if it determines that the merger is an L-type, then the merger will be enjoined. Therefore, an H-type merger will be allowed with probability P, and an L-type merger will be allowed with probability 1 - P. Stage 3: Acceptance or dejection Suppose that the merger is enjoined at Stage 2. The MFs can decide whether to challenge it. If they litigate, then their expected profit is Pr(winning)y - C, where Pr(winning) is the probability of the MFs winning in court. Therefore, they will challenge the merger only if Pr(winning)y is larger than C. If y [ xH, then Pr(winning) is 0, so the MFs will never challenge the merger. If y B xL, then Pr(winning) = 1, and the MFs will challenge the merger only if y [ C. If y 2 ðxL ; xH , then for L-types, Pr(winning) = 1 - P and for H-types, Pr(winning) = P. The L-type MFs will litigate only if (1 - P)y [ C and the H-types MFs will do so only if P y [ C. Suppose that a merger settlement is proposed at Stage 2. The MFs will compare the expected profit of litigation and the expected profit of accepting the settlement offer. Therefore, they will accept the settlement offer if and only if z PrðwinningÞy C
ð1Þ
We adopt a tie-breaking rule that the MFs will always accept the settlement proposal if the expected profits are equal. Stage 2: Merger settlement offer For any merger proposal y B xL, the CA will allow the merger because the merger is at least competitively neutral. If the structure of the proposed merger is such that y [ xH, then the merger is definitely anticompetitive; thus, the CA will enjoin the merger.
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When y 2 ðxL ; xH , the CA can either enjoin the merger, allow the merger or propose a merger settlement. Suppose that the CA offers a merger settlement to reduce market power x from y to z. The MFs will accept the offer if and only if Eq. 1 is satisfied. For L-type MFs, Pr(winning) = 1 - P and for H-types, Pr(winning) = P. L-type MFs will accept any offer equal to or larger than (1 - P)y - C, and H-types will accept any offer equal to or larger than P y C. Therefore, if the CA proposes a settlement for y 2 ðxL ; xH , then they have two different strategies. If they offer P y C, then all of the MFs will accept the offer. If they offer ð1 PÞ y C, then only L-type MFs will accept it. The social welfare effects are r WL ðP y CÞ þ ð1 rÞWH ðP y CÞ or r WL ðð1 PÞ y CÞ þ ð1 rÞP WH ðyÞ respectively. Because the merger proposal increases with y and the probability of winning is the same for all y 2 ðxL ; xH , both types of MFs will propose the upper bound of the range, which is xH. This result will be reviewed more thoroughly when we analyze Stage 1. When y = xH, the social welfare effects become either r WL ðP xH CÞ þ ð1 rÞ WH ðP xH CÞ or r WL ðð1 PÞ xH CÞ þ ð1 rÞP WH ðxH Þ ¼ r WL ðð1 PÞ xH CÞ. Therefore, the CA will either propose z = (1 - P)xH - C or z ¼ P xH C. If (1 - P)xH - C is proposed, then only L-types will accept the offer, and H-types will be screened out. We call this strategy the S-Strategy. If the CA offers z ¼ P xH C, then L-types are pooled together with H-types. We call this the P-Strategy. For reference, let xP ¼ P xH C and xS = (1 - P)xH - C. Definition 1 Let xP ¼ P xH C and xS = (1 - P)xH - C. If the CA proposes z = xP for y = xH, then we call this a P-Strategy. If the CA proposes z = xS for y = xH, then we call this an S-Strategy. Suppose that xL \ð1 PÞ xH C. Because ð1 PÞ xH C is the smallest possible profit obtainable by proposing xH for both types of MFs, all of the MFs will propose xH, resulting in a trivial result. Therefore, let us assume that ð1 PÞ xH C\xL . However, if xL [ P xH C, then no MFs will propose xH because P xH C is the largest possible profit obtainable by proposing xH. To rule out these trivial results, let us assume that ð1 PÞ xH C\xL \P xH C. Note that the first inequality guarantees litigation by both types of MFs when the merger is challenged. Assumption 1 0\xS ¼ ð1 PÞxH C\xL \xP ¼ P xH C One may argue that if the CA is proposing xS, then the CA is asking the MFs to engage in a procompetitive merger rather than a competitively neutral merger by sacrificing their profit. Because the CA may not demand the MFs to sacrifice their profit, they may argue that the lower bound of the settlement proposal should be xL. Even if we accept this argument, as long as there is a cost incurred by the settlement process, the result of the model does not differ qualitatively.
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If the CA allows the merger, then the expected social welfare is r WL ðyÞ þ ð1 rÞWH ðyÞ. Note that the expected social welfare that is accomplished by allowing the merger is strictly smaller than the expected social welfare of proposing z ¼ P y C. Therefore, the CA will never allow the merger. If the CA enjoins the merger, let us assume that challenging the merger is profitable for both types of MFs, which is guaranteed by the first inequality of Assumption 1. Because the probability of winning does not differ by y, as long as y 2 ðxL ; xH , all of the MFs will propose y = xH. When both types of MFs challenge the merger, the expected social welfare is rð1 PÞ WL ðxH Þ þ ð1 rÞP WH ðxH Þ CA ¼ rð1 PÞ WL ðxH Þ CA . Under Assumption 1, because WL(xS) is strictly positive whereas WL(xH) is strictly negative, following condition holds: r WL ðð1 PÞ xH CÞ þ ð1 rÞ½P WH ðxH Þ CA ¼ r WL ðð1 PÞ xH CÞ ð1 rÞCA [ rð1 PÞ WL ðxH Þ CA Therefore, an S-Strategy increases the social welfare relative to enjoining the merger. Therefore, we have Lemma 1. Lemma 1 For any merger with y 2 ðxL ; xH ; the CA will always propose a merger remedy, z. Stage 1: Initial proposal Suppose that the MFs propose y B xL. In such a case, the social welfare effect of the merger is non-negative regardless of the type of the merger. Therefore, as analyzed at Stage 2, the CA will allow the merger. Because the profit increases with y, they will choose the largest possible y, which is xL. Suppose that the MFs propose xL \ y B xH. If the merger is allowed, then the MFs will propose the largest possible y, which is xH. If the merger goes to trial, then the expected profit is Pr(winning)y - C. Because Pr(winning) does not change within the given range of y, the MFs will choose the largest possible y, which is xH. As proved by Lemma 1, as long as xL \ y B xH, either P y C or (1 - P)y - C will be proposed as a merger settlement at Stage 2. Therefore, the MFs can induce the largest possible settlement offer by choosing y = xH. Therefore, as long as xL \ y B xH, both types of MFs will propose y = xH. Suppose that the MFs propose y [ xH, then both the CA and the court will enjoin the merger; hence, no MFs will propose y [ xH. Last, let us analyze the dominant strategy of the MFs. For all of the H-types, if they propose y = xH, the expected profit is xP ¼ P y C. By Assumption 1, it is always more profitable for H-types to choose y = xH. However, for L-types, if they choose y = xH, then their profit can be either xP or xS. By Assumption 1, if the CA adopts a P-Strategy, then y = xH dominates y = xL, but if the CA adopts an S-Strategy, then the opposite occurs. Therefore, no dominant pure strategy exists for L-type MFs. From the analysis presented above, we have Lemma 2.
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Lemma 2 H-type MFs always propose y = xH. L-type MFs can either propose y = xL or y = xH. When the proposed merger is y = xH, then the CA can either adopt an S-Strategy, z ¼ ð1 PÞ xH C; or a P-Strategy, z ¼ P xH C: When the proposed merger is y = xL, then the CA will allow the merger without a challenge. Lemma 2 states that L-type MFs have two pure strategies: y = xL or y = xH. From the view point of the CA, because all H-type MFs choose y = xH, if MFs propose y = xL, it is an indication that the merger is an L-type. However, if the proposed merger structure is y = xH, then the CA cannot discern a competitively neutral merger of H-type MFs from anticompetitive mergers of L-types. Therefore, if L-type MFs propose y = xH, then they are mimicking H-type MFs. If the initial proposal is y = xH, then the CA can choose one of two strategies: they can either separate L-types and H-types by proposing a merger settlement z = (1 - P)xH - C = xS (S-Strategy) or pool both types together by proposing a settlement condition z ¼ P xH C ¼ xP (P-Strategy). From the second and third inequality of Assumption 1, when the CA adopts an S-Strategy, it is more profitable for the L-types to truthfully reveal their type by proposing y = xL. However, if the CA adopts a P-Strategy, then L-types can earn more by mimicking H-types. Therefore, the CA faces a dilemma. If the CA adopts an S-Strategy, then all of the L-types will truthfully reveal their type; hence, there exists no reason to adopt an S-Strategy. However, if CA switches to a P-Strategy, then all of the L-type MFs will start to mimic H-types; hence, the CA has to switch to an S-Strategy. This scenario is only true under certain conditions. If the cost of litigation is too large relative to the negative social welfare effect of L-type MFs mimicking H-types, then the CA would not switch to an S-Strategy. This condition can be reduced to Assumption 2. Assumption 2 r½WL ðxS Þ WL ðxP Þ [ ð1 rÞ½WH ðxP Þ þ CA LHS is the welfare gain of switching from a P-Strategy to an S-Strategy, which is the reduction of negative social welfare produced by L-type MFs. However, there is a cost incurred because litigation with H-type MFs is required. If the merger with H-type firms goes to trial, then the market power allowed to H-type MFs will be xH instead of xP. Thus, the CA is giving up the opportunity to induce H-type MFs to agree on a welfare-increasing merger. Also, there is a cost of litigation for the CA. The sum of these costs is the RHS of the equation. Therefore, the CA has an incentive to switch to an S-Strategy if and only if the welfare gain is larger than the welfare loss. Lemma 3
Under Assumption 2, there is no pure strategy Nash equilibrium.
Proof Suppose that the CA is adopting a P-Strategy; the L-type MFs will mimic H-types by proposing y = xH, and the expected social welfare effect of the merger
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will be r WL ðxP Þ þ ð1 rÞWH ðxP Þ. If the MFs switch to an S-Strategy, then the expected social welfare effect is r WL ðxS Þ þ ð1 rÞ½P WH ðxH Þ CA . Because WH(xH) = 0, this effect reduces to r WL ðxS Þ ð1 rÞCA . Therefore, they will be incentivized to switch if and only if r½WL ðxS Þ WL ðxP Þ [ ð1 rÞ½WH ðxP Þ þ CA Note that this condition is equivalent to Assumption 2. Now let us prove that the S-Strategy is not a Nash equilibrium. Suppose that the CA adopts an S-Strategy. As mentioned above, all of the H-type firms will propose xH, and because of Assumption 1, all of the L-type firms will propose xL. Note that because the CA is adopting an S-Strategy for y = xH, they will propose z = xS, which will be rejected by all of the H-type firms. In such a case, the social welfare will be r WL ðxL Þ þ ð1 rÞ½P WH ðxH Þ CA However, if the CA switches to a P-Strategy, then the social welfare will be r WL ðxL Þ þ ð1 rÞ WH ðxP Þ Therefore, the CA always has an incentive to switch from an S-Strategy to a P-Strategy, and an S-Strategy is not a Nash equilibrium. h Because there is no pure strategy Nash equilibrium, let us find the mixed strategy Nash equilibrium. Let l be the mixed strategy of L-type MFs, where l is the probability of truthfully revealing its type (y = xL) and 1 - l is the probability of mimicking H-type firms (y = xH). When l is either 0 or 1, the mixed strategy becomes a pure strategy. Also, let k be the mixed strategy of the CA, where k is the probability of adopting an S-Strategy and (1 - k) is the probability of adopting a P-Strategy. The social welfare function (S(k)) and the profit function of L-type MFs (PðlÞ) are SðkÞ ¼ r l WL ðxL Þ þ k½rð1 lÞWL ðxS Þ ð1 rÞCA þ ð1 kÞ½rð1 lÞWL ðxP Þ þ ð1 rÞWH ðxP Þ PðlÞ ¼ l xL þ ð1 lÞ½k xS þ ð1 kÞxP
ð2Þ ð3Þ
First, consider the social welfare function. The first term of Eq. 2 is the social welfare produced by L-type MFs who propose xL. The second term (k[r(1 - l) WL(xS) - (1 - r)CA]) is the welfare produced by adopting an S-Strategy. Among those who propose y = xH, r(1 - l) of them are L-type MFs and (1 - r) of them are H-type MFs. Therefore, when the CA adopts an S-Strategy (proposes z = xS), r(1 - l) of them, who are L-type MFs, will accept the settlement offer and produce WL(xS) [ 0 social welfare. However, (1 - r) of them, who are H-type MFs, will refuse the remedy proposal and go to trial. If they win, they will be allowed a competitively neutral concentration level xH; thus, they produce no positive social welfare. If they lose, they will not be able to engage in the merger. In either case, they will produce no social welfare. However, the CA has to spend a litigation cost, CA. The third term ((1 - k)[r(1 - l)WL(xP) ? (1 - r)WH(xP)]) is the welfare
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produced by adopting a P-Strategy. When the CA adopts a P-Strategy, all of the MFs will accept the proposed remedy, and the L-types will produce a social welfare WL(xP), whereas H-types will produce a social welfare of WH(xP). Now let us turn our attention to the profit function. If the L-type MFs truthfully reveal their type, they will earn xL without any risk. If they mimic H-types and propose y = xH, they will earn xS with probability of k and xP with probability of (1 - k). By solving Eqs. 2 and 3, we have the following proposition. Proposition 1
There exists a unique mixed strategy Nash equilibrium: k¼
xP xL 1 r CA þ WH ðxP Þ and l ¼ 1 P S r WL ðxS Þ WL ðxP Þ x x
By Assumption 1 and by Assumption 2, we know that k; l 2 ð0; 1Þ. When the CA adopts an S-Strategy, the social welfare is reduced in two ways: first, there are litigation costs, CA. Second, the CA cannot induce H-types to accept a more welfare-increasing value of x. However, by adopting an S-Strategy, the CA can deter the L-types from engaging in anticompetitive mergers. This effect is often called the Deterrence Effect. The CA will compare the deterrence effect with the social waste of adopting an S-Strategy and determine the value of k. The value of k indicates how often the CA adopts an S-Strategy; hence, it is an index of the strictness of the merger settlement offer. Note that it is an increasing function of both xP and xS. Both xP and xS increase the expected profit of L-type MFs mimicking H-type MFs. Therefore, if both values increase, then the CA should focus more on deterring L-types from engaging in anticompetitive merger by increasing the value of k. One interesting result is that the social welfare effect of mergers that are concluded by settlements can be lower than the effect of mergers that end up in the court. All of the merger cases that end up in the court are H-types, and if allowed, the social welfare effect is WH(xH) = 0. The mergers that are settled involve either L-type or H-type mergers. The L-type mergers, which are settled with xP, produce a negative social effect. The overall social welfare effect of mergers settled is k r ð1 lÞWL ðxS Þ þ ð1 kÞ½rð1 lÞWL ðxP Þ þ ð1 rÞWH ðxP Þ, which can be negative for sufficiently small WL(xP). Therefore, if the negative social welfare effect of an L-type merger with a structure of x = xP is sufficiently large, then the overall social welfare effect of settled mergers can be negative; thereby, the aggregate social welfare effect of settled mergers is lower than the social welfare effect of litigated mergers. By Proposition 1, the social welfare effect of negotiating merger remedies is negative if and only if WL ðxP Þ\WL ðxS Þ
CA ðxL xP Þ þ WH ðxP ÞðxS xP Þ \0 CA ðxL X S Þ
Proposition 2 If WL(xP) is sufficiently small, then the social welfare effect of settled mergers can be smaller than the social welfare effect of litigated mergers.
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Crandall and Winston (2003) observed that unsuccessful merger challenges decrease price-cost margins in the U.S. manufacturing industries but that consent decrees (divestitures) increase them. From this empirical result, they assert that the merger settlement process is anticompetitive. However, they overlooked the possibility of self-selection. As indicated by this model, those MFs who believe that the merger is procompetitive will be more likely to litigate, whereas anticompetitive mergers will end up in a settlement. This difference in behavior originates from the difference in the probability of winning in court. Therefore, this empirical result does not indicate that the merger settlement is an inefficient social policy. Alternative social policies may induce less efficient outcomes. For instance, as proved in the previous section, allowing every merger, the structure of which falls in the range of y 2 ðXL ; xH , always induces a less efficient outcome than does a P-Strategy. If Assumption 1 does not hold, enjoining every mergers might be more efficient policy. When xL B (1 - P)xH - C, every L-type MFs will mimic an H-type MF. Therefore, it is necessary to adopt a stricter strategy; in some extreme cases, S
Þ . enjoining every merger is the socially optimal policy. Suppose P [ 1 WLWðxLHðxÞC A This condition indicates that if the court decision is sufficiently accurate, the CA should enjoin all mergers because it is better for the CA to shift the responsibility for the decision to the court. Sims and McFalls (2001) assert that the current practices of the CA are overly intrusive. This over-intrusion originates from the superior bargaining power of the CA during the settlement process. Therefore, they recommend that we should prohibit the CA from entering into a consent decree and force agencies to challenge only those transactions for which they are prepared to seek a litigated injunction. Let us call this the no-settlement policy. They believe that the no-settlement policy will lead to a less intrusive practice. The no-settlement policy results in more efficient outcome under two conditions. First, the problem of the L-type MFs is sufficiently serious. Second, the court’s decision must be accurate enough that the CA should shift the burden of decision to the court. Under these two conditions, the no-settlement policy leads to more efficient results. However, the rationale provided for the no-settlement policy in this paper is opposite to the rationale provided by Sims and McFalls. When mimicking is sufficiently profitable for L-type MFs, the CA should adopt a stricter policy. It can involve adopting an S-Strategy more often or litigating every merger (no-settlement policy). However, the no-settlement policy is the most -intrusive of the alternative policies.
4 Merger settlement without a second request Under the current US and European competition law, the CA can issue additional requests for information after the initial review period, commonly known as the second request. In this section, we plug the second request process into the model presented above. For this purpose, let us remodel Stage 2.
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At Stage 2, if y = xL, then the CA allows the merger, but if y = xH, then the CA asks for the second request. After evaluating additional information, the CA receives a signal j, where j = i with probability q 2 ð1=2; 1Þ and j = i with probability 1 - q. Thus, q is the accuracy of the evaluation. If j = H, then we call the state an H-State, and if j = L, then it is an L-State. Therefore, the CA can adopt a different mixed strategy depending on the state of the outcome. Let kj be the probability of the CA adopting an S-Strategy under a j-State. Therefore, we can easily predict that when signal j is H, the CA is more likely to adopt a P-Strategy and vice-versa when j equals L, i.e., kL [ kH. The tendency to rely on the signal j to determine the value of kj should be related to the accuracy of the signal, q. If the signal is not very accurate (q has a low value), then L-type MFs will be more likely to mimic H-types. Therefore, the CA should adopt an S-Strategy more often to deter the L-types from mimicking H-types. However, if the signal is accurate, then L-type MFs are less likely to mimic H-types. Hence, the CA is more likely to adopt a P-Strategy. Proposition 3
If q
xP xL xP xS
then the mixed strategy Nash equilibrium is
ð1 rÞ ðCA þ WH ðxP ÞÞ q S P r ðWL ðx Þ WL ðx ÞÞ ð1 qÞ ð1 qÞxP þ q xS xL kL ¼ 1 and kH ¼ : ð1 qÞðxP xS Þ l¼1
If q [
xP xL xP xS
then, it is ð1 rÞ ðCA þ WH ðxP ÞÞ ð1 qÞ r ðWL ðxS Þ WL ðxP ÞÞ q P x xL kL ¼ and kH ¼ 0: qðxP xS Þ l¼1
Proof
See Appendix 2.
h
If the information obtained by the second request process is sufficiently accurate, P L (q [ xxP x xS ), then the CA should adopt a P-Strategy more often than an S-Strategy. However, if the second request is not sufficiently accurate, then the opposite should occur. We call the former the Loose Equilibrium and the latter, the Strict Equilibrium. This result is not surprising. As previously mentioned, if the signal is not very accurate (q has a low value), then L-type MFs will be more likely to mimic H-types. Therefore, the CA should adopt a stricter position. However, if the signal is accurate, then L-type MFs are less likely to mimic H-types and the CA is more likely to adopt a P-Strategy. It is trivial to show that if and only if there is no cost related to the second request process, the second request policy is always the optimal policy. However, if there is a cost related to the second request, then the CA will have to balance the cost and the benefit of the second request by requiring that the second request policy apply only to some MFs, the initial proposal of which is xH.
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As argued by Sims and McFalls (2001), the MFs solely bear the burden of the cost of this process. Therefore, there is a large possibility of the CA abusing the second request process: the CA asks for a second request even when the cost outweighs the benefit. There are two alternative policies to resolve this problem. First, the CA may share some of the cost of the second request. However, this alternative requires the MFs to truthfully reveal the cost of producing information. Therefore, the MFs might exaggerate the cost of a second request as a deterrent. A second alternative is to give the MFs the right to refuse a second request. If the second request is refused, then the CA must obtain a court order to force a second request. The court will evaluate the overall social cost and benefit of a second request and decide to allow or to prohibit it. Because the second request is similar to discovery process, this alternative seems more reasonable.
5 Conclusion The first contribution of this paper is to develop a rigorous economic model to explain the merger settlement process. Second, we use this simple economic model to show how self-selection can cause the empirical puzzle that was presented by Crandall and Winston (2003). Therefore, although an individual settlement may result in an inefficient outcome, the overall deterrent effect is still welfare increasing. If the competition authority has full information about the true nature of the merger, then the deterrence effect of the settlement process can be maximized without any social cost. However, when the competition authority has limited information, the competition authority can only deter inefficient mergers from mimicking efficient ones by adopting a stricter strategy, resulting in more court challenges. Therefore, merger litigation is the cost society must pay for deterring inefficient mergers.
Appendix 1: When PL ðxÞ 6¼ PH ðxÞ The result of this paper depends on the assumption that H-type MFs are more willing to litigate in the court than the L-type MFs. However, if this assumption is relaxed and the profit gain produced by the merger differs (PL ðxÞ 6¼ PH ðxÞ), then the qualitative result may change. The profit gain (or loss) produced by the merger can depend on several different factors. More specifically, there are largely two factors that affect the size of the profit: first, the market power and second, the efficiency gain produced by the merger. In this section, we analyze how each factor may affect the qualitative result of this paper. The market power: unilateral effect and the coordinated effect The first factor that affect the profit gain is the increase in the market power produced by the merger. Many economists and competion authorities may agree that this factor can be divided into two different effects: the unilateral effect and the coordinated effect (Federal Trade Commission 2010). The former refers to the case
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where the market power increases because the competition between two merging firms is eliminated. In this case, the market power will highly depend on the structure of the merger (x) which is a common knowledge. Therefore, if we only consider this effect, the assumption that PL ðxÞ ¼ PH ðxÞ is not so unreaslitic. For example, suppose x represents the divesture ratio of a merger. Unilateral effect of the merger is highly correlated with the divesture ratio (x), therefore, the assumption that PðxÞ is linearly correlated with x is not unrealistic. Now, let us consider the coordinated effect. A merger can allow firms to coordinate collusion more easily, and in turn, increase profit but reduce social welfare. This effect will not only depend on the structure of the merger, but also on other factors such as the history of the interaction among firms in the industry. This kind of history may be hidden information of the MFs so that it is not reflected in the common knowledge (x). The stronger the coordinated effect is, the higher the profit but lower the social welfare. Therefore, in such a case, the assumption that PL ðxÞ [ PH ðxÞ is more realistic. However, even if we adopt this assumption, the qualitative result of this paper only changes in a few special cases because the willingness to litigate depends on the difference in the expected profit of litigation and the expected profit of settlement rather than on the expected profit of litigation alone. Let us consider a simple case where the profit difference PL PH is independent of x. To simplify the problem, let us assume that PL ðxÞ ¼ x þ p whereas PH ðxÞ ¼ x (p [ 0) so that PL ðxÞ [ PH ðxÞ. Let us further define xL and xH as the smallest settlement offer (z) L-type and H-type are willing to accept, so xL = (1 - P)xH - C - (2P - 1)p and xH ¼ xP ¼ P xH C. Note that xL \ xS, which indicates that the L-type firms’ willingness to actually accept the settlement offer will increase when PL ðxÞ [ PH ðxÞ. The difference in willingness to litigate between H-type MFs and L-type MFs does not depend on the size of the profit of litigation but on the difference between expected profit of litigation and settlement. This difference mainly depends on the probability of winning in the court. Moreover, when there is a profit gain, MFs are less likely to litigate because if they litigate the expected profit decreases by (1 - P)p, which denotes the risk of loosing the profit gain, p. Therefore, the opportunity cost of litigation increases. The only case where the result of the paper can differ qualitatively is when the profit difference (p(x)) increases with x (p0 (x) [ 0). In this case, xL will satisfy xL ? p(xL) = (1 - P)[xH ? p(xH)] - C and xH ¼ xP ¼ P xH C. There can be three different results depending on the value of xL. The first case is when xL \ xL. In this case, it is trivial that the incentive structure of each MFs have not changed, therefore, the qualitative result remains unchanged. Now, we will concentrate on case where xL C xL. First, suppose xL B xL \ xH = xP. Since all MFs will gain more by initially offering y = xH, i.e., all MFs will initially propose y = xH in Stage 1. In this case, the strategy set available to CA is simple. CA can offer xL, which H-type will reject and L-type will accept, or they can offer xH, which both types will accept. CA will weigh between the litigation cost and welfare gain produced by screening out L-type
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MFs. More precisely, if and only if litigation cost CA is large enough so that (1 - r) CA [ r(WL(xS) - WL(xP)) - (1 - r)WH(xP), CA will offer xP to avoid costly litigation. Second, suppose xL C xH. In this case, L-type MFs are more willing to litigate than H-type MFs. Since the willingness to litigate is reversed, CA will have to propose more to L-type MFs to settle. Although the litigation incentive has been reversed, CA still has to weigh between the litigation cost and the welfare gain produced by screening H-type MFs. More preceisely, if and only if the litigation cost CA is large enough so that r CA [ ð1 rÞ½WH ðxP Þ WH ðxL Þ þ r½ð1 PÞ WL ðxH Þ WL ðxL Þ, CA will offer xL to avoid costly litigation. The case where p0 (x) [ 0 is when the profit of L-type merger increases more rapidly with x as compared to H-type merger. For example, suppose one of the merging firms is a maverick in the industry. In this case, the elimination of this maverick can substanitally increase the overall profit of the industry because it can now allow firms to collude. However, if MFs have to divest a substantial portion of the asset so that a new maverick is highly likely to emerge, the profit produced by the merger will decrease sharply. In such a case, the socially inefficient L-type MFs will litigate more aggressively, and the merger settlement procedure may not be able to function as a screening device. The efficiency gain The second factor that affects profit of a merger is the efficiency gain. In this case, the merger will increase profit as well as social welfare, therefore, it is realistic to assume x ¼ PL ðxÞ\PH ðxÞ ¼ x þ p. In this case, the incentive structure reverses. The opportunity cost of litigation for H-type MFs increases, so they are more likely to accept a smaller settlement offer. (z ¼ xH ¼ P xH CA ð1 PÞp). The qualitative result will change when xH \ xL because now H-type MFs can earn less from litigation as compared to initially offering xL. Therefore, both L-type and H-type MFs will offer xL at the initial stage and CA will accept such an offer. If there is a large efficiency gain produced by the merger and that efficiency gain does not depend on the structure of the merger, then MFs will initially design the merger so that there is no risk that CA will challenge the merger. However, this result can also change if the efficiency gain is strongly correlated to the structure of the merger. In such a case, the H-type MFs will aggressively litigate to defend this effect; therefore, the settlement procedure will still function as a screening device and the qualitative result of this paper remains unchanged.
Appendix 2 Proof of Proposition 3 Under a j-state, the social welfare function of Sj(kj) and the profit function PðlÞ are
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Sj ðkj Þ ¼ r l WL ðxL Þ þ ðpopulation of MFs choosing y ¼ xH Þ ½kj fPrði ¼ LjjÞWL ðxS Þ Prði ¼ HjjÞCA g þ ð1 kj ÞfPrði ¼ LjjÞWL ðxP Þ þ Prði ¼ HjjÞWH ðxP Þg PðlÞ ¼ l xL þ ð1 lÞðð1 qÞ½kH xS þ ð1 kH ÞxP þ q½kL xS þ ð1 kL ÞxP where Pr(i = H|j) is the probability that i = H in State j and Pr(i = L|j) is the probability that i = L in State j. The population of MFs choosing y = xH is (1 - r) ? (1 - l)r. The first term (1 - r) represents H-type MFs choosing xH and the second term is the portion (1 - l) of L types choosing x = xH. Let us calculate Pr(i = H|j = H) and Pr(i = L|j = H). By the Bayesian Conditional Probability rule, we can conclude that Prði ¼ Ljj ¼ HÞ ¼
Prði ¼ L; j ¼ HÞ Prðj ¼ HÞ
where Prði ¼ L; j ¼ HÞ ¼ Prðj ¼ Hji ¼ LÞPrði ¼ LÞ Note that Pr(j = H|i = L) = (1 - q) by definition. It holds that Prði ¼ LÞ ¼ ð1lÞr ð1rÞþð1lÞr
because out of (1 - r) ? (1 - l)r MFs, (1 - l)r MFs are L-types. Also, q portion out of (1 - r) H-type MFs and (1 - q) out of r(1 - l) L-type MFs . Therefore, generates a j = H signal, so Prðj ¼ HÞ ¼ ð1rÞqþð1lÞrð1qÞ ð1rÞþð1lÞr ðpopulation of MFs choosing y ¼ xH Þ Prði ¼ Ljj ¼ HÞ ð1 qÞð1 rÞ þ ð1 qÞð1 lÞr ¼ rð1 lÞ qð1 rÞ þ ð1 qÞð1 lÞr Because q [ 1=2; ð1qÞð1rÞþð1qÞð1lÞr qð1rÞþð1qÞð1lÞr \1 and Pr(i = L|j = H) \ r(1 - l). By the same reasoning, we can calculate ðpopulation of MFs choosing y ¼ xH Þ Prði ¼ Hjj ¼ HÞ ¼ ð1 rÞ
qð1 rÞ þ qð1 lÞr [ ð1 rÞ qð1 rÞ þ ð1 qÞð1 lÞr
ðpopulation of MFs choosing y ¼ xL Þ Prði ¼ Ljj ¼ LÞ ðqð1 rÞ þ qð1 lÞr [ rð1 lÞ ¼ rð1 lÞ ð1 qÞð1 rÞ þ qð1 lÞr ðpopulation of MFs choosing y ¼ xL Þ Prði ¼ Hjj ¼ LÞ ð1 qÞð1 rÞ þ ð1 qÞð1 lÞr \ð1 rÞ ¼ ð1 rÞ ð1 qÞð1 rÞ þ qð1 lÞr Therefore,
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ð1 qÞð1 rÞ þ ð1 qÞð1 lÞr qð1 rÞ þ ð1 qÞð1 lÞr qð1 rÞ þ qð1 lÞr CA ð1 rÞ qð1 rÞ þ ð1 qÞð1 lÞr ð1 qÞð1 rÞ þ ð1 qÞð1 lÞr þ ð1 kH Þ½rð1 lÞWL ðxP Þ qð1 rÞ þ ð1 qÞð1 lÞr qð1 rÞ þ qð1 lÞr þ ð1 rÞ WH ðxP Þ qð1 rÞ þ ð1 qÞð1 lÞr
SH ðKH Þ ¼kH ½rð1 lÞWL ðxS Þ
ðqð1 rÞ þ qð1 lÞr ð1 qÞð1 rÞ þ qð1 lÞr ð1 qÞð1 rÞ þ ð1 qÞð1 lÞr ð1 rÞ CA qð1 rÞ þ ð1 qÞð1 lÞr ðqð1 rÞ þ qð1 lÞr þ ð1 kH Þ½rð1 lÞWL ðxP Þ ð1 qÞð1 rÞ þ qð1 lÞr ð1 qÞð1 rÞ þ ð1 qÞð1 lÞr þ ð1 rÞ WH ðxP Þ qð1 rÞ þ ð1 qÞð1 lÞr
ð4Þ
SL ðKL Þ ¼kL ½rð1 lÞWL ðxS Þ
ð5Þ
Let lj be the value of l that makes the welfare effect of value of an S-Strategy and an P-Strategy equal at State j. The values of lH and lL are ð1 rÞ ðCA þ WH ðxP ÞÞ q r ðWL ðxS Þ WL ðxP ÞÞ ð1 qÞ ð1 rÞ ðCA þ WH ðxP ÞÞ ð1 qÞ lL ¼ 1 r ðWL ðxS Þ WL ðxP ÞÞ q
lH ¼ 1
Let l0 be the value of l derived in the above section (in which there is no second request). Then, because q [ 1/2, note that lH \ l0 \ lL, and now we derive the Nash equilibrium. If l \ lH, then kH = 1 and kL = 1. Because the CA adopts an S-Strategy for either state, it is more profitable for L-type MFs to truthfully reveal their type. Therefore, l* = 1. So, it is not a Nash equilibrium. If l [ lL, then kH = 0 and kL = 0. Because the CA adopts a P-Strategy for either state, it is more profitable for L-type MFs to mimic H-types. Therefore, l = 0, and it is not a Nash equilibrium. If lH \ l \ lL, then kL = 1 and kH = 0. We can derive that it is a Nash equilibrium only if xL ¼
q xS ð1 qÞxP
This situation is very limited. P
S
þqx xL If l = lH, then kL = 1 and kH ¼ ð1qÞx ð1qÞðxP xS Þ . Note that if q [
kH \ 0. Therefore, it is a Nash equilibrium if and only if q kH = 0 and kL ¼
xP xL qðxP xS Þ.
However, if
P L q\ xxP x xS ,
xP xL xP xS .
xP xL xP xS , L
then
If l = l , then
then kL [ 1. Therefore, it is a Nash
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equilibrium if and only if q
xP xL xP xS .
Note that the two equilibria are identical when
P
L q ¼ xxP x xS .
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