Uncertain Efficiency Gains and Merger Policy

Transcription

1 Uncertain Efficiency Gains and Merger Policy Mariana Cunha Paula Sarento Hélder Vasconcelos February 17, 2014 Abstract This paper studies the role of uncertainty in erger control and in erger decisions. In a Cournot setting, we consider that ergers ay give rise to uncertain endogenous efficiency gains and that every erger has to be subitted for approval to the Antitrust Authority (AA). We assue that both the AA and the firs in the industry face the sae uncertainty about the future efficiency gains induced by the erger. It is shown that an increase in the degree of uncertainty benefits both insider and outsider firs but also the consuers. Further, when uncertainty is high, there is a greater likelihood that firs propose a erger to the AA and that the AA accepts it. Interestingly, however, although uncertainty enhances erger approval chances, it also decreases erger s stability, by increasing outsiders incentives to free-ride on it. Keywords: Efficiency gains; Merger control; Uncertainty JEL Codes: L13; D41; D28; D81 We are very grateful to Joana Pinho, João Correia da Silva and Ricardo Ribeiro for their helpful coents and suggestions that substantially iproved this paper. FEP-UP, School of Econoics and Manageent, University of Porto, Address: Rua Dr. Roberto Frias, Porto, Portugal; E-ail address: acunha.phd@fep.up.pt. The author thanks Fundação para a Ciência e Tecnologia for financial support (SFRH/BD/70000/2010). FEP-UP, CEF-UP; E-ail address: sarento@fep.up.pt. FEP-UP, CEF-UP and CEPR; E-ail address: hvasconcelos@fep.up.pt. 1

2 1 Introduction The assessent of the efficiency gains resulting fro a erger usually raises an inforation issue for antitrust authorities. Although soe ergers can actually generate significant efficiency gains, these are usually difficult to easure and verify. In practice, it is often the case that both the firs and the antitrust authority (henceforth, AA) cannot predict exactly the post-erger efficiency gains, iplying that they are not aware of all the conditions they are going to face after the erger. Soeties, only after the erger firs and antitrust authorities will understand the true level of induced efficiency gains. For instance, soe pharaceutical firs ay adopt erger decisions without knowing whether their R&D efforts will be successful or not. Also, any type of firs investent could generate uncertainty about future costs and, soeties, a erger could actually occur before the uncertainty is resolved. The purpose of this paper is to contribute to the literature that studies the efficiency gains role in erger decisions, departing fro a deterinistic environent by considering a setting in which there is (syetric) uncertainty. In particular, we assue that the decisions of the antitrust authority, when evaluating a erger case, crucially depend on the uncertainty regarding the efficiency gains realization. In the proposed odel, firs and the AA are uncertain about the level of efficiency gains and, therefore, this uncertainty is going to influence the decision of the AA but also firs incentives to erge. This analysis is useful to the AA in order to ore properly evaluate erger proposals when there is uncertainty about the cost savings that ergers ay induce or not. 1 In the absence of uncertainty and in a context of syetric Cournot oligopoly with linear deand and costs, a erger is profitable if it coprises a pre-erger arket share of at least 80% (Salant et al., 1983; Perry and Porter, 1985). Also, when both firs and the AA are perfectly infored about the erger induced efficiency gains, the antitrust authority usually allows the erger when there are iportant efficiency gains that would lead to lower prices (Motta and Vasconcelos, 2005; Vasconcelos, 2010). The present paper is related to two strands of literature on ergers in a Cournot fraework: (i) the studies of antitrust authority s erger decisions, where the AA evaluates the welfare effects of ergers and allows for erger reedies under uncertainty, such as Cosnita and Tropeano (2009), Besanko and Spulber (1993), Corchón and Faulí-Oller (2004); and (ii) works that, investigating the ipact of uncertainty on the incentives to erge, conclude that the incentives to erge depend on the inforation structure, such as Gal-Or (1988), Stenbacka (1991), Wong and Tse (1997), Stennek (2003), Qiu and Zhou (2006), Banal-Estañol (2007), Zhou (2008a,b), Air et al. (2009). 2 1 See Morgan (2001) for the discussion about the significance of reviewing erger cases with uncertainty. 2 Uncertainty can also be seen as an inforation sharing proble, for instance, firs can have ore inforation about their own costs than the AA. Previous contributions to the literature on inforation sharing aong oligopolists did not consider the possibility of ergers aong firs nor AA intervention. 2

3 To our knowledge, however, none of the previous papers has addressed the role of efficiency gains which are uncertain for all players in the erger foration process (firs and the AA). The present paper then contributes to fill this gap in the extant literature by assuing that, when firs propose the erger to the AA, all the players (insider, outsiders and AA) are uncertain about the post-erger efficiency gains and therefore they decide by considering the expectations on those gains. Once the erger is consuated, both insider and outsider firs can observe the efficiency gains and copete à la Cournot. This is different fro Air et al. (2009) s paper where, after the erger, only the insider fir observes its cost. Our odel is also different fro the literature cited before, where it is usually assued that the erging firs have an inforational advantage, knowing ore about the erger induced efficiency gains than its rivals and the AA. Further, our analysis is close to Le Pape and Zhao (2013) s paper. Le Pape and Zhao (2013) analyse Stackelberg ergers decisions when there is uncertainty on productivity and inforational asyetry between firs. However, here we focus our analysis on both ergers and AA decisions, assuing that the firs copete in a Cournot setting and that all firs have the sae degree of uncertainty. We find that the increase in the degree of uncertainty about erger s efficiency gains benefits firs (in ters of higher expected profits) and consuers (with higher expected consuer surplus). Further, when the degree of uncertainty is high, there is a greater likelihood that firs propose a erger to the AA and the AA accepts it. Therefore, uncertainty enhances both the occurrence of erger proposals and the likelihood that those proposals are cleared by the AA. We also find that, higher degree of uncertainty hinders erger s stability, by increasing outsider firs incentives to free-ride on the erger. The reainder of the paper is organized as follows. In section 2 the basic fraework of the odel is described. Section 3 presents the pre-erger equilibriu results. Section 4 analyses the equilibriu of the proposed erger foration gae. Also, in this section we study erger s stability. In section 5 we present and discuss the obtained nuerical results. Finally, section 6 offers soe concluding rearks. All the proofs are relegated to the appendix. In ost of the papers, it is assued that there is arket uncertainty because the arginal cost and/or the arket deand are unknown to the firs, such as, Novshek and Sonnenschein (1982), Clarke (1983), Sakai (1985), Gal-Or (1985, 1986), Shapiro (1986), Vives (1984, 2002), Li (1985), Sakai and Yaato (1989), Raith (1996), Lagerlöf (2007), Jensen (1992), Elberfeld and O. Nti (2004), aong others. 3

4 2 Basic Fraework We consider a hoogeneous good industry with n firs that copete à la Cournot. The inverse deand function is given by P = 1 Q, where Q = n q i is the aggregate output and q i is the quantity produced by fir i {1,..., n}. Let k i denote fir i s capital holdings, where k i {1, 2,..., K}. The cost function of a fir i, which owns k i units of the industry capital and produces q i units of output, is given by: 3 C(α j, q i, k i ) = α jk k i q i, where K is the total capital in the industry, Σ i k i = K, that is fixed and α j easures the endogenous efficiency gains, with α j 0. 4 In the next sections we analyse the results before the erger, where the efficiency gains are known with certainty. We then discuss the results obtained after the erger, for both AA and erger decisions, in a context where there is uncertainty about erger induced efficiency gains. i=1 3 Pre-Merger equilibriu Before the erger (BM), we assue that firs are syetric and that each fir owns one unit of capital, that is, k i = 1. Also, each fir knows, with certainty, its level of efficiency gains and therefore α j = α, where α is the coon efficiency level of all firs before the erger. The equilibriu profits and consuer surplus are then given by: 5 π BM i = (1 nα)2 2, where i = 1,.., n. (1) (n + 1) CS BM = 1 n 2 (1 nα) 2 2 (n + 1) 2. (2) Assuption 1. Assue that α < 1 n. The previous assuption is iposed in order to exclude the case in which firs in the industry do not produce (are inactive) in the pre-erger equilibriu. 3 This is a siplified version of the cost structure proposed by Motta and Vasconcelos (2005) and captures also the specific case studied in Horn and Persson (2001). This cost function is based on the one proposed by Perry and Porter (1985). In their fraework firs arginal cost is linear in output and ergers reduce variable costs. 4 Efficiency gains ay result fro fir s cobined ability to exploit econoies of scale or raise larger aounts of capital, but also fro copleentarity between technological or adinistrative capabilities of firs (Röller et al., 2001). 5 For a detailed description of the results before the erger see Appendix A1. 4

5 4 Merger Analysis In this section we analyse both the AA s and firs erger decision, in a setting where all firs in the industry and the AA are uncertain over the erger induced efficiency gains. Assue that, at the status quo industry, one fir in the industry is randoly selected and has the opportunity to propose, to the AA, a erger involving 2 firs. This fir ay propose a erger with all or a subset of its rivals. Since each fir operates with a constant arginal cost of production, but the level of its arginal cost is a decreasing function of its capital holdings, the resultant erged fir becoes ore efficient than outsiders by having k i = units of assets. We assue that is given exogenously. Hence, the erger brings the capital of erging parties into a single larger fir and, therefore, gives rise to endogenous efficiency gains by decreasing the arginal cost. The level of these potential efficiency gains is captured by the paraeter α j. When the level of efficiency gains is the sae both before and after the erger (α j = α), all firs and the AA know with certainty what will be the erger s cost savings. Hence, the higher is the value of α, the stronger the efficiency gains induced by a erger are (Motta and Vasconcelos, 2005; Vasconcelos, 2010). However, in our odel, the erger also brings uncertainty about the induced efficiency gains, that is, all firs (insiders and outsiders) and the AA cannot predict precisely the level of the future erger-induced efficiency gains. Thus, we assue that all players are uncertain on what will be the exact value of the efficiency gains level, as easured by α j = α u. This level of future efficiency gains, α u, could be higher, lower or equal than the level of efficiency gains before the erger, given by α. If α u is equal to α then, after the erger, the erged fir s cost decreases and the outsider fir s cost does not change. If α u is lower than α, the costs of both insider and outsider firs decrease after the erger. Different results are obtained when α u is higher than α: if α u = kα, then the insider fir s cost reains the sae as before the erger however, the outsider firs costs increase; if α u > kα both insider and outsider firs costs increase after the erger; and if α u < kα then, after the erger, the insider fir s cost decrease and the outsider firs costs increase. Assuption 2. Let α u be a rando variable distributed over [0, 1 2n ]. By assuing that α u < 1, we are excluding the case where outsiders exit the arket 2n after the erger takes place. The expected value of the efficiency gains in the future is denoted by E (α u ) = µ, where µ [0, 1 2n ], and the variance is denoted by V (α u) = σ 2 > 0. The σ 2 represents the degree of uncertainty and captures the efficiency gains fluctuation. The higher is σ 2, the greater is the uncertainty about the erger s efficiency gains. Fir i has to decide whether or not to erge and the AA has to decide whether or not to accept the proposed erged, both without knowing the actual cost of the erged fir in the future. We assue that firs set output decisions after uncertainty is solved, 5

6 given that we want to study the effects of uncertainty on the decisions of both erger firs and the AA. We assue that firs are risk neutral and therefore firs decisions regarding the erger are based on the expected values of their profits. We also assue that the AA is risk neutral, and that its decision is based on the expected value of consuer surplus. We consider that the AA s decision is based on expected consuer surplus instead on social welfare and, thus, the AA approves the erger if the expected consuer surplus increases. 6 Thus, the private incentives to erge and the AA decisions are based on expected values. We odel the interactions between the antitrust authority and the erging firs as a four-stage gae, with the following tiing: Stage 1: Firs have to decide whether or not to propose a erger to the AA. Stage 2: The AA decides whether or not to accept the proposed erger. Stage 3: Nature chooses α u and reveals it to all players. Stage 4: Insider and outsider firs choose quantities copeting in the usual Cournot fashion. In what follows, we will solve the odel by following the usual backward induction procedure. 4.1 Product Market Copetition The results presented below refer to the Cournot-Nash equilibriu after the erger (AM), where firs know the level of efficiency gains (since uncertainty has been resolved in the previous stage of the gae). In the fourth-stage of the gae, firs have already observed the actual value of α u so, they choose to produce the quantities that axiize their profits. The Cournot equilibriu profits of insider fir (I) and outsider firs (O) and the consuer surplus (CS) are, respectively, given by: 7 π AM I = [ nα u (( 1) ( n) + 1)] 2 2 (n + 2) 2 (3) π AM O = [ nα u (2 1)] 2 2 (n + 2) 2 (4) 6 By assuing that the AA evaluates ergers according to a consuer surplus standard this does not ean that this is always better than the total welfare standard. However, as Lyons (2002) argued, the consuer surplus standard is applied in ost antitrust jurisdictions. Other papers also study how the AA should apply the consuer surplus standard when challenging a erger, such as Besanko and Spulber (1993), Neven and Röller (2005), Vasconcelos (2010), Nocke and Whinston (2010), Jovanovic and Wey (2012), aong others. 7 For a detailed description of the results obtained after the erger see Appendix A2. 6

7 CS AM = [ (n + 1) nα u ( (n ) + 1)] (n + 2) 2. (5) Under uncertainty, outsider firs would exit the arket if they expected to produce zero in equilibriu, that is, if µ. If the expected efficiency gains fro erger n(2 1) are very high, outsider firs would not be able to ake positive expected profits and ay exit the arket. However, since we assue that µ < 1, we exclude this possibility. 2n The next subsection presents the expected insider and outsider profits, the expected consuer surplus and discusses the effects of uncertainty on these outcoes. These results are based on the results obtained after the uncertainty about the efficiency gains has been resolved. 4.2 Expected Profits and Consuer Surplus The expected profits of both insiders and outsider firs, respectively, E [ ] πi AM and E [ ] [ π ] O AM, and the expected consuer surplus, E CS AM, are then given by: 8 E [ ] πi AM [ nµ (( 1) ( n) + 1)] 2 = 2 (n + 2) 2 + σ 2 n2 [( 1) ( n) + 1] 2 2 (n + 2) 2 (6) E [ CS AM] = E [ ] πo AM [ nµ (2 1)] 2 = 2 (n + 2) 2 + σ 2 n 2 (2 1) 2 2 (n + 2) 2 (7) [ (n + 1) nµ ( (n ) + 1)]2 2 2 (n + 2) 2 + σ 2 n2 [ (n ) + 1] (n + 2) 2 (8) As we can see, uncertainty affects both the expected profits and the expected consuer surplus. Lea 1 : An increase in the level of efficiency gains uncertainty benefits both insider and outsider firs but also the consuers, i.e., both E [ ] [ ] [ π ] I AM, E π AM O and E CS AM are increasing in σ 2. Moreover, uncertainty benefits ore the insider fir than the outsider firs, if: E [ ] πi AM > E [ ] π AM O n > σ 2 σ 2 Proof. See Appendix B. ( + 1) 1 n > 1. (9) A higher degree of uncertainty iproves firs expected profits, because profit functions are convex in α u. Since a fir s profit is convex in its own cost, uncertainty increases the fir s expected profit. Both insider and outsider firs will choose their quantities without knowing the exact value of the costs. 9 The insider fir expects that, after the erger, the cost is going to decrease due to the synergies generated, that is, due to an 8 For a detailed description of the results obtained with expectations see Appendix A3. 9 This is a siilar result as obtained by Zhou (2008a) s paper. 7

8 increase in the capital stock of the erged fir. However, the insider fir does not know how uch is this cost saving, since the insider fir s cost decreases in three different scenarios: (i) α u < α, (ii) α u = α and (iii) α < α u < kα. Since the insider fir expects a lower cost, it knows that, even without uncertainty, the resultant fir is going to produce a large quantity. The uncertainty about how uch the cost reduces also affects the outsider firs. Although each outsider fir still has one unit of capital, if the cost saving is very high, we know that, without uncertainty, outsiders will respond by reducing quantity. However, under uncertainty, only if α u is saller than α, there will also be significant cost savings for outsider firs and this will increase both quantities and profits of all outsider firs. If this is the case, the expected net effect is an increase in the total quantity and a decrease in the total price (which also happens without uncertainty). Without uncertainty and cost synergies, ergers usually lead to a sharp reduction of the total output. As consequence, in deterinistic odels, ergers usually reduce the consuer surplus. However, when there are cost synergies, the reverse can actually occur even without uncertainty. In our odel, the higher is the uncertainty about the cost synergies generated by the erger, the larger the value of σ 2 and the greater the expected consuer surplus will be. After the erger, both the insider and outsider firs expect to benefit fro cost synergies if α u is saller than α and, therefore, expect to increase the quantities produced. However, it ay happen that, after the erger, α u is greater than α and, therefore, the insider fir s cost decreases but the outsider firs cost increase. In this case, the insider fir still produces ore quantity but the outsider firs will respond by producing a lower quantity. Nevertheless, under uncertainty, both insider and outsider firs do not adjust so sharply their production. Consequently, the net effect is an increase in the total quantity in the arket, which affects positively the consuer surplus. Hence, both profits and consuer surplus are increasing functions with respect to the uncertainty paraeter, σ 2. Additionally, under uncertainty, the profits of the insider and outsider firs are affected differently. More precisely, if the nuber of firs in the arket is higher than a threshold n, uncertainty has a higher effect on insider fir s profits than on outsiders. However, if the nuber of firs in the arket is lower than n, the reverse occurs. Further, the extent of the uncertainty effect on both expected profits and consuer surplus is shown to depend on the nuber of firs in the arket (n) and on the nuber of firs involved in the erger (). The higher is the nuber of firs in the arket, the higher the ipact of uncertainty on consuer surplus and on insider profits is, but the lower the ipact on outsider profits is. Also, the higher is the nuber of insider firs, the larger the effect of uncertainty on (insider and outsider) profits and on consuer surplus is. However, fro nuerical siulation, we have seen that as the nuber of insider firs increases, that is, when insiders involve ore than 50% of the firs in the arket, uncertainty begins to have a negative effect on both consuer surplus and insider profits since these start to decrease. 8

9 Lea 2 : If: (i) = n (full erger), both expected consuer surplus and insider profits always decrease with the expected ean over the efficiency gains level; (ii) < n (partial erger), the expected outsider profits and the expected consuer surplus decrease with the level of expectations over the efficiency gains, however the expected insider profits increase if those expectations satisfy the following threshold: µ > n[( n)( 1)+1]. Proof. See Appendix B. Lea 2 states that, after the erger, the expected outsider firs profits and the expected consuer surplus decrease with the expected ean over the efficiency gains (µ). Also, the expected insider firs profits increase if the expectations over the efficiency gains are not too high and if the erger does not involve all the firs in the arket. Before looking at the results obtained to the AA decision, we assue the following: 10 Assuption 3. Assue that µ = α. Assuption 3 states that the expected efficiency gains level are equal to the benchark fir s efficiency gains level, that is, the efficiency gains level of both insider and outsider firs at the status quo industry. After the erger, the insider fir expects that its cost is going to reduce, since now only one fir encopasses all capital assets of the erging firs. However, the insider fir does not know how uch is this reduction. Therefore, for siplicity, we assue that the expectations on the level of efficiency gains are rational and equal to the efficiency gains before the erger. Hence, the erged fir expects the cost reduction to only depend on the level of capital of the erging parties. This assuption allows us isolate the effects of uncertainty on both AA s and firs erger decisions. By assuing µ = α the interpretation of the results is the sae as before: the higher is α, the stronger the efficiency gains induced fro the erger are. Recall that we are only considering the scenario in which outsider firs do not exit the arket after the erger. Hence, the erger induced arket structure consists of n + 1 firs: n outsiders with one unit of capital and one fir with k = units of capital. 11 In what follows, both AA and erging firs decisions are ade under uncertainty. 10 This assuption is not crucial. Actually, we obtain our ain results without assuing it, but, in order to present clear expressions we need to ipose it. See Appendix C for further inforation on the results obtained without Assuption However, we do not exclude the case where the erger involves all the firs in the industry. See Appendix A4 for further inforation on full erger results. 9

10 4.3 Antitrust Authority s Decision The AA decides whether to allow or block any proposed erger. The AA accepts the erger if the expected consuer surplus after the erger is greater or equal than the consuer surplus before the erger (E [ CS AM] CS BM ). Proposition 1. The AA will accept the erger if E [ CS AM] CS BM > 0, i.e. iff: σ 2 σ 2 AA{,n } 2 (n + 2) 2 n 2 (1 nα) 2 [ (n + 1) nα ( (n ) + 1)] 2 (n + 1) 2 (n + 1) 2 n 2 [ (n ) + 1] 2. Proof. See Appendix B. Proposition 1 states that when uncertainty is high, there is a greater likelihood that the AA accepts the erger. Since the consuer surplus before the erger (whose expression is given in (2)) does not depend on the uncertainty paraeter, the higher is the uncertainty, σ 2, the greater is the expected consuer surplus after the erger. Consequently, when uncertainty is high, the expected consuer surplus variation also increases. When there are cost synergies, ergers can iprove consuer surplus by increasing output. This iproveent could actually be higher when there is uncertainty about cost synergies. Therefore, under uncertainty there is a greater likelihood that the erger is accepted by the AA. (10) 4.4 Merger Decision In this section, we exaine firs incentives to erge. Firs decisions on whether to erge or not result fro the coparison between the expected profits of the erged fir with the profits before the erger. Hence, the erger profitability condition depends on the expected profits of the erged fir, that is, firs will propose the erger if E [ πi AM ] π BM. Proposition 2. If the level of uncertainty is sufficiently high, there is a greater likelihood that firs propose a erger. Firs will propose the erger if they anticipate that it will be profitable, i.e. iff: 12 σ 2 σ 2 MP {,n } (1 nα)2 3 (n + 2) 2 [ nα (( 1) ( n) + 1)] 2 (n + 1) 2 (n + 1) 2 n 2 [( 1) ( n) + 1] 2. Proof. See Appendix B. Fro Proposition 2, we conclude that uncertainty prootes the expected erger profitability. As the extent of the variance exceeds a certain threshold (σmp 2 {,n }) the expected profit of the erged fir becoes larger than the su of the fir s profits in the benchark case, and firs that face cost uncertainty choose to erge. In the deterinistic odel, without efficiency gains, unless the erger involves a sufficient nuber of insiders, ost of the horizontal ergers are unprofitable (Salant et al., 1983). However, in our odel, as the uncertainty increases, the 12 Note that n > 3, otherwise insider fir s profit would not depend on the σ 2 paraeter and therefore this expression would not exist. (11) 10

11 expected profit also increases because the gain of the optial quantity adjustent increases, and therefore it is possible that the expected profit of insider fir (as easured by (6)) exceeds the su of profits of the pre-erger firs (whose expression is given in (1)). Hence, the insider fir has a higher profit both directly fro the cost advantage and indirectly fro the favourable responses fro outsider firs. Since the pre-erger profits are not affected by uncertainty, it is expected that the erger becoes at least ore profitable than in the deterinistic odels. As the degree of uncertainty grows larger, firs have ore incentives to erge and therefore, we conclude that cost uncertainty is able to induce the firs to erge. This relationship between erger profitability and cost uncertainty is also investigated by Banal-Estañol (2007) and Zhou (2008a,b). In a different fraework fro ours, Banal-Estañol (2007) considers that firs face idiosyncratic uncertainty about costs and that uncertainty generates an inforational advantage only to the erging firs, increasing erger profitability. Also, Zhou (2008a,b) argues that when costs are uncertain and firs choose quantities before the uncertainty is resolved, a erger is ore profitable the greater the uncertainty. However, differently fro our paper, the author assue that after the erger, costs are realized and each fir learns its own costs but not the cots of its rivals. Zhou (2008a,b) shows that fir s incentives to erge are enhanced by production rationalization. 4.5 Free-riding Proble In this subsection we study the effects of uncertain efficiency gains on erger s stability. In the deterinistic odels, ergers are usually not stable, given that outsider firs are the ones that benefit ost fro the erger (free-riding proble). In order to assess if there is a free-riding proble in our odel, we copare the expected profit of the erged fir with the expected profits of outsiders. Proposition 3. There is a free-riding proble if E [ π AM I σ 2 > σ 2 fr ] [ ] < E π AM O, i.e., iff: ( 1)[2nα(+n+1) ] n 2 (2 1) 2 n 2 [( 1)( n)+1] 2 α 2 Proof. See Appendix B. Proposition 3 states that, if the uncertainty over erger s efficiency gains is high, outsider firs benefit ore fro the erger than the insider firs. Hence, as the uncertainty increases, ergers becoe less stable. After the erger, the erged fir expects to produce ore quantity than each outsider fir, due to the synergies generated. The outsider firs production depends on whether α u is greater, equal or lower than α. If the level of expected efficiency gains increases and becoes higher than α after the erger, the insider fir still produces ore quantity but the outsider firs will respond by producing a lower quantity. While the profit of the insider fir always increases with the uncertainty, that of an excluded rival also increases as a result of the erger. For high degree of uncertainty, firs would prefer to wait for their rivals to erge and, thus, benefit fro the erger. 11

12 Lea 3. Keeping the nuber of firs constant (n), as the nuber of insider increases (), σfr the region of uncertainty level below which there is no free-riding decreases, i.e., 2 > 0. Also, keeping the nuber of insiders constant, an increase in the nuber of firs in the arket, increases the region of uncertainty level below which there is no free-riding, i.e., σ2 fr n < 0. We find that, under uncertainty about cost synergies and keeping the nuber of firs constant, as the nuber of insider firs increases, ore difficult is for the erger to be stable. Firs have ore incentives to deviate and to copete against its rivals as an outsider. Also, keeping the nuber of insiders constant, we find that the erger becoes ore stable, as the nuber of firs in the arket increases. 5 Nuerical Application In what follows, assue that the total quantity of capital available in the industry is equal to four units (K = 4) and that this capital is equally distributed aongst four firs (n = 4) in the status quo industry structure. We analyse the results obtained for both firs and AA decisions for three cases: 1) Merger involving two firs ( = 2); 2) Merger involving three firs ( = 3); and 3) Merger to onopoly ( = 4). Again, we restrict our attention to the case in which, after the erger, outsiders do not exit the arket (α u < 1 8 ). Further, we also analyse if there is a free-riding proble for both cases 1 and 2. The following proposition sus up the AA decisions for the three erger cases. Proposition 4. The AA accepts the erger involving two firs (case 1) if: σ 2 σ 2 AA{2,1,1} ; The AA accepts the erger involving three firs (case 2) if: σ 2 σ 2 AA{3,1} ; The AA accepts the erger to onopoly (case 3) if: σ 2 σ 2 AA{4}. Proof. See Appendix B. The following proposition sus up firs decisions for the three erger cases. Proposition 5. Firs will propose a erger involving two firs (case 1) if: σ 2 σmp 2 {2,1,1} ; Firs will propose a erger involving three firs (case 2) if: σ 2 σmp 2 {3,1} ; Firs will propose a erger to onopoly (case 3) if: σ 2 σmp 2 {4}. Proof. See Appendix B. The following proposition sus up the results obtained for the free-riding proble for the first two erger cases. 12

13 Proposition 6. There is a free-riding proble (case 1) if: σ 2 σ 2 fr{2,1,1} ; There is a free-riding proble (case 2) if: σ 2 σ 2 fr{3,1}. Proof. See Appendix B. The next three figures represent graphically the results obtained in Propositions 3, 4 and 5. Figure 1: AA s decision ( = 2) Analysing Figure 1, we conclude that, when uncertainty and expected ean about the future efficiency gains level are low, σ 2 < σmp 2 {2,1,1} and µ < µ 2 = , any two-fir erger will never be proposed to the AA. As the expected efficiency gains increase, σmp 2 {2,1,1} < σ2 < σaa{2,1,1} 2 and µ 2 < µ < µ 1 = 1 14, the two fir erger will be proposed to the AA, however it will be blocked since it is expected to reduce the consuer surplus. Further, if both expectations and uncertainty are high, σ 2 > σaa{2,1,1} 2, any two fir erger will be proposed and accepted by the AA. Additionally, there exist a free-riding proble when σ 2 > σfr{2,1,1} 2, that is, outsider firs earn ore fro the erger than the insider firs and this could decrease erger s stability. Also, if the expected efficiency gains are higher than µ 3 = and if uncertainty is not very high σ 2 < σfr{2,1,1} 2 there is a possibility that the erger is accepted by the AA and there is no free-riding proble. 13

14 Figure 2: AA s decision ( = 3) Figure 3: AA s decision ( = 4) Figure 2 suarizes the results obtained when the erger involves three firs. We can observe that when both expected efficiency gains and uncertainty are low, σ 2 < σmp 2 {3,1}, µ < µ 5 = , any three-fir erger will never be proposed to the AA. As the expected efficiency gains increase, σmp 2 {3,1} < σ2 < σaa{3,1} 2 and µ < µ 4 = 3 32, any three-fir erger proposal will be proposed and blocked by the AA. However, when both the expected efficiency gains and the uncertainty increase, σ 2 > σaa{3,1} 2 and µ 4 < µ < 3 32, the three-fir erger will always be proposed and accepted by the AA. Further, in this case there is also a free-riding proble when σ 2 > σfr{3,1} 2, that is, the only outsider fir earns ore fro the erger than 14

15 the insider firs and this could also decrease erger s stability. Also, if the expected efficiency gains are higher than µ 6 = and if uncertainty is not very high σ 2 < σfr{3,1} 2 there is a greater likelihood that the erger of three firs is accepted by the AA and outsiders have no incentives to free ride it. The results obtained for the full erger case are illustrated in Figure 3. Since the σ 2 MP {4} is always negative, for any level of uncertainty, the firs have always incentive to propose a erger to onopoly. However, if the expected efficiency gains and uncertainty are low, σ 2 < σ 2 AA{4} and µ < µ 7 = 1 9, any erger proposal to onopoly will be blocked by the AA. As both uncertainty and expected efficiency gains increase, µ > µ 7 = 1 9, and σ2 > σaa{4} 2, the erger to onopoly will always be accepted by the AA. Figure 4 sus up the results obtained for the three erger cases. Figure 4: AA s decision ( = 2, 3, 4) We conclude that when the level of uncertainty and expected efficiency gains are high, the firs have incentives to propose any type of erger and this erger has a greater likelihood of being accepted by the AA. When both levels of uncertainty and expected efficiency gains are low, the firs have less incentives to propose the erger. As the expected efficiency gains increase, the firs usually propose the erger in each case, however the AA rejects it for all or soe particular cases. Usually in the odels without uncertainty about the future synergies generated by the erger, the AA only accepts the erger if these efficiency gains are sufficiently high (Motta and Vasconcelos, 2005; Vasconcelos, 2010). In contrast, the present paper shows that, with uncertainty, the probability of the erger being accepted is higher than without uncertainty and, for soe cases, ergers could be accepted even if the expected efficiency gains are interediate. Finally, as the nuber of insider firs increases it is ore difficult for the erger to be approved by any AA, even with uncertainty, unless the expected efficiency gains are very high. 15

16 6 Concluding Rearks In this paper we investigate the effects of ergers in a context wherein, both firs and the AA are uncertain about the level of efficiency gains and, therefore, this uncertainty is going to influence the decision of AA but also firs incentives to erge. In the absence of uncertainty and when firs are syetric, the erger will not be profitable unless 80% of the firs in the industry are part of the erger. However, we find that, under uncertainty and asyetric firs, even when the erged fir is not coposed of at least 80% of the firs in the industry, when the uncertainty increases, the expected profit of the erged fir exceeds insiders pre-erger profits, and therefore firs have incentives to erge. Moreover, we find that the higher the level of uncertainty in the arket regarding erger induced efficiencies, the higher the expected consuer surplus after the erger. This then iplies that, given the AAs usually base their erger policy decisions on a consuer welfare standard, higher uncertainty also increases the likelihood that a erger proposal ends up being approved by the AA. Further, we find that a higher degree of uncertainty decreases erger stability, by increasing the likelihood that outsider firs benefit ore fro the erger than the insider fir. The fraework and the assuptions we have assued are of a particular kind. It would be interesting to extend our odel to assess the effects on the decisions of all players, when both firs (insider and outsiders) and the AA face different degrees of uncertainty over the erger s cost savings. We think that this is a very iportant subject for further research. References Air, R., Diaantoudi, E. and Xue, L. (2009), Merger perforance under uncertain efficiency gains, International Journal of Industrial Organization 27(2), Banal-Estañol, A. (2007), Inforation-sharing iplications of horizontal ergers, International Journal of Industrial Organization 25(1), Besanko, D. and Spulber, D. (1993), Contested ergers and equilibriu antitrust policy, Journal of Law, Econoics and Organization 9(1), Clarke, R. (1983), Collusion and the incentives for inforation sharing, The Bell Journal of Econoics 14(2), Corchón, L. and Faulí-Oller, R. (2004), To erge or not to erge: That is the question, Review of Econoic Design 9(1), Cosnita, A. and Tropeano, J.-P. (2009), Negotiating reedies: Revealing the erger efficiency gains, International Journal of Industrial Organization 27(2), Elberfeld, W. and O. Nti, K. (2004), Oligopolistic copetition and new technology adoption under uncertainty, Journal of Econoics 82(2), Gal-Or, E. (1985), Inforation sharing in oligopoly, Econoetrica 53(2),

17 Gal-Or, E. (1986), Inforation transission Cournot and Bertrand equilibria, The Review of Econoic Studies 53(1), Gal-Or, E. (1988), The inforational advantages or disadvantages of horizontal ergers, International Econoic Review 29(4), Horn, H. and Persson, L. (2001), The equilibriu ownership in an international oligopoly, Journal of International Econoics 53(2), Jensen, R. (1992), Innovation adoption and welfare under uncertainty, The Journal of Industrial Econoics 40(2), Jovanovic, D. and Wey, C. (2012), An equilibriu analysis of efficiency gains fro ergers, DICE Discussion Papers 64, Lagerlöf, J. N. (2007), Insisting on a non-negative price: Oligopoly, uncertainty, welfare, and ultiple equilibria, Journal of Law, Econoics and Organization 25(4), Le Pape, N. and Zhao, K. (2013), Horizontal ergers and uncertainty, Econoics Discussion Papers, No , Kiel Institute for the World Econoy. URL: Li, L. (1985), Cournot oligopoly with inforation sharing, The RAND Journal of Econoics 16(4), Lyons, B. (2002), Could politicians be ore right than econoists? a theory of erger standards, Center for Copetition and Regulation UEA Norwich ISSN , Morgan, E. (2001), Innovation and erger decisions in the pharaceutical industry, Review of Industrial Organization 19, Motta, M. and Vasconcelos, H. (2005), Efficiency gains and yopic antitrust authority in a dynaic erger gae, International Journal of Industrial Organization 23(9 10), Neven, D. and Röller, L.-H. (2005), Consuer surplus vs. welfare standard in a political econoy odel of erger control, International Journal of Industrial Organization 23(9 10), Nocke, V. and Whinston, M. (2010), Dynaic erger review, The Journal of Political Econoic 118(6), Novshek, W. and Sonnenschein, H. (1982), Fulfilled expectations Cournot duopoly with inforation acquisition and release, The Bell Journal of Econoics 13(1), Perry, M. and Porter, R. (1985), Oligopoly and the incentive for horizontal erger, Aerican Econoic Review 75(1), Qiu, L. and Zhou, W. (2006), International ergers: Incentives and welfare, International Journal of Industrial Organization 68(1),

18 Raith, M. (1996), A general odel of inforation sharing in oligopoly, Journal of Econoic Theory 71(1), Röller, L.-H., Stennek, J. and Verboven, F. (2001), Efficiency gains fro ergers, European Econoy 5, Sakai, Y. (1985), The value of inforation in a siple duopoly odel,, Journal of Econoic Theory 36(1), Sakai, Y. and Yaato, T. (1989), Oligopoly, inforation and welfare, Journal of Econoics 49(1), Salant, S., Switzer, S. and Reynolds, R. (1983), Losses fro horizontal ergers: The effects of an exogenous change in industry structure on Cournot-Nash equilibriu, Quarterly Journal of Econoics 98(2), Shapiro, C. (1986), Exchange of cost inforation in oligopoly, The Review of Econoic Studies 53(3), Stenbacka, R. (1991), Mergers and investents in cost reduction with private inforation, International Journal of Industrial Organization 9(3), Stennek, J. (2003), Horizontal ergers without synergies ay increase consuer welfare, The B.E. Journal of Econoic Analysis and Policy 3(1), Vasconcelos, H. (2010), Efficiency gains and structural reedies in erger control, The Journal of Industrial Econoics 58(4), Vives, X. (1984), Duopoly inforation equilibriu: Cournot and Bertrand, Journal of Econoic Theory 34(1), Vives, X. (2002), Private inforation, strategic behavior, and efficiency in Cournot arkets, RAND Journal of Econoics 33(3), Wong, K. P. and Tse, M. (1997), Mergers and investents in cost reduction with private inforation revisited, International Journal of Industrial Organization 15(5), Zhou, W. (2008a), Endogenous horizontal ergers under cost uncertainty, International Journal of Industrial Organization 26(1), Zhou, W. (2008b), Large is beautiful: Horizontal ergers for better exploitation of production shocks, The Journal of Industrial Econoics 56(1),

19 Appendix Appendix A - Model derivations A1. Pre-Merger equilibriu Before the erger, firs decide individually their quantity. Knowing that firs are syetric and that each fir owns one unit of asset, the quantity produced by each fir is given by: q i = 1 nα (n+1), with i = 1,.., n. Therefore, the total quantity and price are respectively given by Q = n 1 nα (n+1) and P BM = 1+n2 α n+1. The profit and the consuer surplus are then given by: π BM i = (1 nα)2 (n+1) 2 and CS BM = 1 2 A2. Post-Merger equilibriu n 2 (1 nα) 2 (n+1) 2. After the erger of firs, insider fir now owns units of capital while the outsiders still own 1 unit of capital. Then the erged fir will produce, in equilibriu, Q I = nα u(( 1)( n)+1) (n +2) and the outsiders will produce q o = nαu(2 1) (n +2). The equilibriu profits are then given by: π AM I = [ nαu(( 1)( n)+1)]2 2 (n +2) 2 and π AM O The consuer surplus (CS) is then given by: CS AM = [ (n +1) nαu((n )+1)]2 2 2 (n +2) 2. = [ nαu(2 1)]2 2 (n +2) 2. A3. Expected Insider and Outsider Profits and Expected Consuer Surplus that: Applying the expectations on equation (3), we obtain equation (6): E [ [ ] πi AM ] 2 2nα u (( 1) ( n) + 1) + n 2 α 2 = E u (( 1) ( n) + 1) 2 2 (n + 2) 2 = 2 2nE (α u ) (( 1) ( n) + 1) + n 2 E ( αu 2 ) (( 1) ( n) + 1) 2 2 (n + 2) 2. Knowing that V (α u ) = E ( α 2 u) E 2 (α u ) and that E (α u ) = µ and V (α u ) = σ 2 we get E [ πi AM ] 2 2nµ (( 1) ( n) + 1) + n 2 ( σ 2 + µ 2) (( 1) ( n) + 1) 2 = 2 (n + 2) 2 = [ nµ (( 1) ( n) + 1)]2 2 (n + 2) 2 + σ 2 n2 [( 1) ( n) + 1] 2 2 (n + 2) 2. Applying the expectations on equation (4), we get equation (7): E [ ] [ ] πo AM ] [[ nα u (2 1)] 2 2 2nα u (2 1) + n 2 α = E iu 2 (2 1)2 2 (n + 2) 2 = E 2 (n + 2) 2 = [ nµ (2 1)]2 2 (n + 2) 2 + σ 2 n 2 (2 1) 2 2 (n + 2) 2. 19

20 Applying the expectations on equation (5) we get equation (8): E [ [ ] CS AM] [ (n + 1) nα u ( (n ) + 1)] 2 = E 2 2 (n + 2) 2 = ( (n + 1) nµ ( (n ) + 1))2 2 2 (n + 2) 2 + σ 2 n2 ( (n ) + 1) (n + 2) 2. A4. Full Merger Results The onopoly (M) profit, price and consuer surplus for Stages 3 and 4 are given by: ( ) 2 π M nαu = 2 Appendix B - Proofs B1. Proof of Lea 1 Deriving E [ π AM I ], E [ π AM O E[π AM I ] σ 2 = n2 (( 1)( n)+1) 2 2 (n +2) 2 > 0 E[π AM O ] σ 2 = n2 (2 1) 2 2 (n +2) 2 > 0 E[CS AM ] σ 2 = n2 ((n )+1) (n +2) 2 > 0 E[π AM I ] σ 2 E[π AM I ] σ 2 P M = + nα u 2 CS M = 1 ( nα u ) 2 2 (2) 2 E [ π M] = 2 2nµ + n 2 ( σ 2 + µ 2) 4 2 E [ CS M] = 2 2nµ + n 2 ( σ 2 + µ 2) 8 2. E[πAM O ] = n2 ( 1)[n( 1) (+1)] σ 2 2 (n +2) ] and E [ CS AM ] with respect to the variance, σ 2, we obtain: > E[πAM O ] n > (+1) σ 2 1 n > 1 n > 2. Both E [ πi AM ] [ ] [, E π AM O and E CS AM ] are increasing with respect to the variance, σ 2. Thus the profits and the consuer surplus increase as the uncertainty grows. B2. Proof of Lea 2 Differentiating E [ πi AM ] [ ] [, E π AM O and E CS AM ] with respect to µ we find that the derivatives are positive if and only if: 20

21 E[π AM I ] µ = 2n(( 1)( n)+1)+2n2 µ(( 1)( n)+1) 2 2 (n +2) 2 > 0 µ > n(( n)( 1)+1). E[π AM O ] µ = 2n(2 1)+2n2 µ(2 1) 2 2 (n +2) 2 > 0 µ > n(2 1). In the region of paraeter values wherein the outsiders are active after the erger, µ < n(2 1), their expected profits always decrease in the level of expected efficiency gains. Otherwise, they will exit the arket (and here we assue that all firs are active after the erger takes place).hence, when the erger does not involve all the firs in the industry (n > ), outsiders profits could increase with the level of expectations if µ > n(2 1). However, in this region outsiders would exit the arket. Since we have excluded this scenario, outsiders profits always decrease with the µ. E[CS AM ] µ = 2n(n +1)((n )+1)+2n2 µ((n )+1) (n +2) 2 > 0 µ > (n +1) n((n )+1). Different results are obtained when the level of expectations is not too high and the erger does not involve all the firs in the industry (n > ). Both expected insider profits and expected consuer surplus increase if the expectations satisfy the following thresholds: µ > n(( n)( 1)+1) and µ > (n +1) n((n )+1), respectively. Fro the nuerical siulation we know that µ > is always negative and since we assue that µ > 0, hence when the n(( n)( 1)+1) erger does not involve all the firs in the industry, the expected insiders profits increase with the expected efficiency gains level. However, we also know that µ > (n +1) n((n )+1) is always greater than 1 2n. Hence, when the erger does not involve all the firs in the industry, the expected consuer surplus decreases with the expected efficiency gains level. Additionally, if the erger involves all the firs in the industry (n = ) both expected consuer surplus and expected insider profits increase if µ > 1. Since we assue that µ < 1 2n < 1, therefore both expected consuer surplus and insider profits always decrease with the level of expectations, when the erger is to onopoly. B3. Proof of Proposition 1 Equation (9) is obtained fro the expression for the expected variation of the consuer surplus. It is straightforward to show that ECS > 0 holds for σ 2 > σ{,n } 2. Hence, the AA will accept the erger if it anticipates it will enhance expected consuer surplus, i.e., iff: E [ CS AM] CS BM. This happens when: E[CS] = [(n +1) nµ((n )+1)]2 + σ 2 n 2 [(n )+1] 2 1 n 2 (1 nα) (n +2) (n +2) (n+1) 2 Fro Assuption 3, we know that α = µ: [(n +1) nα((n )+1)] 2 + σ 2 n 2 [(n )+1] 2 1 n 2 (1 nα) (n +2) (n +2) (n+1) 2 Solving with respect to σ 2, we get: σ 2 2 (n +2) 2 n 2 (1 nα) 2 [(n +1) nα((n )+1)] 2 (n+1) 2 (n+1) 2 n 2 [(n )+1] 2. 21

22 B4. Proof of Proposition 2 Firs will propose the erger if: E [ π AM I ] π BM E[MP ] [ nµ(( 1)( n)+1)]2 + σ 2 n 2 [( 1)( n)+1] 2 (1 nµ)2 0 2 (n +2) 2 2 (n +2) 2 (n+1) 2 Solving with respect to σ 2 and knowing that µ = α get: σ 2 (1 nα)2 3 (n +2) 2 [ nα(( 1)( n)+1)] 2 (n+1) 2 (n+1) 2 n 2 [( 1)( n)+1] 2. B5. Proof of Proposition 3 There is a free-riding proble when E [ π AM I ( [ nµ(2 1)] 2 2 (n +2) 2 + σ 2 n 2 (2 1) 2 2 (n +2) 2 ) Solving with respect to σ 2 : ] [ ] < E π AM O, that is, ( ) [ nµ(( 1)( n)+1)] 2 + σ 2 n 2 [( 1)( n)+1] 2 > 0 2 (n +2) 2 2 (n +2) 2 σ 2 > ( 1)[2nα(+n+1) ] n 2 (2 1) 2 n 2 [( 1)( n)+1] 2 α 2. B6. Proof of Proposition 4 Replacing n = 4 and = 2, 3, 4, for each erger case, we get the results for the AA s decision in Proposition 4: The AA accepts the erger of two firs (case 1) if: σ 2 σ 2 AA{2,1,1} (14µ 1)(114µ 31) 2500 ; The AA accepts the erger of three firs (case 2) if: σ 2 σ 2 AA{3,1} (32µ 3)(112µ 33) 1600 ; The AA accepts the erger to onopoly (case 3) if: σ 2 σ 2 AA{4} 3(9µ 1)(37µ 13) 25. B7. Proof of Proposition 5 Replacing n = 4 and = 2, 3, 4, for each erger case, we get the results for the erger profitability in Proposition 5: Firs will propose a erger of two firs (case 1) if: σ 2 σ 2 MP {2,1,1} 356µ+412µ ; Firs will propose a erger of three firs (case 2) if: σ 2 σ 2 MP {3,1} 1272µ+1744µ ; Firs will propose a erger to onopoly (case 3) if: σ 2 σ 2 MP {4} 3(11µ+1)(7µ 3) 25. B8. Proof of Proposition 6 Replacing n = 4 and = 2, 3, 4, for each erger case, we get the results for the free-riding proble in Proposition 6: There is a free-riding proble (case 1) if: σ 2 σ 2 fr{2,1,1} µ µ 1 68 ; 22

23 There is a free-riding proble (case 2) if: σ 2 σ 2 fr{3,1} µ µ Appendix C - Results without Assuption 3 If µ < n(2 1), outsiders do not exit (NE) the arket, hence the AA will accept the erger if E [ CS AM] CS BM, that is, if: CS NE = 2 (n +1) 2 2µn(n +1)((n )+1)+n 2 (σ 2 +µ 2 )((n )+1) (n +2) 2 n2 (nα 1) 2 2(n+1) 2 0; σ 2 > n2 µ 2 ((n )+1) 2 (n+1) 2 +2µn(n +1)((n )+1)(n+1) 2 n 2 ((n )+1) 2 (n+1) (n 2 (nα 1) 2 (n +2) 2 (n +1) 2 (n+1) 2 ) n 2 ((n )+1) 2 (n+1) 2. CS NE µ < 0 µ < (n +1) n((n )+1) ; CS NE σ 2 = 1 2 n2 (( n) 1) 2 2 (n +2) 2. The higher is the σ 2 the greater is the CS AM, the greater the CS NE is. CS NE α = n 3 1 nα (n+1) 2 ; CS NE α before the erger. > 0 α > 1 n, however α ust be lower than 1 n, otherwise firs do not produce If µ > n(2 1), then outsider firs will exit the arket, hence the AA will accept the erger if E [ CS AM] CS BM, that is, if: CS E (n + 1)2 2 nµ + n 2 ( σ 2 + µ 2) (n + 1) n 2 (nα 1) 2 8 (n + 1) CS E µ > 0 µ > 2n(n+1) 2 ; CS E α = 162 n 4 α+16 2 n 3 2(n+1) CS E α = n 3 1 nα (n+1) 2 ; > 0 α < 1 n, which is always true. CS E σ 2 = n2 (n+1) 2 8(n+1) 2 2 > 0. The higher is the σ 2 the greater the CS M is and, thus, the greater is CS E. Hence, with high uncertainty on the level of efficiency gains, the greater is the likelihood that the AA accepts the erger to onopoly. If µ < n(2 1), outsiders do not leave the arket. Hence, firs will propose the erger ] π BM : if it is profitable, i.e., E [ π AM I 2 2nµ(( 1)( n)+1)+n 2 (σ 2 +µ 2 )(( 1)( n)+1) 2 2 (n +2) 2 (1 nα)2 (n+1) 2. MP NE 2 2nµ (( 1) ( n) + 1) + n 2 ( σ 2 + µ 2) (( 1) ( n) + 1) 2 (1 nα)2 2 (n + 2) 2 (n + 1)