Merger Failures

∗

Albert Banal-Estañol†

Jo Seldeslachts‡

This version: January 2007 First version: March 2004

Abstract This paper proposes an explanation as to why some mergers fail, based on the interaction between the pre- and post-merger processes. We argue that failure may stem from informational asymmetries arising from the pre-merger period, and problems of cooperation and coordination within recently merged firms. We show that a firm may optimally agree to merge and abstain from putting forth any post-merger effort, counting on the partner to make the necessary efforts. If the two partners follow the same course of action, the merger goes ahead but fails. Our setup is a global game in which players decide whether to participate. Our unique equilibrium allows us to make predictions on which mergers are more likely to suffer from organisational problems. Keywords: mergers, synergies, asymmetric information, complementarities. JEL Classification: D82, G34, L20. ∗

We are grateful to Marcus Asplund, Heski Bar-Isaac, Miguel Garcia-Cestona, Rafael Hortala, Jos Jansen,

Inés Macho-Stadler, Marco Ottaviani, David Pérez-Castrillo, Carmelo Rodríguez-Álvarez, Joel Sandonís, Armin Schmutzler, Oz Shy, Xavier Vives and Christopher Xitco for valuable comments and discussions. We have also benefited from comments of seminar participants at Cambridge, UB, UAB, UMA, KUL, UPV, WZB, Guelph, Michigan State, Brock, Southampton, CREST, Canadian Economic Theory 2004, EEA 2004, JEI 2004, ASSET 2004, SAE 2004, IIOC 2005, CEPR Applied IO Workshop 2005 and ESSET 2005. Financial support from the ICM/CIM, Spanish Ministry of Science and Technology (BEC2003-01132) and EC 5th Framework Programme RTN (HPRN-CT-2002-00224) is gratefully acknowledged. All remaining errors are our own responsability. † Department of Economics, City University of London, Northampton Square, London EC1V 0HB, UK. Tel. +44 (0) 20 7040 4576. E-mail: [email protected]. ‡ Social Science Research Center Berlin (WZB), Reichpietschufer 50, 10785 Berlin, Germany. 3025491404. E-mail: [email protected]

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Tel: +49-

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Introduction

A large number of mergers and acquisitions are unsuccessful. Over the last fifteen years, 43% of all merged firms worldwide reported lower profits than comparable non-merged firms (Gugler et al. [17]). DaimlerChrysler, the outcome of the largest industrial merger ever, for example, has only posted low or negative profits since its birth in 1998 — including the biggest loss in German business history in 2001.1 The disappointing results of mergers have been puzzling commentators and academics alike.2 In the organisational literature, poor merger performance has often been connected to postmerger problems (see Larsson and Finkelstein [24] for an overview). For example, difficulties in forging a common corporate culture out of two disparate ones may result in low degrees of synergy realisation (Chatterjee et al. [9]). Also failure to integrate tasks, that is, too little functional and material interaction between newly merged firms, may prevent combinations from exploiting key strategic interdependencies (Pablo [31]). As Dessein et al. [11] confirm, “there are countless examples of failed mergers that were unable to achieve the synergies that motivated the deal”. The question that then emerges is why so many firms fail to implement the right post-merger actions. A seemingly straightforward answer may be that the execution of these actions often requires costly efforts. But if this is the only problem, then firms should simply decide not to merge when these costs are too high. Managers however, although being aware of future organisational costs, nevertheless propose a merger to their shareholders.3 Shareholders do not use their opportunity to reject this proposal either.4 And yet, often subsequent insufficient post1

By mid 2004, the firm’s market value had fallen to less than half of the pre-merger combined value, while

rivals improved in the same period (The Economist, 02/2004). “DaimlerChrysler’s CEO is the only one in the industry who’s still arguing that the merger was a smart move” (Business Week, 02/2004). “I would get rid of Chrysler” (James Schrager of Chicago GSB in Business Week, 08/2005). 2 Agrawal et al. [2] report in a sample of 765 US mergers over the period 1955-87 that more than 50% of the mergers earn negative cumulative abnormal returns on the stockmarket, and this percentage increases when the time horizon beocmes longer (1-5 years). Porter [32] reveals in a longitudinal study that 50% of merged firms later divested. Practitioners’ studies estimate failure of mergers to be even more frequent; their estimated failure rate lies well above 50%, and is sometimes believed to be even as high as 85% (Copeland et al. [10]). 3 Daimler and Chrysler for example anticipated post-merger challenges. The DaimlerChrysler Merger Statement (1998) reports: “Although the management of Chrysler and Daimler-Benz expects the merger will produce substantial synergies, the integration of two large companies presents significant challenges”. 4 Daimler’s and Chrysler’s shareholders agreed with the merger; 99.9% and 97.5%, respectively, voted in favor

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merger effort leads to a disappointing outcome. A joint investigation of merger and post-merger decisions may shed light on why some combinations do not succeed and when this is more likely to happen. This paper proposes an intuitive explanation of merger failure that takes explicitly into account the interaction between the pre- and post-merger processes. We will argue that failure may stem from informational asymmetries arising from the pre-merger period, and problems of cooperation and coordination when recently merged. In our setup, prior to the merger decision, two independent firms collect information about the potential gains of merging. Based on this information, the managers of each firm decide whether to seek the approval of their respective shareholders. If shareholders give the go-ahead, the partners of the newly merged company attempt to obtain the potential merger gains. These will be fully obtained if the managers of each of the forming firms exert a post-merger effort. We will show, however, that both firms may optimally agree to merge and subsequently exert no effort, leading to a merger failure. Our setup contains key features of a merger for synergies. By integrating specific hardto-trade resources, merging companies attempt to realise synergies, which are efficiency gains obtained through the generation of knowledge and capabilities that did not exist before the merger (Farrell and Shapiro [13]). Suppose, for example, that a firm specialised in basic programming merges with a firm that employs experts in system design. By combining their specialised knowledge, they might be able to produce a new and superior computer apparatus, both in calculus performance (speed) and usefulness for an organisation (functionality). Synergies are by definition not achievable through the actions of a single merging party (Farrell and Shapiro [13]). In our example, it is only when one partner writes the necessary programs and the other designs the adequate system that a more cost-effective and superior product can be developed. Accordingly, only when both partners exert post-merger efforts then the merged firm realises the synergies, merger gains that exceed the return of the individual efforts.5 Synergy gains in our setting are thus akin to the indirect gains from interdependent activities in organisations, as defined by Milgrom and Roberts [27]’[28]. As a consequence, of merging (DaimlerChrysler Case Study, Herbert Paul, Fachhochshule Mainz, 2003). 5 This does not mean that synergies are the only obtainable merger gains. If one partner does an effort, then other (non-synergetic) merger gains can be realised. It may be, for example, that when one partner develops a better computer system, this still may lead to gains through using the specific warehousing and delivery operations from the other partner. See Röller et al. [35] for an extensive discussion on merger gains.

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post-merger efforts exhibit strategic complementarities.6 Both merger and post-merger decisions are taken under a great deal of uncertainty. First, the reaction of competitors, the economic fundamentals or the unknown strategic fit of the partners make the potential merger gains uncertain (Haspeslagh and Jemison [19]). Before merging, however, each firm collects information about these gains. Based on its information, each firm considers whether to merge. If the merger takes place, each merging partner updates its beliefs and chooses whether to exert a post-merger effort. These efforts are uncertain when taking merger decisions, but are difficult to observe even during the post-merger process. Indeed, actions in this phase are usually difficult to describe in sufficient detail (Mailath et al. [25]) and decisions are often plagued by ambiguity (Vaara [41]). These observational difficulties make that post-merger efforts towards synergy realisation are subject to problems of cooperation and coordination.7 Within this framework, we find a unique equilibrium in symmetric switching strategies. If both partners expect substantial gains, then each agrees on merging and exerts a post-merger effort. All potential merger gains, including synergies, are obtained and the merger is successful. If a firm has low expectations, then the merger does not go through. More interestingly, we show that a firm may optimally agree on merging and abstain from exerting any post-merger effort if it receives an intermediate signal. While by not doing effort one precludes the possibility of obtaining synergy gains, merging might still be profitable. By hoping to free-ride on the effort of the other partner, one expects to obtain some (non-synergetic) gains that compensate the costs of merging. Indeed, the other partner might expect higher potential merger gains and be thus more willing to exert effort, in the believe to realise together synergy gains. If post-merger efforts are not strongly complementary and merging costs are not too high, one should agree on merging and abstain from exerting any post-merger effort.8 6

This is consistent with the findings of a large literature in management that concludes that tasks are more

valuable when they cluster together (see Dessein and Santos [12] for an overview). 7 Indeed, non-cooperation exists in a recently merged firm, since parties’ primary objective will be to ensure their interests rather than sacrificing those interests for the benefit of all (Flynn [14]; Seabright [37]). Further, the fact that efforts are complementary may then lead to coordination problems. 8 One way to interpret the words of the CEO of Daimler in the Financial Times two years after the merger with Chrsyler is as having employed this strategy. He described himself as a chess player keeping his next moves secret, and argued that “If I had gone out and said, [...], everybody on their side would have said, ’No way will we do a deal like that. But it’s precisley what I wanted to do.’” (FT, October 2000).

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If both partners follow the same course of action, however, the merger goes ahead and fails, because both abstain from exerting any post-merger effort. Failure may thus occur even though the management of each firm takes the appropriate merger decision in expected terms.9 Provided that shareholders do not have more information than the managers of their own firm, they should also accept the agreement. Failure could not have been avoided by post-merger communication either. Each partner has incentives to overstate its information, independently of its effort decisions. Indeed, it always prefers that the other exerts effort. Under these conditions, credible communication cannot be supported in equilibrium, as shown by Baliga and Morris [4]. Our explanation provides thus a formal rationale for why and how post-merger problems can be the cause of merger failure, as is often claimed by the management and organisational literature. It must be stressed that, although all the mergers in our setting have the potential for synergy gains, failure happens because the merger partners do not pursue synergy gains. Indeed, as pointed out in Banal-Estañol et al. [5] and Dessein et al. [11], synergy implementation is a strategic decision. It is further important to note that it is the very characteristics of post-merger efforts that may lead to the explained course of actions. Indeed, to explain failure, not exerting effort should not always be the optimal decision. If there was this problem only, firms would not enter a merger. Solely pure post-merger coordination problems (with Pareto ranked equilibria) would not lead to failure either, since firms would exert effort if they merged. The followed approach and consequently the unique equilibrium helps to make predictions on which mergers are more likely to suffer from organisational problems. First, mergers with higher expected potential gains suffer less from post-merger issues. In general, however, one should not just rely on the value of potential synergies, but must consider organisational variables as well. In particular, the lower the cost of post-merger effort and the higher their degree of complementarity, the lower the probability of failure. Further, the lower the opportunity costs 9

Although many mergers may fail through this mechanism, mergers should be profitable on average. Rhodes-

kropf and Viswanathan [34] use a similar rationale to explain why targets may accept bids from overvalued bidders in periods of high market valuations. Of course, there are other reasons apart from organisational difficulties that may explain failure. Managers can be empire-builders and merge, not to increase shareholder’s profits, but to belong to a larger firm (Jensen [20]). Unprofitable mergers may also occur because firms may merge to preempt their partners from merging with rivals (Fridolfsson and Stennek [15]). Finally, managers may irrationally overestimate the future performance of the merged entity, so-called “managerial hubris”, due to the wrong underestimation of internal conflicts (Banal-Estañol et al.[5]) or not foreseeing problems derived from conflicting organisational cultures (Weber and Camerer [44]).

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of merging -i.e. what firms earn as stand-alone profits plus the (fixed) cost of the merger- the higher the probability of failure. Firms merge then more often and, by taking this decision more easily, they transmit less positive information to their partners. As a result, partners exert effort less often in the post-merger process. Our model can be seen as a variant of a global game (Carlsson and van Damme [7]). In these type of games, agents’ payoffs (realised merger gains in our model) depend on the action chosen by the other agents (the post-merger effort) and some unknown economic fundamental (the potential merger gains). Agents receive public and private signals that generate beliefs about the economic fundamental and about the actions and beliefs of the other agents. Morris and Shin [30] showed that this incomplete information game has a unique equilibrium as long as the public signal is noisy enough. If the public signal becomes too precise, coordination problems and multiple equilibria arise as in the complete information case. In our setting, prior to the global game (the post-merger stage), the decision of whether to participate (the merger decision) allows players to update their beliefs about the signals of the other players. Uniqueness in our setup is then only ensured when the private signals are noisy enough, which is a consequence of the fact that the decision to participate in the game makes part of the private information public.10 The remainder of the paper is organised as follows. Section 2 presents the model. Section 3 studies the private information version of our model. Section 4 performs comparative statics and Section 5 discusses the general case where part of the information is public and part is private. Section 6 concludes. In Appendix A we provide preliminaries for the proofs, which are assigned to Appendix B. 10

Angeletos et al. [1] obtain a result in the same spirit as ours in a dynamic version of Morris and Shin’s [30]

model.

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2

Model

2.1

Main Setting

Two firms examine the possibility to merge. If the merger does not occur, each will earn the stand-alone profits π s ∈ R. Merging profits, on the other hand, depend on the uncertain potential efficiencies from merging and on the extent to which these gains will be actually obtained in the post-merger process. Accordingly, the profits for each merging firm can be written as π s + fθ/2 − k, where θ ∈ R represents the potential gains from merging, f ∈ [0, 1] the degree of fulfillment and k > 0 a (net) fixed cost for merging.11 We consider thus the case

of two symmetric firms deciding upon a merger of equals, whereby profits are shared equally. In line with Rajan and Zingales [33], we think it is realistic to claim that managers -and more specifically the top management- take the decisions within the firm. While it is reasonable to expect that employees at all levels impart their own influence on the post-merger process, the top management of each forming firm play the crucial role in establishing and shaping the strategic direction of the whole group (Chatterjee et al. [9]). This allows us to concentrate on the managerial decisions. We will further on use the terms ’firm’ or ’merger partner’, bearing in mind that it is always the top management of these firms that takes the decisions. The decision to merge though needs approval of the firm’s shareholders. But as we will argue below, shareholders in our setup approve the merger if this is proposed by the management. We analyse the merger process by using the following game. In the pre-merger period, both firms collect information about the potential gains from merging. In the merger period, firms decide whether to merge. One firm, denoted as Firm 1, decides first whether to propose a merger to the other, Firm 2, which in turn decides whether to accept.12 If both firms agree to merge, then in the post-merger period, each merging partner decides whether to exert a post-merger effort. At the end of the post-merger process, firms evaluate whether the merger was successful. 11

There could be merger gains obtainable independent of the results of the post-merger process, e.g. through

the elimination of fixed costs by having one headquarter instead of previously two. In our setup, these gains would be substracted from the costs k of merging. If they were so large that they compensate the costs of merging, then we would have k ≤ 0. In this case, however, a merger would always be profitable and as a consequence, no failure could occur. We limit ourselves for the remainder of the paper to the case of k > 0. 12 Merger decisions are modeled as sequential decisions to avoid the equilibrium where both firms decide not to merge for any level of potential gains. This equilibrium appears only when firms take the merger decision at exactly the same point in time.

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The timing of the game, described in more detail in the following subsections, is represented in Figure 1.

P RE − MERGER

P OST − MERGER

MERGER

Inf ormation

F irm 1 decides

F irm 2 decides

Each decides

Merger

collection

if propose

if accept

if ef f ort

Evaluation

Figure 1: Timing of the Game.

2.2

Pre-merger Period

In the pre-merger period, prospective partners collect information about the potential gains from merging, by hiring for example investment banks (Servaes and Zenner [38]). Although part of this information might be available to both firms, another part is certainly private. Indeed, at this point it is not sure that the merger is going to materialise and firms could use the obtained information against each other when competing. Full information disclosure before the merger materialises may also violate competition laws.13 In short, we will assume that firms are not willing or able to credibly exchange all their private information at this point in time. Formally, before any information gathering, the gains are completely uncertain and therefore θ is a priori randomly drawn from the real line, with each realisation equally likely.14 Obtained information can be classified into private or public. The information derived from non-shared research and knowledge is summarised into two noisy private signals of the true gains, xi = θ + εi 13

for i = 1, 2.

(1)

The Federal Trade Commission articulates that the exchange of sensitive information prior to the clearance of

the merger may amount to a breach of the United States competition legislation. Several successful legal actions have been brought in on this basis (see for example FTC Watch No. 265, at 3; 232-233, and the Case United States v. Input/Output, Inc. and Laitram Corp., 1999 WL 1425404, at *1 ). More generally, the formation of informational coalitions among competing firms is often illegal in practice (Kühn and Vives [23]). 14 The assumption that θ is uniformly distributed on the real line presents no technical difficulties as long as we are concerned only with conditional beliefs. As Morris and Shin [30] argue, such an improper prior is the same as assuming that the prior distribution of θ becomes diffuse.

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Parameters εi represent the noise and are assumed to be independently identically distributed with εi ∼ U (−l, l) and independent from θ. The knowledge available to both firms is assumed to be summarised in a noisy public signal of the true gains, y = θ + υ.

(2)

Parameter υ represents again the noise and we presume υ ∼ U (−l, l), and υ, εi and θ to be independent. For simplicity, we set the three signals equally precise.

2.3

Merger Decisions

The merger period starts with Firm 1 deciding whether to make a merger proposal to Firm 2. Equivalently, Firm 1 is the first firm to publicly announce whether it agrees to merge.15 In taking this decision, it uses its available information, I1m ≡ {x1 , y}, to update its beliefs

about the potential gains, (θ | I1m ), and its beliefs about the private signal received by Firm 2,

(x2 | I1m ). If Firm 1 decides not to propose, both firms obtain the stand-alone profits π s and the game ends.16 If it decides to propose, then it is Firm 2’s turn to respond.

Subsequently, Firm 2 decides whether to accept or reject the proposal, based on its available information I2m ≡ {x2 , y, Firm 1 agreed to merge}. It can reject and terminate the game,

resulting into the stand-alone profits π s for each firm. If on the other hand, Firm 2 accepts, the merger takes place. Each firm pays the merging costs k and becomes a partner in the new entity. The two partners enter then into the post-merger process. Assuming that the (risk-neutral) management of each firm is paid an exogenous fraction of the profits that accrue to their initial (risk-neutral) shareholders, managers will always obtain the consent of their shareholders if they decide to seek merger approval. Indeed, if shareholders have access to the same information as their managers, then they will have the same beliefs

about the gains and the private signal received by the other firm. Moreover, although they will also get a proportion of the expected merger benefits, they will not bear the costs of post-merger efforts. Therefore, if a merger is profitable for the management, then it should also be profitable 15

We will show that the order in which firms announce their decision does not matter. It would be therefore

equivalent to assume that only proposals or acceptances are observed. 16 We assume that both the costs of merging and the stand-alone profits are certain. Results would not change if these parameters were random, as long as their expected values are the same for both firms.

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for their shareholders. For simplicity, we normalise the exogenous fraction of the profits that go to the managers of each firm to one.17

2.4

Post-merger Process

In the post-merger period, and based on the information available Iip ≡ {Iim , Firm j agreed to merge}, each merging partner decides, unilaterally, whether to exert an effort. Indeed, in a recently merged firm, parties’ primary objective will be to ensure their interests, rather than sacrificing those interests for the benefit of all in the newly merged firm (Flynn [14]).18 These unilateral efforts are assumed to be not only non-verifiable but also unobservable during the post-merger process and therefore chosen as if they were exerted simultaneously (as in e.g. Banal-Estañol et al. [5] and Dessein et al. [11]). Actions in the post-merger phase are likely to be plagued by ambiguity about what the other is doing (Vaara [41]). Further, in the initial postmerger context it is intrinsically hard to describe the desired actions to distinguish them from seemingly similar actions with very different consequences (Mailath et al. [25]). Additionally, interdependencies may make it even more difficult to measure separate contributions of partners at this stage (Simon [39]). In short, we assume that each merging partner decides unilaterally and simultaneously whether to exert an effort. The degree of fulfillment of potential merging gains is given by f (e1 , e2 ) ∈ [0, 1], where ei is the post-merger effort exerted by partner i. More efforts raise the extent of the merging gains obtained and therefore f (·) is increasing in both arguments. By assuming that providing effort is a binary decision, ei ∈ {0, 1}, there are three scenarios. When both partners exert effort, f (1, 1) = 1 and gains are not discounted. If only one partner does effort, the fulfillment factor is f (0, 1) = f (1, 0) ≡ 17

1 d

where d > 2 as we will argue below. If none of them does an effort, we

An alternative interpretation of our assumptions is that the sharing of profits of any firms is exogenously

set to giving all its managers an equal part. Dessein et al. [11] and Kretschmer and Puranam [22] analyse the use of optimal incentives to manage interdependence in multi-product firms. We concentrate in this study on the interaction between merger and post-merger decisions and use therefore for simplicity an exogenous sharing rule. Our results, however, would remain qualitatively unchanged when optimal contracts are used, as shown by Banal-Estañol et al. [5] in a similar setting. 18 Managers’ motivation to cooperate comes from team spirit and trust (Kandel and Lazear [21]). But, this is exactly what may be lacking in a newly merged firm (Seabright [37]). For a similar rationale, see e.g. Scharfstein and Stein [36] who model this type of conflict as divisional rent seeking and Fulghieri and Hodrick [16] as managerial entrenchment.

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let the penalty to be extremely high, f (0, 0) = 0, and zero merger gains are obtained.19 Each partner’s effort comes at a private cost t. Following Farrell and Shapiro [13], we divide merger efficiencies obtained in the post-merger process into synergy and non-synergy gains. The direct benefits from the effort of a single partner are called non-synergy gains. Synergies, on the other hand, are indirect gains realised only when the management of both partners exerts effort, exceeding the direct return of the individual efforts. Indeed, they are obtained because of merger parties’ integration of specific hard-totrade resources, generating knowledge and capabilities that did not exist before (Farrell and Shapiro [13]). Therefore, remembering that θ represents the total potential gains from merging and the fulfillment factor of one partner doing effort is d1 , indirect extra gains from both partners doing effort are represented by θ − dθ − dθ . Hence, potential non-synergy and synergy gains are θ d2

and θ(1 − d2 ), respectively. Clearly, in a merger for synergies one should have d > 2. As a result,

post-merger efforts to achieve positive gains are strategic complements;20 that is the marginal return of a partner’s effort is increasing in the level of effort of the other partner (see e.g. Vives [43]).21 A larger d implies that the efforts are more complementary; rewards from effort become larger when the partner has exerted effort and smaller when it has not. The uncertain payoffs for the management of each partner, gross of merging costs and stand alone profits, are summarised in Table (3). Effort (e2 = 1) Effort (e1 = 1) No Effort (e1 = 0)

θ 2

−t , θ 2d

,

θ 2 −t θ 2d − t

No Effort (e2 = 0) θ 2d

−t ,

θ 2d

(3)

0,0

In a complete information setting (for example if firms received a public signal y only), three scenarios would arise depending on the level of (expected) efficiency gains. If the gains were low, not doing effort would be a strictly dominant strategy for both firms. If the gains were high, merging partners would exert effort since this would be a strictly dominant strategy. Finally, in the intermediate case, there would be multiple equilibria. The two partners doing effort and 19

As argued before, to fully discount the potential gains if none does any effort is just a normalisation of k (see

footnote 10). 20 In the case of negative gains, θ < 0, not to do effort will be a dominant strategy. 21 This is in line with Milgrom and Roberts [27]’[28], who emphasise that interdependent activities in organisations show strategic complementarities due to the presence of indirect gains.

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none doing effort would both be Nash equilibria. This indeterminacy is problematic when one goes backwards to the merger stage. At the moment of taking merger decisions, firms do not know in which equilibrium of the post-merger process they are going to coordinate. Similar to the global games literature, the presence of asymmetric information enables us to find a unique equilibrium. The payoffs in our setup however are different from the basic global game as described in Morris and Shin [30], in which doing no effort yields a fixed payoff. This difference will prove to be crucial for the occurrence of failure. If the payoffs of not doing effort were fixed (and lower than the fixed cost of merging), it would be impossible that a firm agrees to merge and exerts no effort later on. Here, the payoffs from not exerting effort while the partner exerts effort increase with the expected efficiency gains θ. In other words, a partner gains more from free riding in the post-merger stage when the expected gains are higher.

2.5

Definition of Post-merger Failures

In what follows, we provide the definition of post-merger failure. Mergers are evaluated at the end of the post-merger process, once partners observe the equilibrium efforts, e∗1 and e∗2 .22 Definition 1 A post-merger failure occurs when both firms agree to merge but, at the end of the post-merger process, the gains expected by each merging partner are lower than the costs of merging, i.e. for i 6= j

¢ ¡ f e∗i , e∗j E(θ | Iip , e∗i , e∗j )/2 < k

We define failure gross of the cost of effort. Indeed, to evaluate whether a merger is a failure in terms of profits (and share prices), the cost of effort of the management teams should not be included. Second, we define failure in expected terms. Failure can of course always occur when the realisation of the uncertain gains θ is lower than expected, independently of the level of effort exerted by the partners. Third, we consider the merger a failure when it is considered a failure by each individual partner. This is done for notational ease, but our definition would be equivalent to each partner evaluating the sum of profits, given its information. Finally, each individual partner considers whether the merger is a failure using the information it has available. This is the strongest possible definition of failure. As we show in the following lemma, post-merger 22

Even though partners can observe the post-merger effort level chosen by the other at the end of the process,

these efforts are, as mentioned above, asssumed to be non-verifiable and therefore non-contractible.

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failures can then only occur when none of the partners exerts effort. As such we establish a lower bound of the failure rates in function of our parameters. Lemma 1 A post-merger failure occurs if and only if both partners merge and exert no effort. The proof of this result is straightforward. First, if none of the partners does any effort, this is a post-merger failure by definition. Second, if they merge and only one does effort, this is not a failure. The partner that did no effort merged because this was a profitable decision, even before knowing with certainty the effort choice of its partner. After observing that the partner has exerted effort, it should expect even higher profits. Third, if both exert effort, the same reasoning holds. Both entered the merger without knowing the action of the partner in the post-merger stage and should expect higher profits after observing it.

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Private Information and Post-Merger Failures

To simplify our discussion, we consider in this section the case in which firms receive only a private signal. A strategy in this setting does not consist of two binary decisions as in the complete information case, but in a mapping from the range of possible signals to those two binary choices.23 Definition 2 A strategy si for Firm i, i = 1, 2, is a function specifying, for each possible private signal xi ∈ R, an action s1 : R → [{Propose, Not propose} , {Effort, No Effort}] and s2 : R → [{ Accept, Not accept } , {Effort, No Effort}] . We concentrate on monotonic strategies, which in binary choice settings is equivalent to the class of switching strategies. Depending on whether the signal is below or above a cutoff point, the player takes one action or the other. In our case, since we have two decisions, a strategy is uniquely defined by two cutoff points. 23

Remember that Firm 2 only decides whenever Firm 1 has proposed. Similarly, the two firms have only to

decide upon doing effort whenever both firms have agreed to merge. This means that strategies are fully defined without specifying the action of the other.

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e Definition 3 A double switching strategy si for Firm i, i = 1, 2, with cutoffs x ei and x ei for merging and doing effort respectively can be described as ⎧ ⎨ Propose iff x > x e1 1 s1 (x1 ) = ⎩ Effort e iff x1 > x e1 ⎧ ⎨ Accept e2 iff x2 > x and s2 (x2 ) = ⎩ Effort e iff x2 > x e2 .

The sequential ordering introduces an informational asymmetry. The first-mover firm, Firm

1, has to take the proposing decision without knowing whether Firm 2 will accept or reject later on. The following lemma shows that in practice there is no asymmetry. Lemma 2 When deciding whether to propose, Firm 1 decides as if it knew that Firm 2 were going to accept. As a result, both firms take the merger decision based on the same information, ej }, for i = 1, 2 and i 6= j. Ii ≡ {xi , xj ≥ x

Firm 1’s decision is only relevant when Firm 2 accepts the merger because the stand-alone

profits do not depend on who rejects the merger. Given this result, we denote from now on for expositional ease both the P ropose and Accept decisions as M erge, and similarly N ot P ropose and N ot Accept as N ot M erge. e ej ), Firm i exerts From Table (3), if Firm j chooses a double switching strategy around (e xj , x

effort whenever

e e e ej , x ej ) ≡ (d − 1)E(θ | Iie ) Pr ob(xj ≥ x ej | Ii ) + E(θ | Iine ) Pr ob(xj ≤ x ej | Ii ) − 2dt ≥ 0, g(xi , x

e e where Iie ≡ {Ii , xj ≥ x ej } and Iine = {Ii , xj < x ej } and recall that Ii ≡ {xi , xj ≥ x ej }. Intuitively,

a higher private signal xi raises the expected merger gains and the probability that the partner exerts effort. Hence, the function g() is increasing in xi and the partner does more easily effort

when it receives a higher signal. As a consequence, this condition uniquely defines a post-merger e e xj , x ej ). Firm i exerts effort effort cutoff x ei for each double switching strategy of the other firm (e

e ei . if and only if xi ≥ x

At the merger stage, therefore, Firm i knows whether it is going to do effort later on. If e Firm i knows that it would do effort in the post-merger stage, xi ≥ x ei , it merges whenever e e e ej , x ej ) ≡ dE(θ | Iie ) Pr ob(xj ≥ x ej | Ii ) + E(θ | Iine ) Pr ob(xj ≤ x ej | Ii ) − 2d(t + k) ≥ 0. h(xi , x 14

e Similarly, if Firm i knows that it would not do effort later on, xi < x ei , it merges whenever e e ej , x ej ) ≡ E(θ | Iie ) Pr ob(xj ≥ x ej | Ii ) − 2dk ≥ 0. m(xi , x

Intuitively again, a higher private signal xi increases h() and m() and induces Firm i to merge e e e e ej , x ej ) = m(x ei , x ej , x ej ), the previous conditions uniquely define a more easily. Given that h(x ei , x e merger cutoff x ei for each (e xj , x ej ) such that Firm i will decide to merge if and only if xi ≥ x ei . In

summary, Firm i’s best response to a switching strategy is also a switching strategy.24

Given the symmetry of the model, we concentrate on equilibria in the class of symmetric

ej ≡ x e and strategies whereby partners i and j play the same double switching strategy, x ei = x e e e ej ≡ x e. We proceed in three steps. In a first step, we provide necessary and sufficient x ei = x

conditions for double symmetric switching strategies to be equilibria. In a second step it is shown that, provided that the information gathered carries some noise, there exists a unique equilibrium for each combination of the exogenous parameters.25 In a last step, we find the unique equilibrium in function of these parameters. Lemma 3 : characterisation of the equilibrium. e A pair of cutoffs (e x, x e) is an equilibrium in symmetric switching strategies iff e e e e (a) g(x e, x e, x e) = 0, h(e x, x e, x e) = 0 and x e≥x e or

e e e e (b) g(x e, x e, x e) = 0, m(e x, x e, x e) = 0 and x e≤x e.

An equilibrium is found by the intersection of the post-merger effort decision function, im-

plicitly defined by g(·) = 0, and either the “I-will-later-do-efffort” merger decision function (h(·) = 0) or the “I-will-later-not-do-effort” merger decision function (m(·) = 0). The first intersection is an equilibrium if and only if, in this intersection, firms exert effort for a larger e range of private signals than they merge (e x≥x e). Indeed, in such intersections, if the private

e signal is higher than the effort cutoff (xi ≥ x e), a firm merges when the private signal is higher

e). If the private than the merger cutoff defined by the “I-will-later-do-effort” function (xi ≥ x 24

This implies that when solving for equilibria within the class of switching strategies, we can restrict attention

to potential deviations within that class. If there is no profitable deviation to a switching strategy, there will not be a profitable deviation to a non-switching strategy. 25 Uniqueness of equilibrium is not straightforward in our game. Although effort decisions are strategic com-

plements with respect to each other, merger and effort decisions are not. For a comprehensive analysis of games with strategic complementarities, see Vives [43].

15

e signal is lower than the effort cutoff (xi < x e), the firm would never merge. On the other hand, e an intersection of g(·) and h(·) where x e
same reasoning holds for the other intersection.

The next step is to show that when the private signal has enough noise there exists a

unique pair that satisfies (a) or (b) of the previous lemma, and therefore there exists a unique equilibrium. Proposition 1 : Existence and Uniqueness of the equilibrium. If l ≥ l∗ ≡

6d(d−2)t (3d−4)(d−1)

there is a unique equilibrium in symmetric switching strategies.

The merger decision of each firm transforms part of its private information into public. This public information has a “multiplier effect” on all actions, because both firms know that the partner received this information. Public information, therefore, exceeds its pure informational content and the problem of self-fulfilling beliefs arises again. This is a feature that keeps on returning in the global games literature: one needs the public signal to be noisy enough to reach a unique equilibrium (Morris and Shin [30]). The particular feature in our model, however, is that the private signal becomes partly public through the merger decision. Thus, in order to have uniqueness, we need the private signal to be noisy enough. Angeletos et al. [1] obtain a result in the same spirit as ours in a dynamic version of the game of Morris and Shin [30]. Assuming that this condition is satisfied, we are able to characterise the unique equilibrium in function of the parameters of our model. Proposition 2 : Equilibrium. e − 3l , the symmetric switching equilibrium (e x, x e) satisfies: e then x e = x∗ = x e. e then x e > x∗ > x e.

Defining x∗ ≡ (a) If k = (b) If k > (c) If k <

t d−1 t d−1 t d−1

2dt d−1

e then x e < x∗ < x e.

First, for a special case of the exogenous parameters, merger and effort decisions are the same. Firms find it profitable to merge in the same cases where they optimally exert effort (part a). Second, if the costs of merging are higher, then merging becomes more expensive. As a direct consequence, firms merge less and the cutoff from merging is higher than before. 16

Indirectly, since the acceptance of merging transmits a more positive signal, firms exert effort more easily than before and the cutoff from doing effort is lower (part b). Finally, following the same reasoning, if the opportunity costs of merging are lower firms merge more and exert effort less often (part c). We are now ready to formally state our explanation of merger failures. In the next corollary, that follows directly from the previous proposition, we describe in which situations post-merger failures occur. Corollary 1 : post-merger failures. When all information about uncertain merger gains is private, post-merger failures occur e e ≤ xi < x e for i = 1, 2. when k < t and x d−1

As shown in Lemma 1, a post-merger failure can only occur if both firms choose to merge

but not to exert post-merger effort. For this to happen, it is necessary that the merger decision e is taken more easily than the effort decision, i.e. in equilibrium one must have that x e
Proposition 2, this occurs when the costs of merging (k) are low, the degree of complementarity

of efforts (d) is low and the costs of effort (t) are high enough such that k <

t d−1 .

In order

for a failure to de facto occur, it must be that the private signals received by both partners e e for i = 1, 2. Both partners have gathered information about the are intermediate, x e ≤ xi < x merger gains, good enough to merge (merging costs are low) but not so good to exert effort (cost

of effort is high). Indeed each gives a reasonable probability that the other will exert effort and

prefers to free-ride on it (the degree of complementarity is low). The merger goes then ahead but fails because both choose not to exert effort. We have assumed that signals remain private throughout. But failure could not be avoided even if communication was possible. As argued in the introduction, a potential partner does not want or is not allowed to give out all its information before merging. Failure could not be avoided by post-merger communication either. Each partner has incentives to overstate its private signal independently of its effort decisions. Indeed, it always prefers that the other exerts effort. Under these conditions, credible communication cannot be supported in equilibrium, as shown by Baliga and Morris [4]. From Lemma 1 it is clear that if post-merger efforts were guaranteed, a post-merger failure would never occur. Notice that in that case, merging partner i would choose to merge whenever

17

E(θ | xi , xj ≥ x ˆj ) − 2(t + k) ≥ 0 and the symmetric equilibrium in switching strategies would e e < xi < x e and be x ˆ = 2(t + k) − l . Then, in our model, when xi for i = 1, 2 is such that x 3

ˆ, a post-merger failure would have been avoided if both partners had merged and had xi ≥ x e ˆ or xj < x ˆ, and x e < xi < x e for i = 1, 2 then the exerted effort. On the other hand, if xi < x post-merger failure would not have occurred if the post-merger efforts were guaranteed since the merger would not have gone through.

4

Comparative Statics

In the previous section, we showed that our game has a unique equilibrium in the class of symmetric switching strategies if the private signal is not very precise. Here, we exploit this property to analyse which situations should lead to more merger failures. We analyse how the probability of failure, given θ, varies with the exogenous parameters of the model. To avoid uninteresting situations, we analyse the cases where it is possible that firms merge (e x ≤ θ + l) e and where it is possible that they do not exert effort (x e > θ − l). Further, we concentrate on

the most natural case in which more post-merger effort leads to more incentives to merge, which e corresponds to the case in which the sum of the thresholds is positive, x e+x e > 0 (see proof of

Proposition 1).

Although most of our results will be the same with either, one can distinguish two definitions

of probability of failure. The first concerns the probability with respect to the whole population of pairs that consider a merger, which we will call total probability of failure. The total probability of failure is directly related to the probability that a firm i decides to merge and not to exert a post-merger effort, e e | θ) = Prob(e x < xi < x

⎧ ⎨ ⎩

min{e x e,θ+l}−max{e x,θ−l} 2l

0

e if x e≤x e e if x e>x e.

Definition 4 The total probability of failure (T P ) is the probability of failure for all pairs that decide upon merging: e e e | θ) ∗ Prob(e x < x2 < x e | θ). TP = Prob(e x < x1 < x

The second definition concerns the probability of failure, given that firms have already decided to merge, which we will call conditional probability of failure. The conditional probability 18

of failure is directly related to the probability that a firm i does not exert a post-merger effort when it has decided to merge, e Prob(xi < x e | xi > x e, θ) =

⎧ ⎨ ⎩

e min{x e,θ+l}−max{e x,θ−l} θ+l−max{e x,θ−l}

0

e if x e≤x e e if x e>x e.

Definition 5 The conditional probability of failure (CP ) is the probability of failure, given that both firms have agreed to merge: e e CP = Prob(x1 < x e | x1 > x e, θ) ∗ Prob(x2 < x e | x2 > x e, θ).

Let us first consider comparative statics with respect to fixed costs of merging k. Similar to the intuition provided for Proposition 2, higher costs of merging lead firms to merge less easily. Then the acceptance of the merger by the other partner yields more positive information. Thus, expected merger gains and the likelihood of the partner exerting post-merger effort become e higher. Hence, the firm is more prone on exerting effort. The distance between x e and x e becomes therefore smaller and the possibility of a failure lower, not only in total but also in conditional terms.

Corollary 2 : Costs of merging. Higher costs of merging (k greater) lead to less mergers (e x greater) and more post-merger e effort (x e lower) and therefore to less failures, both in total and conditional terms.

The following figure shows as an example both cutoffs for the case in which d = 3, l = 2 e and t = 0.5, with k varying from 0 to 0.5. For k going from 0 to 0.25, x e
of failure exists. And, the lower k, the bigger the range where failure might occur. The figure also depicts the merging cutoff if post-merger efforts were guaranteed. As argued in the previ-

ous section, this cutoff shows that the post-merger failure would have been avoided either by exerting effort (in the region above) or by not merging (in the region below).

19

cutoffs 1.5

1

0.5

0 0.125

0.25

0.375

0.5 k

-0.5

Figure 2: Merging cutoff

e e (dotted line) and merging cutoff when the x e (thick line), post-merger effort cutoff x

post-merger efforts are guaranteed

x b (thin line) as a function of the costs of merging k.

We now turn to the cost t of exerting post-merger effort. First, higher costs t lead partners to exert less effort. As a result, firms merge less since they expect also their partners to exert less effort. However, while the cost of effort t has a first-order effect on a firm’s effort decisions, e on the merger decision it has only a second-order effect. Cutoff x e rises therefore faster than

cutoff x e and the possibility of a failure becomes higher, both in absolute and conditional terms. Corollary 3 : Costs of post-merger efforts.

Higher costs of post-merger effort (t greater) lead to less mergers (e x greater) and less effort e (x e greater) and to more failures, both in total and conditional terms.

The following figure shows as an example both cutoffs for the case in which d = 3, l = 2 and e k = 0.25, with t varying from 0.25 to 0.75. For t greater than 0.5, x e
failure exists. And, the greater t, the bigger the range where failure might occur.

20

cutoffs

2

1.5

1

0.5

0 0.25

0.375

0.5

0.625

0.75 t

Figure 3: Merging cutoff

e e (dotted line) as a function of the costs of x e (thick line) and post-merger effort cutoff x effort t.

We now turn to the comparative statics with respect to the measure d of how complementary post-merger actions are. The higher d, the more complementary post-merger efforts become. Given the complexity of the expressions, we make use of simulation techniques in Mathematica 4.0 to show the results.26 We let k, l and t range between 0 and 100 and for every given combination {k, l, t}, we let d vary from 2 to dmax , where dmax is defined as l = l∗ (dmax ). This

ensures uniqueness (l∗ (d) ≤ l∗ (dmax ) = l given that l∗ is increasing in d). As an example, the next figure shows the cutoffs for the case {k, l, t} = {0.15, 2, 0.5}. cutoffs 1.5

1.25

1

0.75

0.5

2

2.25

2.5

2.75

3

3.25

3.5

3.75

4 d

Figure 4: Merging cutoff

e e (dotted line) as a function of the x e (thick line) and post-merger effort cutoff x complementarity

d of post-merger efforts.

We find that for each combination of parameters {k, l, t}, an increasing d leads to a decrease 26

All macros and simulation results of this exercise are available upon request.

21

e in x e and an increase in x e. We state these findings in the following result.

Result 6 : Complementarity of post-merger efforts.

A higher complementarity of efforts (d greater) leads to less mergers (e x greater) and more e post-merger effort (x e lower) and therefore to less failures, both in total and conditional terms.

More complementarity punishes more one-sided effort. Thus, if a firm accepts the merger,

giving therefore a reasonably high probability to the other doing effort, it exerts more easily post-merger efforts. Therefore, at the merger stage, each firm gives a higher probability that its partner will exert effort. This effect should induce firms to merge more often. There is, however, a second opposite effect that dominates the merger decisions. Although one-sided effort occurs less often, the losses when this happens are larger for higher complementarity. As a consequence, firms merge less and exert effort more often. The possibility of failure becomes therefore smaller.

5

Private and Public Information

In this section we briefly consider the case in which firms receive a private and a public signal before merging. The introduction of a public signal y along with the private signals xi and xj does not alter significantly the results of the previous section. Lemmas, propositions and corollaries can be restated in terms of the two types of information, as shown in the following proposition. In particular, noisy enough signals are again sufficient to ensure uniqueness. Proposition 3 : Extension to private and public information. There exists a unique l∗∗ such that if l ≥ l∗∗ then there exists a unique symmetric equilibrium 2dt e + 3l − y) and in switching strategies (e x, x e). Defining r ≡ 32 ( d−1 ∗∗

x

≡

⎧ ⎨

6dt d−1

⎩ y + 2l + r −

the equilibrium is such that (a) If k = (b) If k > (c) If k <

t d−1 t d−1 t d−1

− l − 2y

if y ≤

p r2 + 2(2l)2 if y >

e then x e = x∗∗ = x e. e then x e > x∗∗ > x e. e then x e < x∗∗ < x e.

22

2dt l d−1 − 3 2dt l d−1 − 3

Again merger failures can occur when the opportunity costs of merging are low and the actual signals are intermediate. Similar comparative statics can be performed for this case and the results are analogous.

6

Conclusion

This paper proposes a novel explanation as to why some mergers fail while others succeed, based on informational asymmetries, and problems of cooperation and coordination in the postmerger stage. We show that each firm’s management may optimally agree on merging and abstain from exerting post-merger efforts, expecting the merger partner to make the necessary effort. We argue that, provided that they have equal or less information than their management, shareholders of each firm accept the merger agreement. The merger then goes ahead and fails. Accordingly, these mergers are unprofitable. Share prices, on the other hand, can rise at the moment of the merger’s announcement. Indeed, if the market does not have more information than the firm, it should bid up the firm’s price because the firm takes the appropriate merger decision in expected terms. Therefore, our story may serve as an alternative to Fridolfsson and Stennek’s [15] explanation for the empirical merger puzzle that unprofitable mergers often coincide with initially increasing share prices. At the end of the post-merger process, however, and if the market observes that none of the partners has made the necessary efforts, it should adjust the share prices downwards.27 We identify under which conditions mergers are more likely to fail. Lower merger costs not only induce firms to merge more but also to exert effort less often. As a result, failures occur with a higher probability. An empirical test for this prediction may be constructed by comparing the percentage of unprofitable mergers in economic booms and downturns. Economic booms are typically accompanied with higher capital liquidity and thus lower merger transaction costs (Harford [18]) and should, according to our model, show a higher percentage of failures. One could even argue that our mechanism would predict a higher failure rate in countries or periods where antitrust laws are less severe, i.e. where ceteris paribus costs of merging are lower. We further show that higher complementarities of post-merger efforts leads in equilibrium 27

DaimlerChrysler’s market price history is in accordance with these facts. The combined shares rose at the

merger announcement and reached a peak of $108 in January 1999. Prices then fell to $38 by November 2000 and were in March 2006 still only at half of the level reached right after the deal (The Economist, 04/2006).

23

to more effort and less failures. Indirect evidence for this result may be found in the literature that investigates the effects of technologically motivated M&A’s on innovation performance. Cassiman et al. [8], for example, find that mergers between partners coming from technologically more complementary fields lead to a higher R&D effort, a lower reported incidence of organisational problems and a more efficient R&D output. If higher complementarities, however, are due to more dissimilarities between partners -i.e. higher complementarities originate from higher specialisation- firms must also incur higher costs in order to reach synergy gains. These two effects pull in opposite directions in our setting and the resulting effect on the likelihood of a failure is more difficult to predict. This may explain why for example Ahuja and Katila [3] find an inverted U-shaped relation between a priori technological relatedness and innovation performance after having merged. They claim that firms need to avoid too close and too distant knowledge bases, the former due to a lack of complementarities and the latter because of integration problems.28 Our explanation provides thus a formal rationale for why and how post-merger issues can be the cause of merger failure, as is often claimed by the management and organisational literature. A simplified version of our framework could be extended to letting firms decide upon a merger or a takeover.29 In a takeover, one firm buys out the other and gets rid of the strategic uncertainty in the post-merger stage. This forecloses the possibility of failure, at the expense of losing the possibility of achieving synergy gains. In some cases, and especially if the non-synergy gains are high and the merging costs low, it might be optimal for a firm to take over the other. As long as complementarities and therefore synergies are important though, firms should prefer a merger. Indeed, Matsusaka [26] finds empirically that mergers whereby most of the top management is retained, perform on average better. A full investigation of this question is a challenging task for future research. 28

Similarly, conflicting evidence is found on whether mergers between partners with a priori larger (cultural)

differences perform better or worse (see Stahl and Voigt [40] for an overview). This may be attributed to the tension of more diverse merging partners having higher complementarities, but at the same time suffering from higher costs of integration. While some studies found national or oganisational differences to be negatively related to measures of merger performance, others observe a positive relationship (e.g. Morisini et al. [29]). 29 More generally, one could allow for an optimal sharing agreement, which specifies the allocation of fixed cash payments and shares of the profits of the new entity. Among the many possible agreements, the merging firms may split evenly the shares of the new company, in a merger of equals. Alternatively, they may opt for a pure takeover by assigning all the shares to one firm and imposing a cash transfer from this firm to the other.

24

Appendix A: Beliefs If θ is a random variable with an improper distribution and firm i receives a private signal xi = θ + εi , where εi ∼ U (−l, l) with εi and θ independent, we have that θ | xi ∼ U (xi − l, xi + l). Firm i does not observe firm j’s private signal, xj , but knows that xj = θ + εj where εj ∼ U (−l, l) and εj and θ, εj and εi are independent. Since θ | xi and εj are uniforms, we know that xj | xi is a sum of uniforms, which results in a distribution function with density function, ⎧ ⎨ xj −xi +2l if xj ∈ [xi − 2l, xi ] (2l)2 f (xj | xi ) = j ⎩ xi +2l−x if xj ∈ [xi , xi + 2l], (2l)2

and we can obtain

⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨

´ Pr ob(x ≥ x ³ e ej | xi ) j e = ej | xi , xj ≥ x ej = Pr ob xj ≥ x Pr ob(xj ≥ x ej | xi ) ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩

³

e ej xi +2l−x

´2

(xi +2l−e xj )2 ³ ´2 e xi +2l−x ej

2(2l)2 −(e x −xi +2l)2 ³j ´2 e 2(2l)2 − x ej −xi +2l 2(2l)2 −(e xj −xi +2l)2

1

e if xi ≤ x ej ≤ x ej

e if x ej ≤ xi ≤ x ej

e if x ej ≤ x ej ≤ xi

e if x ej > x ej .

We can find θ | xi , xj ∼ (θ | xi ) | (xj | xi ) which is a uniform again, because xj | xi

is a sum of two uniform distributions and (θ | xi ) is a uniform. We have then θ | xi , xj ∼ U [min{xi , xj } + l, max{xi , xj } − l}]. Given that R we have that

e ej , xj ≥ x ej ) = E(θ | xi , xj ≥ x

e ej , xj ≥ x ej ) = E(θ | xi , xj ≥ x e and for x ej ≤ x ej we have that

⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩

e xj ≥max{e xj ,x ej },

R [ θ θf (θ | xi , xj )]dθdxj

e Pr ob(xj ≥ max{e xj , x ej } | xi )

2xi +l+e xj 3 xj +2xi −l)(e xj −xi +2l)2 6xi (2l)2 −(e 3[2(2l)2 −(e xj −xi +2l)2 ] e ej 2xi +l+x 3 e e ej +2xi −l)(x ej −xi +2l)2 6xi (2l)2 −(x ∙ ³ ´2 ¸ e 3 2(2l)2 − x ej −xi +2l

e E(θ | xi , xj ≥ x ej , xj < x ej ) =

R

e x ej ≤xj ≤x ej

[

R

θ

e if xi ≤ x ej and x ej ≤ x ej e if xi > x ej and x ej ≤ x ej e e if xi ≤ x ej and x ej > x ej e e if xi > x ej and x ej > x ej

θf (θ | xi , xj )dθ]f (xj | xi )dxj

e Pr ob(e xj ≤ xj ≤ x ej | xi )

and analogous expressions can be obtained. 25

Appendix B: Proofs Proof of Lemma 2 Firm 1’s payoff from proposing the merger depends on the probability that Firm 2 agrees to merge. From the Law of Total Expectations, we can write Firm 1’s payoff by proposing the e2 ) − 2k − 2e1 t] Pr ob(x2 ≥ x e2 | I1m ) + π s Pr ob(x2 < x e2 | I1m ). merger as [π s + E(fθ | I1m , x2 ≥ x

Firm 1 agrees to propose as long as this expression is greater than π s which, simplifying, amounts to the condition E(f θ | I1m , x2 ≥ x e2 ) − 2k − 2e1 t ≥ 0.

Proof of Lemma 3

e First take a pair (e x, x e) that satisfies part (a). Suppose that firm j is using this switching strategy e with cutoffs (e x, x e). As argued in footnote 23, we only need to consider deviations within the

e class of switching strategies. By definition of (e x, x e), Firm’s i best response is to use, in the e post-merger stage, a switching strategy with cutoff x e. Now consider two cases. Suppose first

e e. Knowing that it is not going to integrate, that Firm i receives a private signal xi below x e e, x e) < 0. Since m() is an we are going to show that it is not going to merge, that is m(xi , x e e e e, x e) < m(x e, x e, x e). By definition of g, h and m, we increasing function of xi we have that m(xi , x e e have that m() = h() − g() and also g(x e, x e, x e) = 0. Since h() is an increasing function in xi and e e e e e e, x e) < 0 and Firm i does not want h(e x, x e, x e) = 0 and x e≥x e then h(x e, x e, x e) < 0. Hence, m(xi , x

e e. Then it is going to to merge. Suppose secondly that Firm i receives a private signal xi above x

e by definition of h(). We have merge, knowing that it is going to exert effort, whenever xi ≥ x shown that Firm i is going to merge whenever its private signal is above x e. 0 0 0 0 0 e e e e e We now show that a pair (e x0 , x e ) that satisfies g(x e ,x e0 , x e ) = 0 and h(e x0 , x e0 , x e ) = 0 but x e >x e0 0 e is not an equilibrium. Suppose that Firm j uses a switching strategy with cutoffs (e x0 , x e ). Firm’s 0 e i best response is to use a switching strategy with cutoff x e in the post-merger stage. Suppose

e0 − ε. Knowing that it does not exert effort, it that Firm i receives a private signal xi = x 0 0 0 0 e e e e e0 , x e ) ≥ 0. But since m(xi , x e0 , x e ) = h(xi , x e0 , x e ) − g(xi , x e0 , x e ) and will merge whenever m(xi , x 0 0 0 e e e e0 , x e ) < 0 and h(xi , x e0 , x e ) is arbitrarily close to 0 when ε tends to 0, m(xi , x e0 , x e ) > 0 and g(xi , x

it will merge. Then x e0 cannot be a cutoff point. The same arguments apply for (b).

26

Proof of Proposition 1 From the definition of g(), we have that e e e e e | Ii ) + E(θ | Iine ) Pr ob(xj ≤ x e | Ii ) − 2dt ≥ 0, g(x e, x e, x e) ≡ (d − 1)E(θ | Iie ) Pr ob(xj ≥ x

e e e e}, Iine = {Ii , xj < x e} and Ii ≡ {x e, xj ≥ x e}. where abusing of the notation Iie = {Ii , xj ≥ x

This expression is increasing in x e. As shown in Appendix A, we can obtain for the uniform e distribution that if x e≥x e, e e g(x e, x e, x e) =

i h e e e e e e e(6l − x e − 3x e) + (x e+x e)(3l + x e+x e) e−x e) x (d − 1)(3x e + l)(2l)2 + (x e 6(2l)2 − 3(e x−x e + 2l)2

e whereas if x e
− 2dt,

e (d − 1)(2x e+l+x e) e e g(x e, x e, x e) = − 2dt. 3 6d(d−2)t e e e We can show that when l ≥ (3d−4)(d−1) , then g(x e, x e, x e) is also increasing in x e. Then, by the e e e implicit function theorem, we get that x e, such that g(x e, x e, x e) = 0 is a decreasing function of x e. 00 e x00 , x e00 , x e ) = 0 is Using the implicit function theorem again we can show that x e00 such that m(e 00

00

00

e e e e00 − x e < 0 and x e00 + x e < 0. Outside this region more an increasing function of x e except when x 00 e effort implies more incentives to merge. Therefore, if x e00 such that m(e x00 , x e00 , x e ) = 0 is never in

0 0 0 0 0 b b b b b ) such that g(x b ,x b ,x b ) = 0 and m(b x0 , x b0 , x b ) = 0. In the this region, there is a unique pair (b x0 , x

case in which it is (and more effort implies less incentives to merge), we can also show that there 0 b b ) because the two curves could never cross twice. This can never happen is a unique pair (b x0 , x 00 e e e ) is increasing and that of x e(e x) is decreasing and the derivative because the derivative of x e00 (x e e. Similarly, we can show of the first function at x e0 is larger than the derivative of the second at x

b b b b that there is a unique pair (b x, x b) such that g(x b, x b, x b) = 0 and h(b x, x b, x b) = 0. b Suppose first that x b≤x b. This is, by the previous lemma, an equilibrium. Now we need to 0 0 0 0 0 0 b b b b b b ) such that g(x b ,x b ,x b ) = 0 and m(b x0 , x b0 , x b ) = 0 is not, i.e. that x b0 ≤ x b . Since show that (b x0 , x

b b b b b b b b b b b g(x b, x b, x b) = 0 and h(x b, x b, x b) ≥ h(b x, x b, x b) = 0, we have that m(x b, x b, x b) = h(x b, x b, x b)−g(x b, x b, x b) ≥ 0. 0 b b b b b ) such that Since x b(b x) such that g(x b, x b, x b) = 0 is a decreasing function, the combination (b x0 , x

0 0 0 0 0 b b b b b b b ,x b ) = 0 and m(b x0 , x b0 , x b ) = 0 should satisfy x b0 ≤ x b and x b ≥x b. But then, since x b≤x b, g(x b ,x 0 0 b b b and therefore, from the previous lemma (b x0 , x b ) cannot be an equilibrium. If, then x b0 ≤ x b b secondly, x b>x b then (b x, x b) is not an equilibrium by the previous lemma. However, following a

0 0 b b similar reasoning as above we can show that x b0 > x b and therefore (b x0 , x b ) is an equilibrium.

27

Proof of Proposition 2 t 2dt 2dt e e (a) Suppose first that k = d−1 . If x e=x e = d−1 − 3l ≡ x∗ then E(θ | x e, xj ≥ x e, xj ≥ x e) = d−1 and e e e e e e|x e, xj ≥ x e) = 1 and g(x e, x e, x e) = h(e x, x e, x e) = m(e x, x e, x e) = 0. This is an equilibrium Pr ob(xj ≥ x

because parts (a) and (b) of Lemma 3 are satisfied. Moreover this equilibrium is unique by Proposition 1.

(b) Second, it k >

t d−1

then h(x∗ , x∗ , x∗ ) = m(x∗ , x∗ , x∗ ) < 0 and following an argument

similar to the one presented in the proof of the previous proposition, the equilibrium satisfies part (a) in Lemma 3. (c) When k <

t d−1

then h(x∗ , x∗ , x∗ ) = m(x∗ , x∗ , x∗ ) > 0 and then the equilibrium satisfies

part (b) in Lemma 3.

Proof of Corollary 2 e e e Given that m(·) is decreasing in k and increasing in x e, x e(x e, k) such that m(x e, x e, x e, k) = 0 is e increasing in k. On the other hand, g(·) is an independent function of k. Given that x e(e x) such

e e e e e that g(x e, x e, x e) = 0 is a decreasing function of x e, we have that if (e x, x e) satisfy g(x e, x e, x e) = 0 0 0 0 0 0 0 0 0 0 0 e e e e e e e e ) satisfy g(x e ,x e ,x e ) = 0 and m(x e ,x e ,x e , k ) = 0 for k > k then and m(x e, x e, x e, k) = 0 and (e x ,x 0 e e e>x e . The same arguments apply for the intersections of g(·) and h(·). x e
Proof of Corollary 3

e e e Given that g(·) is decreasing in t and increasing in x e, x e(e x, t) such that g(e x, x e, x e, t) = 0 is increasing e in t. On the other hand, m(·) is an independent function of t. Hence, given that x e(x e) such that

e e e e e e m(x e, x e, x e) = 0 is an increasing function of x e, we have that if (e x, x e) satisfy g(x e, x e, x e) = 0 and 0 0 0 0 0 0 0 0 0 0 e e e e e e e e ) satisfy g(x e ,x e ,x e ) = 0 and m(x e ,x e ,x e , t ) = 0 for t > t then x e
In order to show that it also leads to less failures both in total and conditional terms, we 0 e e e e e e0 . But this is true given that x e(x e) such that m(x e, x e, x e) = 0 also need to show that x e−x e
e ∂e x(x e) e ∂x e

=

e x e+x e 2(e x+l)

< 1.

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Proof of Proposition 3 e e Following the same procedure as in Section 3, we are going to obtain g(xi , x ej , x ej , y), h(xi , x ej , x ej , y) e ej , x ej , y). The same arguments of the proof of Lemma 3 apply here and we need and m(xi , x

e e e e e e again to look for intersections of g(x e, x e, x e, y) and h(e x, x e, x e, y) when x e≤ x e and of g(x e, x e, x e, y) e e e e e, x e, x e, y) is an and m(e x, x e, x e, y) when x e≥x e. As in Proposition 1, there exists l∗∗ such that g(x e increasing function of x e and therefore the equilibrium is unique. Similar to Proposition 2, we e e=x e satishave that when k = t , an equal cutoff for the merging and effort decisions, x∗∗ = x d−1

fies g(x∗ , x∗ , x∗ , y) = m(x∗ , x∗ , x∗ , y) = h(x∗ , x∗ , x∗ , y) = 0 and is therefore an equilibrium. The expression, in function of y and the exogenous variables, is stated in the text. And, similarly, if k>

t d−1

or k <

t d−1

we have the orderings in (b) and (c), respectively.

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