Structuring M&A Offers: Auctions, Negotiations and Go-Shop. Provisions

Transcription

1 Structuring M&A Offers: Auctions, Negotiations and Go-Sho Provisions Zhe Wang November 4, 01 Job Market Paer Abstract An imortant yet understudied asect of mergers and acquisitions is the selling rocedure. This aer comares a seller s revenue in a standard English ascending auction to that in a negotiation with a go-sho rovision. In the latter, the target rivately negotiates with a few bidders, signs a tentative merger agreement with one of them, and then solicits additional bids ublicly during a go-sho eriod. With a theoretical framework, I show that a go-sho negotiation generates higher seller revenue than does an auction, when (i) the costs to bidders of learning their valuations are sufficiently high, (ii) the bidders valuations are moderately correlated with each other, and (iii) the bidders rior robabilities of the existence of gains from trade are sufficiently low. The theoretical results are broadly consistent with emirical evidence, and they rovide a novel exlanation for the revalence of go-sho negotiations in rivate equity deals. 1 Introduction The rocedures by which comanies are sold in mergers and acquisitions (M&A) take varying forms. Of articular interest is the revalence of two forms: an ascending auction and a negotiation with a go- I am grateful for the suort I receive from my dissertation committee members Steven Grenadier, Peter DeMarzo, Victoria Vanasco, and Jeffrey Zwiebel. I owe my gratitude to Alexander Gorbenko and Andrey Malenko for generously sharing their data. I have also been fortunate to receive numerous valuable comments from Shai Bernstein, Jeremy Bulow, Yi Chen, Darrell Duffie, Piotr Dworczak, Laurie Simon Hodrick, Xing Li, Paul Milgrom, George Triantis, Jing Zhou, and all articiants in my ractice job market talks. I am resonsible for all remaining errors and omissions. zhewang5@stanford.edu 1

2 sho rovision. While the former rocedure has historically been more revalent, go-sho negotiations have been increasingly oular since emerged in a rivate equity deal in 004. For an examle of a standard auction, consider a merger between two healthcare comanies. On August 18th, 015, the board and the senior management of the target comany Sequenom decided to ursue a business combination in the form of a sale to a strategic buyer. 1 The sale rocess began when the target firm hired the investment bank J.P. Morgan Securities to ublicly solicit bids from 5 otential strategic bidders. Then, the target held an auction in which all interested buyers submitted their bids. Finally, the target signed a merger agreement with one bidder, Laboratory Cororations of America Holdings, which submitted the highest bid $.4 er share, and the deal was settled. This tye of mechanism is also called a re-signing market check, because most market checks are conducted before signing a merger agreement. The other selling rocedure, a go-sho negotiation, aeared before the Leveraged Buyout Boom. An examle concerns the sale of CKE Restaurants to a rivate equity firm Aollo Management. In Setember, 009, three rivate equity firms exressed interest in buying the target. The target s board then set u a secial committee to rivately negotiate with all of them, while excluding the senior management from most of the negotiation rocess. At the end of the negotiation, the target signed a tentative merger agreement with the highest bidder among the three, Thomas H. Lee Partners. The agreement secified a minimum bid $11.05 er share for that bidder, the target s right to solicit other bids in a go-sho eriod after announcing the agreement, and a ayment to Thomas H. Lee in case a suerior roosal aeared during the go-sho eriod. Such ayment includes a $9.8 million termination fee lus a cost reimbursement caed by $5 million. Then, the target ublicly announced the merger agreement in a ress release. During the subsequent 40-day go-sho eriod, the target hired investment bank UBS to contact 4 rivate equity firms and 4 otential strategic buyers, soliciting their interest in making a suerior roosal. Among them, a rivate equity firm Aollo Management toed the original offer with a bid of $1.55 er share, which Thomas H. Lee was not able to match. As a result, Aollo won the deal, while the target aid the termination fee and the cost reimbursement to the initial bidder. Practitioners also refer to such mechanism as a ost-signing market check, because most market checks are conducted after signing a tentative merger agreement. 1 Strategic buyers are usually cororate buyers that look for comanies that will create a synergy with their existing businesses.

3 Standard auctions have been a traditional selling mechanism, which are used in 3% of M&A deals between 003 and 015. A go-sho negotiation, on the other hand, reresents a relatively new mechanism. Originated with deals involving rivate equity buyers, go-sho negotiations continue to be more revalent in deals attracting financial buyers, the majority of which are rivate equity firms. 3 Emirical evidence suggests that the revalence of go-sho negotiations is higher in deals attracting mostly financial buyers (1%) than in deals attracting mostly strategic buyers (3%). 4 The frequency of use of a go-sho negotiation is also higher in bankrutcy sales under Section 33 of Chater 11 (84%) than in non-bankrutcy M&As (5%). 5 In addition, it differs across target industries. The emirical evidence motivates two questions: (1) why are both auctions and go-sho negotiations observed in ractice? () why do we observe cross-sectional variations in the use of go-sho negotiations? Conventional wisdom exlains the use of standard ascending auctions, while attributing the use of go-sho negotiations to agency conflicts. Bulow and Klemerer (009) suggest that an auction generates higher revenue for the seller because it increases bidder articiation. Denton (008) believes that a target management chooses a go-sho negotiation to favor a articular bidder, which has romised the management a large comensation ackage. 7 It has also been heavily debated in courts on whether a go-sho negotiation mechanism has fulfilled the Revlon duties that require the target management to maximize the shareholders value. 8 This aer suggests an alternative exlanation for the use of go-sho negotiations. That is, when information acquisition is costly, a go-sho negotiation generates higher seller revenue than does a standard auction by inducing higher bidder articiation. In such a mechanism, the target bribes one bidder to Source of data: MergerMetrics. 3 Unlike strategic buyers whose synergy with the target comes from combining the two businesses, the synergy between the target and a financial buyer stems from the financial buyer s ability to imrove on the target s cororate governance and caital structure after making the target go rivate. 4 Source of Data: MergerMetrics, As the research of Gorbenko and Malenko (014) shows, deals won by a financial (strategic) buyer attract mostly financial (strategic) bidders. In addition, analysis of MergerMetrics database ( ) imlies that the frequency of use of this mechanism is much higher if the deal is won by a financial buyer (1%) than if the deal is won by a strategic buyer (3%) (it reached % in deals won by a financial buyer in 015). Therefore, go-sho negotiations are more frequently used in deals attracting mostly financial buyers than in those attracting mostly strategic buyers. 5 Source of data of bankrutcy sales: Gilson, Hotchkiss and Osborn (015). Source of data for non-bankrutcy M&As: MergerMetrics In articular, the frequency of use of go-sho negotiations is high if the target is in Consumer Durables, Consumer Non-Durables, and Retail Trade (11%), and it is lower in High-Tech, including Technology Services, Electronic Technology, and Health Technology (3%). Source of Data: MergerMetrics, The author believes that the go-sho eriod in the go-sho negotiation mechanism is essentially window-dressing to reduce litigation risk. See also Antoniades, Calomiris, and Hitscherich (013) about litigation risk concerns. 8 See Subramanian (008) s comarison of the Delaware Chancery Court s decision on In re Tos Comany Shareholders Litigation and on In re Lear Cororation Shareholder Litigation. 3

4 conduct costly information acquisition first and to make a ublic bid. The initial bid, if high enough, will reveal the attractiveness of this deal to other similar buyers for free, and therefore will imrove bidder cometition for this deal. In articular, I build a model in which there are two otential bidders and one seller. It is costly for bidders to learn their values for the target firm, and these values are ositively correlated. I show in the benchmark model that the seller s revenue in a go-sho negotiation is strictly higher than it would be in an English ascending auction when (i) bidders costs of learning their values for the target firm are sufficiently high, (ii) bidders values for the target firm are sufficiently correlated, but not too highly correlated, and (iii) bidders rior robabilities regarding the existence of gains from trade are low enough that no otential bidder would make a serious bid 9 without knowing the existence of gains from trade. I further show that the referential treatment involves both a transfer from the seller to the first bidder in the form of a termination fee, and an inefficient allocation rule that assigns the target firm more often to the initial bidder than to the second bidder. In fact, such referential treatment in favor of the first bidder is inevitable whenever the otimal go-sho negotiation outerforms the otimal ascending auction. The key results of the benchmark model are confirmed by a more elaborate model with normally distributed bidder values and more natural assumtions regarding information technology. I then show that, if the bidders values for the target firm are less correlated, a go-sho negotiation dominates a standard auction within a smaller range of arameters. A rediction of the model is therefore that gosho negotiations are used more often than English ascending auctions when bidders values for the target firm are more correlated. This rediction is broadly consistent with the emirical evidence based on the hand-collected data generously rovided by the authors of Gorbenko and Malenko (014) 10, and the data from MergerMetrics between 003 and 015. The intuition for the key results are as follows. When bidders rior robabilities of gains from trade are low, no bidder will make a serious bid without knowing the existence of gains from trade. This could generate a roblem for an English ascending auction, where information acquisition by bidders must be simultaneous. In articular, when information acquisition is too costly comared to the exected rofit from the bidding game, the cometition among bidders leads to little incentive for all bidders to acquire 9 Here, a serious bid refers to a bid that exceeds the target s stand-alone value. 10 The data was hand-collected from SDC database by the authors. 4

5 information at the same time. This may occur due to a high information cost of learning the existence of gains from trade, a essimistic rior robability of the existence of gains from trade, or an exceedingly high correlation between the bidders values for the seller s firm. 11 As a result, there is little bidder articiation, and the seller s revenue is low. The roblem could otentially be alleviated in go-sho negotiations, where information acquisition is sequential. In this mechanism, the seller first incentivizes one bidder to acquire the information about the existence of gains from trade by romising that bidder a termination fee. By announcing the first bid, the seller then reveals the information acquired by the first bidder to the second otential bidder. If the bidders values for the target firm are sufficiently highly correlated, the second otential bidder becomes informed of the existence of gains from trade for free by learning that the first bidder s value is sufficiently high. This raises bidder articiation relative to the case of English ascending auctions. When the benefit of more bidders being informed of the existence of gains from trade outweighs the cost of referential treatment to the first bidder, the seller s revenue is higher in go-sho negotiations. However, if the bidders values are excessively correlated, go-sho negotiations can no longer imrove uon English ascending auctions. This is because the second stage is similar to Bertrand cometition. Execting very low rofit from the second stage auction, the second bidder will not enter the game even if knowing there is gains from trade. I further consider an extension in which the mechanism is the result of a negotiation between the seller and the first bidder. The main results hold in a manner in this extension, as well as in additional variations of the model. Finally, using the data from MergerMetrics and the data rovided by the authors of Gorbenko and Malenko (014), I resent suggestive emirical evidence on the alternative hyotheses that (1) go-sho negotiations are driven by a bidder with strong bargaining ower, and () the target management uses a go-sho negotiation to favor one bidder while sacrificing the shareholders value. The emirical evidence suggests that the former hyothesis is not lausible, though the latter might lay a role in Management Buyouts where agency conflicts are otentially salient. However, the agency conflicts hyothesis is unlikely to be the entire story, because Management Buyouts are only a small fraction of all deals using a go-sho negotiation. 11 When the correlation is too strong, the bidding game if both bidders acquire information is similar to a Bertrand cometition. Therefore, the information rent given to each bidder would be low. The intuition why a high correlation of bidder values leads to low bidder information rent is similar to that of the Linkage Princile in Milgrom and Weber (198). 5

6 The rest of the aer is organized as follows. Following a literature review, Section describes the model setu. Section 3 finds the otimal ascending auction and go-sho negotiation mechanisms, and comares the seller s revenues between the two. Section 4 considers extensions. Section 5 emirically examines the imlications of the model and alternative hyotheses. Section concludes. The aendices rovides the roof and additional emirical evidence. Related Literature To the knowledge of the author, this is the first formal model that catures the institutional features of go-sho negotiations observed in ractice. Still, the aer is related to the literature on sequential negotiations featuring reemtive bidding, including Fishman (1988), Bulow and Klemerer (009), and Roberts and Sweeting (013). These aers show that a high first bid would reemt information acquisition by the second bidder, under the assumtions that it is costly for the bidders to learn the idiosyncratic art of their values, termination fees are not allowed, and the first bidder is free to make any bid. This aer, however, assumes that it is costly to learn the art of the synergy shared by both bidders. Therefore, referential treatment such as termination fees are essential to incentivizing the first bidder to conduct costly information acquisition and to rovide information externality to the second bidder. In addition, this aer assumes that the seller only allows the first bidder to decide whether to bid above a certain threshold, without revealing the actual bid. This assumtion makes reemtive bidding less of a concern, and allows me to focus on the key channel of the aer. Finally, this aer shows that a sequential negotiation generates higher seller revenue than a standard auction because it increases bidder articiation. However, in Bulow and Klemerer (009), a sequential negotiation is dominated by a standard auction because it reduces bidder articiation. This aer is also related to other works on sequential mechanisms. Povel and Singh (00) show that if both bidders are already informed, and the information of one bidder is more imortant to both bidders, then the otimal mechanism for the seller is a sequential bidding game. Betton, Eckbo, and Thorburn (009) considers a sequential negotiation model of hostile takeover with indeendent bidder values and toehold. Glode and O (01) study the trading rotocol for the sale of a financial asset. They comare the social welfare between a sequential trading game and a static auction, in a setting where the two buyers and the seller s values for the security are interdeendent. On the contrary, my aer aims to exlain cororate transactions. Therefore I assume that the seller s stand-alone value (market caitalization before merger) is common knowledge, where the bidders values are otentially correlated. In addition, I focus on seller revenue otimization instead of social welfare.

7 This aer is also related to the following studies on the benefit of information revelation. Milgrom and Weber (198), and Eso and Szentes (007) investigate the information disclosure in auctions, and show that more information revelation increases the seller s revenue. Duffie, Dworczak and Zhu (015) consider a search model of the trading of financial assets, and they show that revealing the common cost of sellers could increase investor articiation. Sherman and Titman (00) and Sherman (005) investigate the IPO book building. They show that IPO underricing serves to comensate the rimary dealers for information acquisition about the quality of the issued equity, and such information is revealed to the secondary market investors by the bids of rimary dealers. My aer is different for the following reasons. First, IPO underricing models involves both the rimary market and the secondary market, while my model involves only the rimary market. Second, all investors values on the issued equity are identical, while in my model it is essential that the bidders values are not erfectly correlated. Third, rimary dealers who care about their reutation are willing to rovide high quality information. In my model, however, the first bidder would like to avoid revealing the existence of gains from trade, so as to minimize second stage cometition. Another related literature is mechanism design with information acquisition. Persico (000) comares the amount of information acquisition in first-rice and second-rice sealed-bid auctions. Assuming the object will always be sold, Bergemann and Valimaki (00) show that the information acquisition exceeds that of the social otimum in a standard English auction when bidder values are indeendent. Assuming instead that the target firm is sold only if the rice exceeds the target s stand-alone value, my model shows that information acquisition is below social otimum in a standard English auction. Shi (01) considers the otimal mechanism with information acquisition and rivate value, while this aer allows for correlated values. The aer is also related to theory works on multi-stage auctions such as Ye (00), and tender offer auctions such as Schwartz (198), Berkovitch, Bradley and Khanna (1989). Finally, the aer is connected to the following emirical studies. First, it is related to Gorbenko and Malenko (014) who investigate the difference between financial bidders and strategic bidders. Second, it is connected to a surrisingly small emirical literature on go-sho rovisions, which are a key feature of go-sho negotiations. Subramanian (008) and Jeon and Lee (014) claim that go-sho rovisions might benefit the seller comared to the deals with no-sho rovisions. Denton (008) states that gosho is chosen over standard auctions due to agency conflicts between the target management and the 7

8 shareholders. Antoniades, Calomiris, and Hitscherich (015) believe that the over-use of go-shos reflects excessive concerns about litigation risks, ossibly resulting from lawyers conflicts of interest in advising targets. Other related emirical literature includes Boone and Mulherin (007b) that comares multibidder takeover deals to single-bidder takeover deals, Boone and Mulherin (007a) and Burch (001) about termination fees and other deal rotections, and Gilson, Hotchkiss and Osborn (015) about stalking horse bid in bankrutcy rocess. Setu of the Model There two bidders and one seller..1 Valuations The seller s outside otion if no sale is m, which can be thought of as the stock market caitalization. The bidders stand-alone values if there is no trade with the seller are both n. The values of the outside otions are common knowledge. The two bidders values for the target firms are W 1 = m + x 1 + V W = m + x + V Therefore, the synergy between bidder i and the target is u 1 = x 1 + V u = x + V where the common art of the synergy is Z, with robability V = Z, with robability 1 with Z > 0. This art is due to the common exertise among the two bidders. The idiosyncratic synergy of bidder i is x i U [l, h], i.i.d., and is also indeendent to the common synergy V. 8

9 I make the following assumtions for the valuations. Assumtion 1. (common synergy as indicator of gains from trade) Z + x i > 0, and Z + x i < 0, x i [l, h]. Assumtion. (uninformed buyer does not bid) E (V ) + x i < 0, x i [l, h]. Discussion on Assumtion 1 and Assumtion. Assumtion 1 imlies that the variation of the common art dwarfs that of the idiosyncratic art, so the common synergy is the indicator of gains from trade. A direct imlication of this assumtion is that bidders values for the target firm are highly correlated. Assumtion states that, if a buyer does not know whether there exists gains from trade, the buyer will not make a bid that exceeds the target s stand-alone value. This is true even if the realized idiosyncratic synergy reaches the highest value ossible. That is, if a otential bidder neither ays the cost to acquire the information of the common synergy nor learns about this information from others, the otential bidder effectively dros out from the bidding game. For this reason, the seller would like as many bidders to become informed about V as ossible.. Information Technology Without information acquisition, neither the seller nor the bidders know V or x i, i = 1,. The seller can invite bidders to conduct information acquisition. If invited, bidder i has the otion to acquire information in the following order: If aying a cost c V, bidder i can learn about V erfectly; Then, if aying a cost c x, bidder i can learn about x i erfectly, indeendent to whether bidder 1 has learned V or not. The information is rivate to the bidder who acquired it. In addition, I follow the tradition of the literature of information acquisition, and assume that the action of information acquisition is non-observable by others. This is because an outsider cannot verify whether a bidder has exerted effort. I make the following assumtion about how the cost of information acquisition is allocated between learning about the common art and the idiosyncratic art. Assumtion 3. (info acquisition mostly on common art) c V > 0, c x = 0. 9

10 Assumtion 3 states that the cost of information acquisition on the common art of the synergy is significant, while the idiosyncratic art of the synergy is negligible. This assumtion is made in accordance with Assumtion 1, following the logic that more (less) information acquisition effort is required if the amount of uncertainty is higher (lower). In addition, I consider the information acquisition of the common art V and the idiosyncratic art x i searately. That is, it is ossible that a bidder learns only x i but does not exert the effort to learn V. I also assume that the otion to learn about the common synergy takes lace before that of the idiosyncratic art of synergy for tractability. 1 In Section 4., I will consider a model with a more natural setting on information acquisition technology and normally distributed valuations. I show with numerical examles that the key results in the benchmark models still hold. Define entry for a bidder in this model as (i) the bidder has learned both V and x i, and (ii) the bidder submits a bid higher than the target s stand-alone value (a serious bid). Under the settings above, knowing V is the necessary and sufficient condition for entry because the idiosyncratic art of synergy x i is always learned 13, and there is no additional logistic bidding cost. The information acquisition cost c V is then equivalent to the entry cost..3 The Ascending Auction and Go-Sho Negotiation Mechanisms I now make formal characterizations of the ascending auction and go-sho negotiation mechanisms by secifying their timelines. A standard English ascending auction t = 0, the seller otimally chooses a reserve rice r, announces it and commits to it. t = 1, the seller invites both bidders for information acquisition, the technology of which is secified in Section.. t =, the seller holds an English auction (ascending auction) with reserve rice r. 1 Hence, there would be no contingent information acquisition on the common art of synergy based on the value of x i. These assumtions allow me to focus on the information acquisition of the common art of the synergy, while avoiding analyzing the interaction between the information acquisition about the common art and the rivate art. 13 For this reason, in my model, a high first bid does not deter entry by the second bidder. 10

11 t=0 t=1 t= The seller otimally chooses reserve rice, announces it and commits to it. The seller invites both bidders for information acquisition. Each bidder first decides on learning, then learns regardless. The seller holds an English auction (ascending auction) with reserve rice. Figure.1: Timeline: An English Ascending Auction A go-sho negotiation t = 0, the seller otimally chooses the trilet (b 1, T F, r B ) (will be defined in the timeline), announces it and commits to it. t = 1, the seller invites bidder 1 for information acquisition, the technology of which is secified in Section.. t = 1.5, the seller asks if bidder 1 is willing to join the English auction haening at the final date and bid at least b 1, in exchange for termination fee T F. If bidder 1 agrees, the seller romises to ay bidder 1 a termination fee T F if bidder 1 loses the deal; otherwise, bidder 1 is excluded from the game, and the seller moves on to bidder. t = 1.75, the seller announces bidder 1 s decision of accetance or rejection. Then, the seller invites bidder to acquire information regardless, the technology of which is secified in Section.. t =, If bidder 1 is not excluded, the two bidders begin an English auction (ascending auction) with a reserve rice b 1 and a termination fee T F to bidder 1; otherwise, the seller sets a reserve rice r B for an English auction with only bidder. Figure.1 and. illustrate the timelines. The italic arts in Figure. are the key elements in go-sho negotiation that makes the mechanism different from a standard English auction. 11

12 t=0 t=1 t=1.5 t=1.75 t= The seller otimally chooses (,, ), announces them and commits to them. The seller invites bidder 1 for information acquisition. Bidder 1 first decides on learning, then learns regardless. The seller asks if The seller bidder 1 accets to announces bid at least, in bidder 1 s exchange for a decision. termination fee. The seller Yes: bidder 1 gets then invites if not winning; bidder for information No: bidder 1 is excluded. acquisition regardless. The seller holds an English auction (ascending auction). Reserve rice: if bidder 1 accets: ; if bidder 1 rejects:. Figure.: Timeline: Go-Sho Negotiation Note that I assume the auctions to be English ascending auctions. In such auctions, the rice continuously increases beginning with the reserve rice. A bidder dros out from the auction if the rice exceeds the bidder s willingness to ay. If, after a bidder has droed out, there is only one bidder left, then the only bidder that remains wins and ays the rice at which the revious bidder droed out. If all excet one bidder dro out as soon as the rice exceeds the reserve rice, the remaining bidder wins and ays the reserve rice. I assume an English auction because, with multile rounds of bidding, a takeover auction in ractice is more like an English auction comared to sealed-bid auctions (first rice or second rice) or a descending auction. 14 I make the following two assumtions for both mechanisms. Assumtion 4. Termination fee is non-negative. Assumtion 5. Reserve rice is no lower than the target s stand-alone value m. Assumtion. If the second bidder wins, the target reduces the firm value by the amount of the termination fee and ays that amount to the initial bidder, before delivering the firm to the second bidder. Assumtion 4 is a common restriction in bidding games due to bidders concern about the bidding game being a scam. It is essentially a restriction of limited liability that imlies no strictly ositive entry fee. Assumtion 5 is made because it is difficult for the seller to commit to sell at a rice lower than 14 This view is shared by Gorbenko and Malenko (014), who furthermore oint out the comlicated nature of the format of auctions used in mergers and acquisitions. Therefore, an English auction is only a reasonable aroximation of the auction format observed in ractice. 1

13 its outside otion. Section shows that if instead of Assumtion, we assume the seller ays the termination fee out of the roceeds collected from the second bidder, all results remained to be the same. 3 Otimal English Auction and Go-Sho Negotiation, and Comarison between the Two 3.1 Seller s Objective and Equilibrium Concet The seller s objective is to maximize revenue. By choosing an ascending auction, the seller otimizes over the reserve rice r; by choosing a go-sho negotiation, it otimizes over the trilet (b 1, T F, r B ), which includes the minimum bids romised by the first bidder (b 1 ), the termination fee ayable to the first bidder (T F ), and the reserve rice in the final stage auction if the first bidder is excluded (r B ). The equilibrium concet used in this model is Perfect Bayesian Nash Equilibrium. As for the equilibrium refinement criterion for multile equilibria in the bidding stage, I consider the weakly dominant strategy equilibrium; for multile equilibria in the information acquisition stage, I follow the tradition of mechanism design by assuming that the seller induces the most desirable equilibrium; if seller is indifferent among all equilibria, I assume that the seller chooses the equilibrium that is continuous in arameters. 3. Seller s Otimal Revenue in a Standard English Ascending Auction Proosition 3.1 summarizes the seller s otimal revenue and corresonding equilibrium. Proosition 3.1. The seller s revenue under the otimal reserve rice and the otimal equilibrium under the reserve rice are: (1) when c V [0, () ], both bidders acquire information. The seller s revenue is m+ () when c V ( (), c], both bidders acquire information with robability 1 c V () (h+l+3z) The seller s revenue is m + 3((h+l+Z) c V ) 4(h+l+3Z). ( Z + l + 3 ). (0, 1). (3) when c V ( c, () ], only one bidder acquires information. The seller s revenue is m + (Z + l). (4) when c V ( (), (Z + l) + (h l)], only one bidder acquires. The seller s revenue is m + ) (Z + 1 (h + l) c V. (5) when c V ((Z + l) + (h l), + ), no one acquires information. The seller s revenue is m. Here, c = (h+l+z) (Z+l)(h+l+3Z) 3. 13

14 0 h +, h Full Entry: Both bidders acquire info about. Partial Entry: Either both bidder acquire info about with mixed-strategy, or only one bidder acquires. No Entry: No bidder acquires info about. Figure 3.1: Bidder Entry in a Standard Ascending Auction Denote c ( (h l)) = (), and c ( (h l), (Z + l)) = (Z + l) + 1 (h l), we have Figure 3.1 summarizing the extent of entry (number of bidders informed of V ). Intuition for Proosition 3.1 and Figure 3.1 When deciding whether to acquire information in a standard English auction, a bidder trades-off the cost of information acquisition c V against the otential rofit from the bidding game. The otential rofit from the bidding game consists of two arts. The first art is the minimum level of synergy, (Z + l). The second art consists of the information rent due to the uncertainty in the rivate art of the synergy, which is roortional to (h l). Therefore, how c V is comared to (Z + l) and (h l) will determine the level of entry. As c V increases, there would be less information acquisition and hence less entry. Therefore, the mechanism of ascending auction has the roblem of insufficient entry. 3.3 Seller s Otimal Revenue in go-sho negotiations From the discussion on an English ascending auction, we know that, when c V is large, there might be insufficient information acquisition about the existence of gains from trade, and hence, there would be insufficient entry. With a go-sho negotiation in the form of a sequential negotiation, however, we could otentially solve the roblem by comensating one bidder to acquire information and revealing it to the other. In this way, both bidders learn the value of V, and the seller achieves full entry. Following this logic, we focus on go-sho negotiation mechanisms that imlement equilibrium of the following form and otimize within this category: For tractability, I restrict attention to go-sho negotiation mechanisms that induce a ure-strategy equilibrium of infor- 14

15 Bidder 1 acquires information about V ; Bidder 1 accets the rice floor b 1 if and only if V = Z; The seller s revenue is non-negative. I denote this case as the go-sho negotiation fully revealing V, in which bidder 1 s decision to accet the rice floor b 1 fully reveals the value of V. Later, I will show that the otimal go-sho negotiation that fully reveals V remains otimal if considering all otential tyes of equilibrium to imlement, as long as the cost c V is in a reasonable range. Incentive Comatible Problems in go-sho negotiations Before deriving the otimal go-sho negotiation ste-by-ste, it is helful to discuss the key difficulties regarding imlementing the equilibrium above. First, the seller needs to incentivize bidder 1 to acquire information and rovide information externality. There is a hold-u roblem, because information acquisition is not contractable. The solution is to comensation bidder 1 for info acquisition with termination fee T F, conditional on the first bid is high enough (higher than b 1 ), because a high willingness to ay imlies that the information has been acquired. Second, the seller has to incentivize bidder 1 with V = Z not to mimic V = Z, because bidder 1 with V = Z tries to hide the existence of gains from trade to avoid cometition. The solution is to exclude bidder 1 if the first bid is too low (lower than b 1 ). Finally, the seller needs to incentivize bidder 1 with V = Z not to mimic V = Z, because bidder 1 with V = Z tries to mimic V = Z to get the termination fee T F. The solution in this case is to set the rice floor b 1 to be high enough, such that acceting it imlies some chance of winning. Next, we will derive the otimal go-sho negotiation mechanism Otimal go-sho negotiation fully revealing V The following roosition describes the equilibrium induced by the otimal go-sho negotiation mechanism that fully reveals V. mation acquisition. Focusing otimization on this category may not be as restrictive as it may seem. It is ossible that the otimal go-sho negotiation mechanism must induce bidder 1 to acquire information, and bidder 1 accets b 1 only if V=Z, as long as the cost of information acquisition is too large. Intuitively, this is because (1) it is not rofitable for the seller to have at most one bidder informed when it is ossible to make both bidders informed, and () there is no oint in retaining bidder 1 if V=-Z. 15

16 Proosition 3.. (equilibrium under the otimal go-sho negotiations) Suose c V min{ (1 ) Z 1 (h l), (Z + l + 54 (h l))}. Under the otimal (b 1, T F, r B ), there exists an equilibrium in which (i) Both bidders articiate in the mechanism. (ii) Bidder 1 acquires information about V, accets the minimum bid if V = Z regardless of x 1, and rejects otherwise. If acceting the rice floor, Bidder 1 s rice at which to dro out of the English auction is. m + Z + x 1 T F b 1 = m + b 1 if x 1 b 1 + T F Z m if x 1 < b 1 + T F Z m (iii) Bidder learns V from bidder 1 s action and therefore does not acquire information about V. Bidder believes that V = Z iff bidder 1 accets the rice floor b 1. Bidder s rice at which to dro out is m + ˆV + x T F in the English auction, where ˆV is the value of V learned from bidder 1 s action. This roosition illustrates the essential strength of a go-sho negotiation over an ascending auction. That is, by making both bidders informed of the existence of gains from trade, a go-sho negotiation imroves entry. However, the referential treatment in a go-sho negotiation mechanism could otentially be a drawback. To see how the forces weigh against each other, I derive the roof of Proosition 3. and look for the exact form of the otimal (b 1, T F, r B ). Using backward induction, I solve the otimal go-sho negotiation mechanism fully revealing V. Suose that bidder 1 has acquired information. Let us consider the English auction at t =. The case with bidder 1 rejecting the rice floor is straightforward. Bidder 1 is excluded from the trade, and bidder also dros out from the game because V = Z is revealed. The lemma below 1 derives the equilibrium 1 Here is a roof of the lemma. In the English auction, bidder 1 makes the first bid b 1. If at b 1, bidder decides to dro out, and bidder 1 therefore wins, aying b 1. If bidder is able to to b 1, each bidder i continues to to the oonent s bid until the rice level reaches the threshold of droing out, which is b i. To rove the form of b 1 and b, we first consider bidder 1 s dominant strategy. We know that bidder 1 has committed not to dro out until b 1. Starting with m + u 1 T F < b 1, suose b < b 1, i.e., bidder dros out at the beginning of the auction. Then, bidder 1 is indifferent about droing out at any b 1 b 1, because bidder 1 always wins and ays b 1. Suose b b 1 ; then, bidder 1 dros out at b 1 because droing out at any level strictly higher than b 1 weakly increases the chance of winning for bidder 1 and weakly increases the rice to ay for b 1. Since m + u 1 b 1 < T F, winning and aying b 1 already gives bidder 1 negative rofit, not to mention if the rice of winning is higher than b 1. Therefore, to minimize loss, bidder 1 will not dro out at a level higher than b 1. Next, consider the case with m + u 1 T F b 1. Then, following the standard argument with a tyical English auction, droing out at the net value of winning m + u 1 T F is the dominant strategy for bidder 1. Second, we consider bidder s dominant strategy to dro out. The standard argument in a tyical English auction leads to the same conclusion that b = m + u T F. 1

17 of the continuation game in the English auction at t = if bidder 1 accets the rice floor b 1. Lemma 3.1. Suose that both bidders know V erfectly and that, in an English auction, the seller has already set a reserve rice b 1 and bidder 1 has agreed to bid at least b 1 for all x 1 [l, h]. In addition, suose that the seller commits to ay T F to bidder 1 if bidder 1 loses. Then it is a weakly dominant strategy for bidder 1 and bidder to dro out at b 1 = m + max (u 1 T F, b 1 ), and b = m + u T F resectively, where u i = V + x i, i = 1, is the synergy between bidder i and the target. Note that m + u i T F, i = 1, are the bidder i s valuation of the firm if winning the auction, net of the rofit if losing because, for bidder 1, winning gives n + m + u 1, while losing gives n + T F ; for bidder, winning gives n + m + u T F because T F is aid out of the value of the firm according to Assumtion, while losing leads to outside otion n. Termination fee T F and rice floor b 1 together determine the allocation distortion in favor of bidder 1 (i.e. the target firm is inefficiently assigned to bidder 1 more often), and the transfer from the seller to bidder 1. In articular, if b 1 increases while fixing T F, it is harder for bidder to to the first bid b 1. However, b 1, which is the rice that bidder 1 has to ay to the seller if bidder does not to the first bid, would be higher too. Therefore, there is more allocation distortion in favor of bidder 1, but less transfer from the seller to bidder 1. On the other hand, if T F increases while fixing b 1, it is also harder for bidder to to the first bid when taking into account of a higher T F. Moreover, if bidder is able to to the first bid b 1, bidder s bid in the second stage would decrease by the amount by which T F increases; then, bidder 1 has to ay less if winning over bidder in this case. Therefore, the target s firm is also inefficiently assigned to bidder 1 more often, and the transfer from the seller to bidder 1 is higher. Since allocation distortion is affected by both T F and b 1, I will define a new variable to isolate the force affecting allocation inefficiency. In articular, I define as = b 1 (m + Z + l T F ). That is, if V = Z is revealed to both bidders, is the difference between bidder 1 s romised minimum 17

18 bid b 1 and bidder s minimum rice to dro out in the second-stage auction. This term measures how difficult it is for bidder to to the first bid b 1, because the robability of the first bid b 1 being toed is Pr (x > ) = 1. The allocation rule of the game if V = Z is uniquely determined by, according to Lemma 3. below. Lemma 3.. Consider the equilibrium described in Lemma 3.1 and consider the case with V = Z. If [0, h l] so that l + [l, h]. (i) if x 1 l +, or if x 1 < l + and x l +, bidder i wins if and only if x i x i. (ii) if x 1 < l + and x < l +, bidder 1 always wins. If 0, there is no distortion; if > h l, bidder 1 always wins. A direct imlication of Lemma 3. is Proosition 3.3. Proosition 3.3. ( ins down allocation distortion, T F determines transfer) 17 (i) The target firm is inefficiently assigned to bidder 1 if and only if > 0. The exected efficiency ( ) loss from such distortion is l+, which is increasing in. (ii) The termination fee T F is only a transfer from the seller to bidder 1 and does not create distortion. In the case of V = Z, Figure 3. summarizes the bidding strategy of both bidders characterized in Lemma 3.1, and the distortion of allocation in Proosition 3.3. The arrows demonstrate the bidding strategies. The arts marked by bold red segments cature the scenario where there exists allocation distortion. That is, when x 1 < l + and x < l +, bidder 1 always wins the target firm, regardless of how x 1 is comared to x. For the rest of the cases, the target firm is allocated efficiently. Now that we know the bidding strategy of both bidders, we are ready to rove Proosition 3. by looking at incentive-comatible conditions and individual rationality conditions. First, we check if bidder does not acquire information after observing bidder 1 s decision. This is trivially true because bidder 1 s action reveals erfectly the value of V. Bidder s articiation constraint that the equilibrium utility must be higher than the outside otion n is also true because no information acquisition cost is aid and the rofit of an informed bidder in an English auction is non-negative. Bidder s belief is also consistent with Bayesian udating and bidder 1 s strategy. Therefore, we have roven art (iii) of Proosition 3.. Next, we study bidder 1 s accetance and rejection decision after acquiring information. Suose the otimal [0, h l], which will be verified later in the Aendix. 17 A higher while fixing T F also imlies a lower transfer from the seller to the bidder 1, because b 1 is higher. 18

19 x 1 x h h l + Distortion l l Figure 3.: Bidding Strategy and Allocation Distortion If V = Z, bidder 1 is suosed to turn down the rice floor and obtain its outside otion n. If bidder 1 accets the offer instead, he will dro out at b 1 to minimize the chance of winning because bidder s net valuation from winning is n Z + x n = Z + x, which is negative according to Assumtion 1. Therefore, bidder 1 with V = Z rejects the rice floor x 1 [l, h] if P (x < l + ) (n + m Z + x 1 b 1 ) + (1 P (x < l + )) (n + T F ) < n, x 1 T F + h l ( Z + x 1 l ) < 0, x 1 T F < (Z h + l + ). (3.1) h l If V = Z, we need to make sure that bidder 1 accets the rice floor. If x 1 l +, bidder 1 s bid is unaffected by the rice floor b 1 = m + Z + l + T F, since this is the minimum rice for him to dro out of the English auction. Then b 1 = m + u 1 T F, b = m + u T F. Then, bidder 1 s exected ayoff by acceting the rice floor is P (x l + ) (P (x 1 x x l + ) E [n + m + Z + x 1 m Z x + T F x 1 x, x l + ] +P (x 1 < x x l + ) (n + T F )) +P (x < l + ) (n + m + Z + x 1 b 1 ) = n + T F + (x 1 l ) (h l) + h l (x 1 l ) U, T F 0, x 1 [l +, h] 19

20 Therefore, bidder 1 with x 1 l + always accets the rice floor for any non-negative T F. If x 1 < l + and bidder 1 accets the rice floor, he would bid b 1 to minimize his loss. Then, bidder 1 with x 1 accets the rice floor if P (x < l + ) (n + m + Z + x 1 b 1 ) + (1 P (x < l + )) (n + T F ) n h l (x 1 l ) + T F 0 x 1 l + T F h l. Therefore, if T F (i.e., T F 0), then all x 1 < l + accet the rice floor and bid b 1. In this case, bidder 1 s bid is m + Z + x 1 T F, b 1 = b 1, x 1 l + x 1 < l + Therefore, bidder 1 with V = Z accets the rice floor for all x 1 [l, h] if and only if T F h l. (3.) Finally, we look for the conditions under which bidder 1 is willing to acquire information. If bidder 1 does not acquire information and rejects the rice floor, he obtains n. If he accets the rice floor, the best he can do is to bid b 1 in the auction because his synergy is negative for all x 1 according to Assumtion. Therefore, he gets P (x < l + ) (n + m + E (V ) + x 1 b 1 ) + (1 P (x < l + )) (n + T F ) = n + h l (Z + (1 ) ( Z) + x 1 Z l + T F ) + h l T F h l = n + T F + h l ( Z (1 ) + x 1 l ) (3.3) Hence, bidder 1 s exected utility if not acquiring information about V is [ n + E x1 {max 0, T F + ] h l ( Z (1 ) + x 1 l ) }. 0

21 We then derive the exression for bidder 1 s exected utility if acquiring information. In this case, with T F, all x 1 accets the rice floor. Bidder 1 s utility of acquiring information is then U 1 = c V + n + P (x l + ) P (x 1 l + ) {P (x 1 x x 1, x l + ) T F +P (x 1 x x 1, x l + ) E (x 1 + Z Z x + T F x 1 x, x 1, x l + )} + P (x < l + ) E (x 1 + Z Z l + T F x < l + ) + P (x l + ) P (x 1 < l + ) T F [ (h l )3 = c V + n + T F + (h l) + ( l + h l ) ]. h l Hence, for bidder 1 to acquire information, we need [ U 1 n + E x1 {max 0, T F + ] h l ( Z (1 ) + x 1 l ) } (3.4) In addition, for bidder 1 to be willing to enter the mechanism, we need U 1 n. (3.5) Combine the conditions (3.1) to (3.5), recall that Assumtion 4 leads to T F 0, and assume that 0 h l. 18 We can then write down the conditions for a go-sho negotiation to induce a searating equilibrium fully revealing V, and the roblem of the seller s otimization of revenue under those 18 Will be verified in the Aendix. 1

22 conditions. max,t F (1 ) m + [P (x < l + ) (m + Z + l + T F ) +P (x l + ) P (x 1 l + ) E (m + Z + min (x 1, x ) T F x 1, x l + ) +P (x l + ) P (x 1 < l + ) (m + Z + l + T F )] = m + (Z } + l + {{ T F } ) (h l ) (h l) rice floorb }{{} 1 extra rofit from cometition s.t. (a) T F 0, (Assumtion 4) (b) 0 h l, (restrictions, will be verified later) (c) T F h l (Z h + l + ), (tye V = Z rejects b 1 ) [ (d) U 1,F A n + E x1 {max 0, T F + ] h l ( Z (1 ) + x 1 l ) }, (Bidder 1 acquires info) (e) T F h l, (V is fully revealed: x 1accets if V = Z) (f) U 1,F A n, (Bidder 1 articiates) (3.) In the case with V = Z, bidder 1 is excluded from the game. Therefore, bidder would also bid below m, and the seller is indifferent between any r B m. Let the otimal r B = m + Z + l. Solving the roblem above leads to the full characterization of the otimal go-sho negotiation mechanism fully revealing V, as stated below. Proosition 3.4. (An otimal go-sho negotiation that fully reveals V) Suose c V < min{ (1 ) Z 1 (h l), (Z + l + 54 (h l))}, and restrict attention to go-sho negotiation mechanisms that induce equilibria in which bidder 1 acquires information and accets the rice floor if and only if V = Z. Then, the otimal (b 1, T F, r B ) within this category includes a rice floor b 1 = m + Z + l + T F and r B = m + Z + l, where (, T F ) is characterized as follows: (i) if c V [ 1/55, min{ (1 ) Z 1 (h l), (Z + l + 54 (h l))}), then ( (, T F ) = 3 17 (h l), 1 (h l) + c ) V.

23 0 h +, h,, Full Entry: Bidder 1 acquires info, and accets rice floor iff =. Bidder learns from bidder 1. Figure 3.3: Bidder Entry in Go-Sho Negotiations (ii) if c V [, 1/55 ), then [0, 3 (h l)) and is the unique solution for [ ] c V = 3 (h l) 3 3 (h l) (h l) and that it is strictly increasing in c V. T F satisfies T F = h l. (iii) if c V [0, ), then (, T F ) = (0, 0). Denote c ( (Z + l), (h l),, Z) = min{ (1 ) Z 1 (h l), (Z + l + 54 (h l))}. Then, similar to Figure 3.1, Figure 3.3 summarizes the level of entry for bidders in go-sho negotiations. Comarison of the two figures show that go-sho negotiations create higher entry for a wide range of c V. 3.4 Go-sho negotiations imlementing other tyes of equilibria The otimal go-sho negotiation mechanism that imlements equilibrium fully revealing V remains to be otimal if I consider imlementation of all tyes of equilibria. Proosition 3.5. The otimal go-sho negotiation mechanism is stated in Proosition

24 0 h +, h,, Seller Revenue: Go-Sho Negotiation = Auction Both: full bidder articiation Seller Revenue: Go-Sho Negotiation > Auction Go-Sho: full bidder articiation Auction: artial/zero bidder articiation Figure 3.4: Comarison between the Two Mechanisms: Seller Revenue and Bidder Particiation 3.5 Revenue Comarison between a Go-Sho Negotiation and an English Ascending Auction This section introduces the key result of the aer by comaring the seller s revenue under the otimal go-sho negotiation mechanism and the otimal ascending auction mechanism. Proosition 3.. Restrict attention to c V such that 0 c V c ( (Z + l), (h l),, Z). (i) If c V is large enough, i.e., c V > c ( (h l)), the seller s revenue in the otimal go-sho negotiation mechanism is strictly higher than that in the otimal ascending auction. (ii) If c V is small enough, i.e., c V c ( (h l)), the otimal go-sho negotiation mechanism achieves the same revenue as in the otimal ascending auction. Moreover, go-sho negotiations can create higher revenue for the seller in go-sho negotiation than in the otimal ascending auction if and only if it increases bidder entry. The result is intuitive. go-sho negotiations imrove the seller s revenue because they increase entry. Recall Figure 3.1 and 3.3 that show the level of entry in the two mechanisms. When c V is very small, both bidders acquire information in an English auction; hence, there is already full entry. Therefore, go-sho negotiations cannot imrove the revenue. When c V is large enough but not unreasonably high, go-sho negotiations induce full entry, while English ascending auctions induce at most artial entry, so the revenue from go-sho negotiations is strictly higher. Figure 3.4 summarizes the key results of the revenue comarison The Trade-offs between a go-sho negotiation and an ascending auction Whenever the revenue in the otimal go-sho negotiation is higher than that of the otimal ascending auction, the difference can be decomoses into the forces in favor of and against go-sho negotiation as 4