Optimal M&A Advisory Contracts

Transcription

1 Optima M&A Advisory Contracts Rajkama Vasu Companion Paper to the Job Market Paper This Version: November 27, 207 Most Recent Version at Abstract Consider a scenario where a firm is in negotiations with a potentia buyer. Both the buyer and the seer are uninformed about the vaue of synergies, but they can hire an M & A Advisor. Suppose, though, that the seer and buyer face a mora hazard probem. If the advisor s effort is not observabe, he has the option of not exerting effort and reporting any of the possibe vaues. Shoud the seer and buyer hire an advisor and what is the optima contract that they shoud sign with him? We find that the probabiities with which the buyer and seer hire their advisors and the optima contracts are determined simutaneousy in equiibrium. Both contracts depend on two variabes- whether the transaction succeeds or not and, if it does, the vaue of the transaction. The seer s optima contract with his advisor is unique, but the buyer s optima contract can take a variety of forms. The compensation of the seer s advisor is monotonicay increasing in the transaction vaue. Neither advisor is paid if the transaction fais. In equiibrium, both advisors exert effort, report truthfuy and do not extract any information rents. However, the first best is not obtained because the transaction can fai even though it is sociay optima. Keywords: Contracts, Negotiations, Mergers and Acquisitions JEL Cassification: D86, D82, G34 Keogg Schoo of Management, Northwestern University, E-mai: rajkamavasu@keogg.northwestern.edu. I am extremey thankfu to Michae Fishman for his vauabe suggestions. In addition, I woud aso ike to thank David Dranove, Ronad Dye, Ben Iverson, Konstantin Mibradt, Nicoa Persico, Mitche Petersen, James Schummer and Danie Spuber for their hepfu feedback. Panteeimon Loupos, Kirti Sinha and Micha Zator, feow PhD students at Keogg, aso provided new perspectives. The errors are a mine.

2 Introduction Mergers and acquisitions are a significant mechanism of aocating assets to their most productive users. A merger transaction need not be a zero-sum game; it can eave both the buyer and the seer better off. Mergers can have rea effects by increasing the market power of firms and affecting ownership patterns in the economy. A we functioning market for corporate contro can serve as a barometer of the heath of the economy and its effectiveness in driving weaker firms out of business In the US, there have historicay been periods of frantic merger activity, commony referred to as merger waves, interspersed with periods of reative cam marked by esser consoidation. The first merger wave at the turn of the nineteenth century was marked by a series of horizonta consoidations instrumenta in the emergence of the arge modern corporation. Five other merger waves foowed, each with its own unique characteristics. There are indications that we might be experiencing a seventh merger wave. In 205, M&A activity reached very high eves, with $ 4.28 triion worth of deas wordwide. There were 4,786 deas amounting to $.97 triion (approximatey % of GDP) in the US aone. Both the goba and American tota dea vaues are the highest ever recorded. Many of these deas featured M&A advisory firms advising the seer, the buyer or both. In fact, some of the prominent deas featured mutipe investment banks heping the same party. The advisory fees from competed transactions aone were estimated to be $ 29.4 biion. 2 If advisory firms are so common in acquisitions, what are the functions they perform? Servaes and Zenner [996] compare acquisitions competed with and without investment banks too see why banks are hired and what functions they perform. They argue that investment banks decrease transaction costs by being abe to anayze acquistions at a ower cost and thus reduce the asymmetric information inherent in any merger transaction. Asymmetric information between the seer and the buyer regarding the synergies of the transaction are pervasive in acquisitions. The buyer and seer often have drasticay different assessment of the synergies in the transaction. This can ead to a sociay efficient transaction faiing or an inefficient transaction going through. A recent exampe is the faiure of Microsoft to acquire Saesforce. Athough Microsoft was wiing to offer roughy $ 55 biion for the company, Microsoft s offer was met with counteroffers from Saesforce which were as high as $ 70 biion. 3 Another exampe of a possiby momentous merger faiing due to disagreements beween the target and bidder over the price occured when Source: Goba and regiona M&A: 205, report by Mergermarket. Web. Accessed 23 October Source: Mergers & Acquisions Review: Financia Advisors. Fu Year 205, report by Thomson Reuters. Web. Accessed 23 October Kedmey, Dan. Heres Why Microsoft Didn t Buy Saesforce. Time Magazine 22 May 205. Web. Accessed 23 October

3 negotiations between Uber and Lyft fe through in Since investment banks decrease the asymmetry of information, their presence may make the difference between the success or faiure of the merger, both in terms of the transaction happening and in terms of the ater performance of the target firms. However, the presence of an investment bank introduces another friction into the dynamics of the transaction, namey mora hazard. This is because exerting effort to vaue the synergies is costy for the investment banks. Since the effort is costy and frequenty not observabe or contractibe, the investment bank has an incentive to report a vaue of synergies without doing any investigation. The seer and buyer must incentivise their advisors to put in effort by structuring the wage contract with him appropriatey. Hunter and Waker [990] find that gains from a merger are associated with the banks exerting effort. 5 McLaughin [990] points out that making fees contingent on the success of the transaction can ead to conficts of interest between banks and bidding firms. These kind of contracts are not optimay constructed to sove the mora hazard probem. The bidder s bank may ask the bidder to bid high to ensure the transaction going through and pocket the fees. Even with optima contracts, it is not obvious that the first best can be reaized. McLaughin [992] finds evidence from examining tender offers that the effectiveness of fee contracts in soving agency probems in tender offers is mixed. It is very much possibe that an expert is hired to provide a vauation for the target rather than an investment bank. A case in point is PE funds in India, who are hiring industry veterans. An expert mentions that providing information on target vauations is the primary function he performs: Sumit Banerjee, a cement hotshot for over a decade, is the go-to man for PE and strategic payers whenever a new target comes into the saemarket. Banerjee, in the ast two years, has advised at east three potentia suitors Apoo, Backstone and even Pirama Enterprises on as many occasions as they went after Lafarge s India operations and Reiance Cement... For each of the evauations, the funds had the bandwidth to do modeing and financia projections. A they needed was someone to vaidate their assumptions on market growth, prices and peope. My desire was to advise them on the fundamenta strength and weaknesses of the target which have a direct bearing on vauations. 6 4 Shen, Lucinda. Uber Confirms 204 Negotiations to Buy Lyft. Fortune Magazine 2 September 206. Web. Accessed 23 October However, their proxy for effort is the ease with which the merger negotiations were conducted. It is not cear that this is the best proxy for effort. For instance, a merger can happen if the buyer s advisor reports the highest possibe vaue of synergies without putting in any effort because the buyer wi bid the highest possibe vaue. 6 Barman, Arijit & Layak, Suman. Why private equity funds and banks are wooing former head 3

4 In practice, M & A advisors may aso perform a number of other services ike ega services, post-merger integration consuting services, searching for bidders or targets, advice on restructuring the target and heping to raise capita to finance the acquisition. In this paper,we focus ony on the vauation services provided by the advisors. As we have argued, this is one of the most important functions of the advisor, if not the most important. In addition, nothing prevents the seer or buyer from offering separate contracts to the advisors for the other functions and the vauation services. Many of the advisory contracts seen in practice are ineary increasing in transaction vaue. Two justifications for this both turn out to be fase under coser examination. First, a fee increasing in vaue is reminiscent of Hömstrom [979]. The resembance is superficia. In Hömstrom [979], the wage depends on output because effort is not observabe, but output, which is increasing in effort, is. However, the vaue of synergies is competey independent of the advisor s effort. underying the optima contract. Hence, that is not the mechanism Second, invesigating the vaue of a big firm might invove a higher cost of effort than for a sma firm, so one woud expect the payment to the advisor to be increasing in vaue. The faacy in this argument is that we are comparing the payments across two transactions, one the sae of a sma firm and another a arge one. This paper is about why the fee paid in a given transaction depends on the vaue of the transaction. It is a comparison among different reaizations of vaue in a given transaction than different expected vaues across transactions. We mode the sae as happening through a take-it-or-eave-it offer made by the seer to the buyer. We aso assume that the seer and the buyer choose to hire an advisor or not without knowing whether the other party has a hired an advisor or not. As aready mentioned, the friction is that the advisor can report a vaue of the synergies without having exerted the effort to find out the vaue. The research question I address in this paper is the structure of the optima contract between the acquirer/target and their M&A Advisor to overcome this mora hazard probem. This can be spit into a number of sub-questions. First, what observabe parameters does the contract depend on? Does it, for exampe, depend on the vaue of the transaction or whether the transaction was a success or not? Is it increasing in the vaue of the transaction? Or is the contract a fat fee? Are the optima contracts unique? Second, if effort is costy for the advisors, for what range of the effort costs are the advisors hired? Intuitivey, there must be an upper bound above which the seer or the buyer do not wish to hire the advisor since the cost is greater than the vaue of knowing the synergies precisey. What is the upper bound, given that neither party knows whether the other is informed or not? Third, do the advisors report truthfuy in equiibrium? Do honchos of India Inc to manage their investments. The Economic Times 8 September 206. Web. Accessed 23 October

5 they extract information rents in equiibrium? In other words, wi the payment to either advisor higher than their cost of effort? Fourth, are there pure strategy equiibria where the buyer/seer aways hires an advisor or doesn t? Can we have mixed strategy equibria too (i.e. seer/ buyer mixes between hiring and not hiring the advisor)? If so, what are the probabiities with which the advisors are hired and how do they depend on the effort costs? Fifth, what are the strategies of the seer/buyer when they are informed/ uninformed i.e. when they have hired an advisor or haven t? Does the seer aways charge the fair price when he is informed? Does the buyer aways accept it? Sixth, what are the impications of the mora hazard probem on efficiency? How cose do we get to first-best? Assuming that the synergies are aways greater than zero and it is optima to se the firm to the acquirer, how often does the transaction fa through in spite of it being optima? How does this affect the tota surpus in the transaction spit between the buyer and the seer? We sove the probem in three steps, starting with a simpe set up and graduay making it more compex. In Part I, we assume that the buyer is aways informed and the seer has to minimize the payment to his advisor subject to incentivising the advisor to exert effort. In other words, this part considers the optima contract under the simper case where the buyer aways hires an advisor. In Part II, we argue that this may not be a reaistic assumption and sove for a mixed equiibrium where the buyer and seer mix between hiring their advisor and not hiring him. I treat the payment to the advisor as an exogenous parameter i.e. do not consider any contract. In part III, we combine Parts I and II. We attack the grand question of how the optima contracts ook ike when both the buyer and seer optimay choose whether to hire an advisor or not. The main resuts I obtain are as foows. First, the optima contract for both the buyer and the seer depends on two variabes- whether the transaction succeeded or not and, if it did, the vaue of the transaction. There is no payment to the advisor if the transaction faied. The seer s optima contract with his advisor is unique and the advisor s compensation is monotonicay increasing in the transaction vaue. The buyer s optima contract with his advisor can take a variety of forms. However, a of these contracts share the feature that the advisor is not paid if he reports the same vaue to the synergies as the maximum offer the uninformed buyer woud have accepted. (Intuitivey, the advisor is not paid if it made no difference to the buyer s decision whether to accept the offer). Second, there is a wide range of effort costs for which the equiibria exist. I make the simpifying assumption that the costs for both the advisors are the same and sove for the equiibrium strategies as a function of the exogenous effort costs. Third, the contract incentivises the advisors to exert effort and report truthfuy in equiibrium. The advisors do not extract information rents in equiibrium. Fourth,there a range of vaues for which 5

6 we observe mixed equiibria. I fuy characterize the strategies of the buyer and seer i.e. their probabiities of hiring their advisor in terms of the exogenous effort costs of the advisor. The buyer s propensity to acquire information increases when the seer doesn t do so. Fifth, There are ranges of the vaue where the informed seer charges a fair price, but there are ranges where he undercharges and overcharges as we. Sixth, the first best is never obtained. Even though the advisors do not obtain information rents, there are two other sources of inefficiency. The first is that in equiibria where one party ends up informed and the other uninformed, the asymmetry of information eads to the transaction faiing. The probabiity of the transaction succeeding decreases as the advisor s cost of effort increases. The second source of inefficiency is that even if the transaction is a success, the advisor has to be a paid its cost of effort which destroys some of the surpus in the transaction. The tota surpus in the transaction is ess than the expected vaue of the synergies. The primary contribution I make in this paper is to characterize the optima contract in a mergers and acquisition setting. Athough there have been a few empirica studies onadvisory contracts in mergers, there have not been theoretica justifications of the same. I sove this contracting probem aong with the reated probem of costy acquisition of sociay inefficient information.the optima contract with the advisor depends on whether the other party hires the advisor or not. To sove for the contract, one needs to know when the parties invoved decide to acquire the information and vice versa. The rest of the paper is organized as foows. Section 2 reviews reevant reated iterature. In Section 3, we provide the finer detais of the mode and discuss the assumptions thoroughy. Sections 4, 5 and 6 sove the mode in three parts as mentioned above. Section 7 summarizes the resuts by giving a compete characterization of the Equiibria. Section 8 anayzes the impications of the equiibria for efficiency. Section 9 generates testabe empirica hypotheses and vaidates empirica work aready done on the topic. Finay, Section 0 concudes. 2 Reated iterature Servaes and Zenner [996] was among the eariest papers to shed ight on the factors affect the hiring of investment banks. They compare 99 transactions from 98 to 992 which featured an investment bank, to 98 transactions that didn t. They find that banks are more ikey to be hired for compex transactions and if the targets operate in many industries. This eads them to concude that transaction costs and, in part, contracting costs and information asymmetries affect the decision to hire a bank. Owsey and Kaufman [2005] is a good description of the roe of investment banks in bankruptcy. They make the case that handing distressed purchase and sae transactions require more ski than saes invoving sovent companies. 6

7 Few empirica studies have ooked at the actua contract between the advisors and the seer or buyer. 7 McLaughin [990] examines 95 tender offers between 978 and 985 and describes incentive probems associated with the various kind of contract designs. The contract fees fa into three basic categories: fixed fees, shares-based fees (used by buers), and vaue-based fees (mosty used by seers). McLaughin [992] finds that fee contracts are used by both firms and bankers to sove agency probems, but they do not eiminate them. There are associations between firm objectives and contract incentives and between incentives and offer outcomes in some tests, but not in others. Hunter and Waker [990] find that in their sampe, the investment bank contracts were mosty fixed fee contracts or were based on the transaction price, contingent on the success. There have been many studies ooking at the association between the decision to hire an investment bank and the outcome of the merger. Hunter and Waker [990] was one of the eariest studies to find a positive reationshietween fees, merger gains and banker effort. They concude that investment banking merger fee contracts are designed with the aim of incentivizing optima banker effort. Servaes and Zenner [996] do not find any difference between the returns earned by acquirers which hired a bank and those that didn t. Danies and Phiips [2009] show that hiring a financia advisor is associated with increases the transaction vaue in REIT mergers because advisors reduce the asymmetric information between the target and the bidder. Goubov et a. [202] argue that the effect of the hiring the advisor may vary depending on the isting status of the target. In recent years, a host of studies, too numerous to recount exhaustivey, have anaysed the roe of bank s reputation on the gains from the merger. Kae et a. [2003] find evidence that the reputation of the financia advisor affects weath gain in the transaction and how it is spit between the target and the acquirer. Hunter and Jagtiani [2003] document a negative reationshietween reputation and merger outcomes. The synergistic gains reaized by the acquirers decined when top advisors were used. However, the contingent fees payed a significant roe in expediting the dea competion. Ismai [200] point out that in their sampe, acquirers advised by tier-one advisors ost more than $42 biion, but those advised by tier-two advisors gained $3.5 biion. They attribute this to the arge oss deas advised by tier-one advisors, citing the differing incentives of banks in arge and sma deas as the reason. Rau [2000] finds that the post-acquisition performance of the bidding firm is negativey reated to contingent fees in tender offers, porssiby because the banks just try to compete the dea. 8 Goubov et a. [202] use a sampe of U.S. acquisitions of pubic, private, and subsidiary firms from 996 to They find that top-tier advisors are associated with higher bidder returns in pubic acquisitions because they garner a greater share of synergies for the bidder. The effect is 7 This may be due to data imitations. Even for pubic deas, the fees paid to the advisor are not aways discosed since the discosure is not mandatory 8 This is exacty the mora hazard probem we mode in this paper. 7

8 dampened when the target advisor is aso top-tier. Another strand of reated iterature ooks at how information acquisition can destroy efficiency. A recent exampe is Gode et a. [202] where two risk-neutra traders exchange an asset. Acquiring expertise is neutraized in equiibrium because the counterparty aso acquires it. 9 Shave [994] considers a scenario where buyers and seers can acquire and discose information prior to sae. He concudes that if discosure is vountary rather than mandatory, there are sociay excessive incentives to acquire information. The contribution I make in this paper is to tie together these two strands of research. I argue that the two probems are connected. Incentives to acquire information depend on the other party s cost of acquiring information, which in turn is a function of the optima contract. So, it is impossibe to describe the optima contract without knowing the probabiities with which the buyer and seer are informed. Simiary, it is impossibe to know the probabiity with which the buyer and seer are informed without knowing the cost of the information if the contract is optima. 3 Modeing the M&A process 3. The framework The target (seer) and the acquirer (buyer) are both risk-neutra. The stand-aone vaue of the firm and the distribution of the synergies are common knowedge. However, the reaized vaue of the synergies V is unknown uness an M&A advisor exerts effort to discover it. The synergies are aways positive, so it is sociay optima to trade. The seer and the buyer thus have to decide how to spit the uncertain synergies between them. (From here on, we use vaue to denote the reaized vaue of the synergies). This creates a probem of asymmetric information if either of them knows the vaue and the other doesn t. As a resut, the transaction may fai even though it is sociay eficient to transfer the asset. The acquisition process can proceed through various mechanisms- by an auction, many rounds of bargaining etc. To simpify the anaysis, we assume that the seer has the bargaining power and the sae happens through a take-it-or-eave-it offer made by the seer to the buyer. The seer and the buyer have the option of hiring an M&A advisor who can exert effort to find the reaized vaue. (For exampe, an Investment Bank. In the rest of the 9 Their mode differs from ours in quite a few ways. First, their vaue is binary, whereas we consider a uniformy distributed vaue. Second, they give the bargaining power to the buyer and we to the seer. Third, they assume that synergies are known and vaue unknown; we assume that the vaue is known and synergies unknown. Lasty and most significanty, they assume an exogenous cost of acquiring information whereas we endogenize the cost through optima contract design. 8

9 paper, we use the terms bank and advisor interchangeaby) Neither party observes whether the other has hired an advisor or not. In other words, the seer, when making the offer, is unaware whether he is facing an informed buyer or an uninformed one. Simiary, the buyer, when deciding whether to accept the offer, is unaware whether the offer was made by an uninformed seer or an informed one. The advisor has a cost of exerting effort c. If the advisor exerts effort, he gets to know the vaue exacty. If he reports truthfuy to the party which hired him, they get to know the exact vaue as we. Both the seer and the buyer face a probem of mora hazard since the effort exerted by the advisor is not observabe and, consequenty, not verifiabe. This prevents the seer and buyer from paying the advisor depending on the effort exerted by the advisor even though they woud ike to. I assume that the wage can ony depend on the vaue reported by the advisor and whether the sae happened i.e. whether the buyer accepted the seer s offer. These assumptions are discussed in more detai in section 3.4 The optima contract between the seer (or buyer) and his advisor minimizes the expected payment to the advisor conditiona on incentivizing the advisor to exert effort. The contract specifies a wage schedue w : R + {0, } R +. The wage w(v, ) depends on the vaue V reported by the advisor and a binary variabe which takes the vaue when the transaction succeeds and 0 when it did not. 3.2 The timing The timing of the game is as foows:. The vaue V is reaized. 2. The seer (buyer) decides whether to hire an advisor or not. 3. If he hires a advisor, the seer (buyer) offers a wage contract to his advisor. 4. The advisor accepts the contract or rejects it. 5. If the advisor has decided to accept the contract, he chooses whether to exert effort or report a vaue without exerting effort. 6. The advisor reports a vaue to the seer (buyer). 7. The seer makes an offer to the buyer. 8. The buyer accepts the offer or rejects it. 9. If the buyer accepts the offer, the sae happens at the offer price. If the buyer rejects the offer, the sae doesn t happen. 0. The seer (buyer) pays his advisor the wage. 9

10 3.3 Soution Concept The soution concept is Perfect Bayesian Equibrium. Reca that in a PBE, the strategies of the payers have to be sequentiay rationa and the beiefs have to be consistent with the equiibrium strategies whenever possibe. Specificay, we ook for mixed equiibria where the buyer and seer are indifferent between hiring the advisor or not hiring it. 3.4 Discussion of the assumptions In this section, we provide justifications for some of the assumptions we make about the M&A process The bargaining power Empirica studies of mergers and acquisitions have repeatedy confirmed a puzzing trendfoowing a merger announcement, the target s stock price increases on an average and the acquirer s stock price fas. 0 For exampe, when AT&T s acquisition of Time Warner was reported, Time Warner s share price rose 9% on the news whie AT&T s dipped cose to 3%. This suggests that if there are any synergies in the transaction, the target extracts most of them. Hence, it seems reasonabe to assume that in the negotiation process, the target (or seer) has the bargaining power The take-it-or-eave-it offer In reaity, firms can be sod through auctions or negotiations. In recent years, approximatey 50% of the transactions are auctions and the other negotiations. 2 Even in a negotiation, the bargaining process can be qute compicated. The assumption that the seer is negotiating ony with one buyer and that the sae happens through a take-it-oreave-it offer is done for tractabiity Neither the seer nor the buyer observes whether the other has hired a bank This might seem ike a strong assumption. However, a bank may be hired for many reasons. As ong as both parties are unaware whether a bank has been hired by the other party specificay for vauation rather than something ese, this assumption is justified. Second, it is sufficient if neither party observes the other hiring a bank ti the sae is 0 One of many such studies is Andrade et a. [200] Rushe, Dominic and Thieman, Sam. AT & T in advanced taks to acquire Time Warner, reports say The Guardian 2 October 206. Web. Accessed 23 October For more detaied empirica anaysis of the same, see for eg. Boone and Muherin [2007]. For the theory underying the choice, see Vasu [205]. 0

11 competed. Lasty, an aternative interpretation is that even if the bank is hired and exerts effort, it gets to know the vaue of the firm ony with a specified probabiity. Even if the parties know that the other party hired a bank, they cannot be sure that the bank got to know the vaue. If the bank doesn t know the vaue, it is tantamount to the bank not being hired at a The wage doesn t depend on the stock market reaction There are two reasons for assuming this. First, we do not want to excude the possibiity that the target or the acquirer may be private. Second, in practice, contracts usuay depend ony on whether the transaction succeeded and what the vaue was, and amost never on the stock market reaction foowing the announcement or in subsequent years. This may have to do with the compexity of an M& A transaction. It may be the case that the market reaction is not an accurate assessment of a merger transaction, which justifies this assumption Both parties don t know the vaue Synergies may depend on the information that both parties possess individuay, which makes it credibe that neither party knows the vaue of synergies. 4 Part I - Optima contract when the buyer is aways informed Before considering the case where both seer and buyer are uninformed, I consider the simper case where the buyer has access to information at zero cost and aways knows the reaized vaue of the synergies. The seer does not know the vaue of the synergies uness he hires an advisor. 4. Three possibe vaues for the synergies To simpify matters further, we start with the the synergies taking one of three possibe vaues with equa probabiity of 3. Without oss of generaity, et V { 3, 2 3, }. If the advisor reports the reaized vaue truthfuy, the the distribution of the reported vaue is the same as that of the actua vaue. (I wi ater impose the constraint that the advisor has no incentive to misreport). Aso, the transaction aways goes through if the advisor reports truthfuy. So, the expected payment made by the seer iif the advisor reports truthfuy is w(, ) + w( 2, ) + w(, )

12 From the advisor s point of view, its payoff is the difference between the expected payment and the cost of effort, c. However, the advisor has the option of not exerting effort and just reporting any one of the three vaues of synergies. reports the vaue to be 2 3 and the seer makes an offer of 2 3 If say the advisor to the buyer, the transaction which happens woud be a success if the reaized vaue is greater than or equa to 2 3 with probabiity 2. In this case, the advisor woud get the wage w( 2, ). However, if 3 3 the transaction fais, which happens with probabiity, the bank gets w( 2, 0). So, the 3 3 advisor s payoff from not exerting effort and reporting a vaue of 2 is 2w( 2, ) + w( 2, 0) To make the advisor exert effort, the seer has to make sure that the payoff is higher than that from not exerting effort, i.e. 3 w( 3, ) + 3 w(2 3, ) + 3 w(, ) c w( 3, ) Simiary, one can write down two other IC constraints for the other possibe vaues he can report, and. 3 The seer s probem is thus to minimize 3 w( 3, ) + 3 w(2 3, ) + w(, ) 3 subject to the constraints 3 w( 3, ) + 3 w(2 3, ) + 3 w(, ) c w( 3, ) 3 w( 3, ) + 3 w(2 3, ) + 3 w(, ) c 2 3 w(2 3, ) + 3 w(2 3, 0) 3 w( 3, ) + 3 w(2 3, ) + 3 w(, ) c 3 w(, ) + 2 w(, 0) 3 It is optima to set w(v, 0) = 0 since the transaction fais ony if the bank either did not exert effort or report truthfuy, both of which he shoud be penaised for. The seer s probem is thus to minimize 3 w( 3, ) + 3 w(2 3, ) + w(, ) 3 subject to the constraints 3 w( 3, ) + 3 w(2 3, ) + 3 w(, ) c w( 3, ) 3 w( 3, ) + 3 w(2 3, ) + 3 w(, ) c 2 3 w(2 3, ) 3 w( 3, ) + 3 w(2 3, ) + 3 w(, ) c w(, ) 3 This is a inear programming probem. The soution is given by w( 3, ) = 6 5 c w( 2 3, ) = 9 5 c w(, ) = 8 5 c 2

13 The optima wage schedue is potted in Figure. Figure : The wage schedue with 3 possibe vaues of the synergies The figure shows the optima wage schedue when the synergies are 3, 2 3 or with equa probabiity. The advisor s cost of effort c is assumed to be (Aternativey, the y axis is scaed by c). The wage is an increasing function of the transaction vaue. Severa features of the optima wage schedue are noteworthy. First, the expected payment to the advisor is given by c. Since the bank s cost of 5 effort is c, the advisor makes an expected profit equa to 6 c. In other words, the advisor 5 is abe to extract information rents from the seer. For what range of c wi the seer hire the advisor? if he doesn t hire the advisor, the seer gets an expected payoff of 4.3 If he hires the the advisor, the seer can charge a fair price and get an expected payoff equa to the expected vaue i.e.. So, he is wiing 2 to hire the advisor as ong as the benefits exceed the cost, i.e c = c 5 44 Second, not ony is the expected profit of the bank greater than 0, but each of the wages is greater than the cost c. In other words, the bank aways extracts information 3 The seer offers Q to maximize Q( Q), Q being the payoff if the buyer accepts the offer and Q being the probabiity with which the buyer accepts the offer. The expression is maximized at Q = 2 and the maximum vaue is 4. 3

14 rents and not just in expectation. Third, note that each of the inequaities is satisfied with equaity since 3 (w( 3, ) + w(2 3, ) + w(, )) c = w( 3, ) = 2 3 w(2 3, ) = 3 w(, ) = 6 5 c This is a genera feature of such contracts, a characteristic we wi revisit ater. Fourth, the advisor has no incentive to misreport once it has exerted the effort. Since the wages are increasing in the vaue reported, misreporting to a ower vaue woud ead to the transaction going through and the bank getting a ower wage than if it had reported truthfuy. Misreporting to a higher vaue woud ead to the transaction faiing i.e. a wage of 0. Intuition might suggest that the optima contract shoud set w(, ) = 0. Just for 3 iustrative purposes, if we were to set w(, ) = 0, the optima contract woud need to 3 sove subject to the constraints the soution to which is given by 3 w(2 3, ) + w(, ) 3 3 w(2 3, ) + w(, ) c w(2 3, ) + 3 w(, ) c 2 3 w(2 3, ) 3 w(2 3, ) + 3 w(, ) c w(, ) 3 w( 3, ) = 0, w(2, ) = 3c, w(, ) = 6c 3 The expected payment to the bank is given by 3c which is greater than 5 c earier. A comparison between the optima wage schedue and this one is potted in Figure Discrete uniform distribution of synergies Now consider the case where the synergies have a discrete uniform distribution taking one of n possibe vaues with equa probabiity. Without oss of generaity, et V n {, 2,..., }. n n The seer s probem is thus to minimize n [w( n, ) + w( 2n, ) w(, ) ] 4

15 Figure 2: A comparison of the optima wage schedue and one where the minimum wage is set to zero The figure shows a comparison between the optima wage schedue and the best wage schedue when the minimum wage is set to 0. The synergies are 3, 2 3 or with equa probabiity. The advisor s cost of effort c is assumed to be. Whie it is true that the optima wage schedue eads to a nonzero payment when the minimum vaue is reported, the esser payment if the vaue reported is 2 3 or more than cances out the gains from setting the minimum wage to 0. subject to the n constraints [w( n n, ) + w( 2n ], ) w(, ) c w( n, ) n n... [w( n, ) + w( 2n ], ) w(, )... [w( n, ) + w( 2n ], ) w(, ) c n k + w( k n n, ) c w(, ) n The optima wage contract satisfies each of the n constraints with equaity. The n wages 5

16 Figure 3: The optima wage contract for different vaues of n The figure shows the optima wage schedue for n = 3, 0, 25, 50 and 00. The advisor s cost of effort c is assumed to be (Aternativey, the y axis is scaed by c). The wage is an increasing function of the transaction vaue. The information rents extracted by the advisor (aso equa to the wage on reporting the owest vaue) decrease to 0 as n becomes very arge. In other words, the expected payment to the advisor approaches the cost of effort. Aso, the maximum wage, which corresponds to reporting the maximum possibe vaue, increases as n increases. in the optima contract are given by w( n, ) = ( n ) c... w( k ( ) n, ) = n n k + c 2 3 n... ( ) w(, ) = nc 2 3 n For proof, see Appendix A. Figure 3 shows the shape of the contract for different vaues of n. The wage is monotonicay increasing in the transaction vaue. A noteworthy feature of the contract is that the expected payment to the advisor converge to c as n. Thus, the information rents extracted by the advisor (aso 6

17 equa to the wage on reporting the owest vaue) decrease to 0 as n becomes very arge. This is potted in Figure 4. How is the advisor abe to break even? It is because the maximum wage, which corresponds to reporting the maximum possibe vaue, increases as n increases, even as the owest wage fas. Figure 5, which pots the maximum wage against n, makes this cear. Another feature of the contract is that it is robust to misreporting once the advisor has exerted the effort. In other words, the advisor has incentive to report the vaue it discovered rather than misreporting it as another possibe vaue. The misreportingproofness foows from the monotonicity of the contract. Misreporting to a higher vaue eads to the transaction faiing and the advisor receiving a wage of 0. Misreporting to a ower vaue resuts in the transaction succeeding, but the advisor being paid a ower wage than it coud have by just reporting truthfuy. 4.3 Synergies Ṽ U(0, ) Now consider the case where the synergies are uniformy distributed in [0, ]. Set w(v, 0) to 0. Reasoning as above yieds the seer s probem to be Minimise w(v, )dv c s.t 0 0 w(v, )dv c ( V )w(v, ) V [0, ] To sove this, I consider a probabiity distribution for Ṽ, U ɛ which is obtained by the foowing transformation of U[0, ] Leave the distribution unchanged in the interva [0, ɛ]. Redistribute the probabiity mass from [ ɛ, ] to an atom of mass ɛ at ɛ This distribution can be made arbitrariy cose to the uniform distribution by etting ɛ 0. The uniform distibution and U ɛ are potted in Figure 6. The optima wage contract satisfies each of the constraints with equaity. The contract is given by w(v, ) = V c n( ɛ ) The wage as a function of reported vaue is potted in Figure 7. It is convex, increasing sharpy as the reported vaue approaches. The expected payment to the bank is given by ( c s = c + ) n( ) ɛ 7

18 Figure 4: The minimum wage (information rent extracted by the advisor) The figure shows the minimum wage that the advisor can guarantee for itsef as a function of n. This corresponds to the wage if the advisor reports the owest possibe vaue i.e. w( n, ). Since in this case the buyer accepts the offer with probabiity, it is aso equa to the information rents extracted by the advisor. It is apparent that the minimum wage decreases as n becomes very arge. As n, the minimum wage approaches 0, though the convergence is very sow as can be seen from the graph. As n the support becomes infinite, i.e. the probabiity distribution becomes a continuous uniform distribution rather than a discrete one. This suggests that if the vaues are uniformy distributed and continuous, the advisor is unabe to extract any rent. 8

19 Figure 5: The maximum wage paid to the advisor The figure shows the maximum wage that the advisor can possiby obtain as a function of n. This corresponds to the wage if the advisor reports the highest possibe vaue i.e. w(, ). As n, the maximum wage approaches. As n, the support of the distribution becomes infinite, i.e. the discrete probabiity distribution approaches a continuous uniform distribution. This suggests that if the vaues are uniformy distributed and continuous, the maximum wage approaches infinity. 9

20 Figure 6: The uniform distibution and U ɛ The uniform distribution U[0, ] and the modified uniform distribution which we refer to as U ɛ. The modification consists of shifting the probabiity mass from the interva [ ɛ, ] to the point ɛ, thus creating an atom of mass ɛ at ɛ. As ɛ approaches 0, U ɛ approaches U[0, ] Just as in the discrete uniform distribution case above where c s c as n, in this case c s c as ɛ 0 In other words, the expected payment to the bank is not greater than the cost of effort. The proof is given in Appendix B. The seer is wiing to hire the advisor as ong as the benefits of being fuy informed exceed the cost. Foowing the cacuation in 4., 2 4 c = c 4 5 Part II - Equiibria when both the seer and buyer can hire advisors 5. The probems with pure strategy equiibria In Part I, we assume that the buyer coud acquire information at zero cost. If this is not possibe, he is ikey to mix between hiring and not hiring the bank for reasonabe costs of acquiring the information by hiring a bank. I now iustrate why any of the pure strategy equiibria woud require unreasonabe parameter vaues of the payments the seer and the buyer have to make to the advisor. 5.. Buyer aways informed In Part I, we assume that the buyer coud acquire information at zero cost. However, if he has to make a non-zero payment to the advisor, he woud never choose to aways 20

21 Figure 7: The wage schedue for a continuous uniform distribution The figure shows the wage paid to the bank w(v, ) as a function of the vaue V reported by it when the vaues are uniformy distributed in [0,]. The wage is monotonicay increasing in the vaue reported. The wage increases sharpy as the vaue reported approaches. As a resut of the optima wage schedue, the bank is kept to its reservation utiity of 0. hire the advisor. Why? Because if the buyer aways hires the advisor, the seer woud aso aways hire the advisor (uness he has to pay theadvisor more than as we saw 4 in Part I above) so as to charge the buyer the fair vaue. But if the seer aways hires the advisor, his offer woud be equa to the vaue. The buyer woud get zero profit from the transaction, but wi have to pay his advisor. He is ceary better off not hiring the advisor. Thus, the buyer paying a pure strategy of aways hiring the advisor is not an equibrium Buyer never informed If the buyer is never informed, the seer has no incentive to be informed since he can just offer without hiring the advisor.5 However, if the seer is never informed, the buyer 2 can benefit by being informed and accepting offers ony when the vaue of the firm is greater than 2. This woud give him an expected payoff of 8.6 Hence, he woud not want to aways be uninformed uness his expected payment to the advisor is greater than 8. 4 subject, of course, to the reasonabe caveat that the seer pays ess than 4 to the advisor. 5 Intuitivey, why find out the vaue if the buyer never conditions his strategy on the vaue of the firm and it is aways optima to se the firm? 6 He accepts with 2 probabiity and gets a profit 4 (equa to the difference between expected vaue in [ 2, ] and the payment of 2 ) if he accepts. 2

22 Thus, the buyer paying a pure strategy of never hiring the advisor is not an equibrium Mixed strategy equiibria Ceary, the decision by either party to hire an advisor depends on the probabiity of the other party being informed. I begin by searching for equiibria where both the seer and the buyer mix between hiring and not hiring an advisor. Let p s and be the probabiities with which the seer and the buyer hire the se-side and buy-side advisors respectivey. In addition, et c s and c b be the expected fees paid to the advisor by the seer and the buyer respectivey. These are assumed to be exogenous for now. In the next section, I endogenize these parameters. 5.3 The buyer s strategy The buyer accepts or rejects the offer made by the seer. If the buyer is uninformed, he wi accept any offer ess than where [0, ] is the expected vaue of the firm conditiona on the seer offering. If the buyer is informed, he wi accept any offer ess than the vaue V. 5.4 The uninformed seer s strategy An offer of Q is accepted if the buyer is uninformed and Q is ess than or the buyer is informed and Q is ess than V. So, the probabiity of an offer of Q being accepted is ( )(Q ) + (Q V ) It foows that the expected utiity from quoting Q is Q(( )(Q ) + ( Q)) The optima offer depends both on and and is given by if [0, ] Q u = if if p 2 b [, ] if [0, Q u = ] 2 2 if [, ] if > 2 2 () (2) For proof, see Appendix C. Intuitivey, if the buyer hires the advisor with very ow probabiity, the seer is facing an uninformed buyer most of the time. So he offers the the 7 subject, of course, to the reasonabe caveat that the buyer pays ess than 8 to the advisor. 22

23 maximum amount the uninformed buyer wi accept i.e.. On the other hand, if there is a high chance that the buyer is informed, the seer s offer offer wi not depend on the threshod of the uninformed buyer. The seer wi choose an offer which maximizes the expected utiity i.e. the product of the payoff from the offer and the probabiity of it being accepted. 5.5 The informed seer s strategy The expected utiity from quoting Q is Q (( )(Q ) + (Q V )) However, since the informed seer knows V, his optima offer can aso depend on V in addition to and. It is given by if V [0, ( )] Q i = V if V [( ), ] if V [, ] if (3) if V [0, ( )] V if V [( ), ] Q i = if V [, ] V if V [, ] if > (4) The optima offer by the seer is not aways equa to the vaue reported by the advisor even though the advisor reports truthfuy. There are intervas where the seer overcharges, charges a fair price and undercharges. The intuition is that if the advisor reports a very ow vaue, the seer is better off taking a gambe that the buyer is uninformed rather than offering the very ow vaue. As the vaue increases, the seer charges a fair price because the aforementioned gambe is no onger optima. Once the vaue reported by the advisor crosses the threshod of the uninformed buyer, the advisor does not want to risk charging a fair price because the uninformed buyer wi reject it. Hence, there is an interva where he undercharges. However, as the vaue increases further, he is wiing to gambe on the fact that the buyer is in fact informed. The optima offer is graphed in Figue 8 as a function of the vaue reported by the advisor. For proof, see Appendix D. 23

24 Figure 8: Informed seer s offers The figure shows the offers made by the informed seer. The informed seer s offer depends on the vaue V that the bank reports, the threshod of the uninformed buyer and the probabiity with which the buyer is an informed one. The graph is for = 0.3 and = 0.6 The optima offer by the seer is not aways equa to the vaue reported by the bank even though the bank reports truthfuy. There are intervas where the seer overcharges, charges a fair price and undercharges. 24

25 5.6 Consistent equiibria after imposing additiona constraints We need to impose subgame perfection of the buyer as an additiona constraint. The buyer cannot be eft with surpus from any offer he accepts, because the seer, knowing this, coud then increase the offer price. Simiary, the buyer shoud reject anything that gives him a negative payoff. The informed buyer conditions his strategy on the vaue of the firm. The uninformed buyer conditions his strategy on the expected vaue of the firm given the seer s offer. He accepts the offer if the expected vaue is geater than or equa to the offer, and rejects if it is ess than or equa to the offer. 8 Once we impose these constraints, the set of equiibria correspond to the foowing: The uninformed buyer aways accepts any offer [0, ] and rejects any other offer. The informed buyer accepts any offer [0, V ]. The uninformed seer offers. The informed seers s strategy depends on V, and and is given by [0.5, 2 ] [0.54, 2 + ] 4 if V [0, ( )] V if V [( ), ] Q i = if V [, ] V if V [, ] (2 ) ( + ) p s = ( p 3 b ) (p2 b + )( ) 8 In fact, at first gance, it may seem that shoud aways be 2 in any equiibrium. After a, the expected vaue is 2, so woudn t sequentia rationaity dictate the buyer to set = 2? Not if we consider the impact of the informed seer s behaviour on the uninformed buyer. To iustrate this, et us consider an uninformed buyer who does set = 2. The uninformed seer woud offer 2 irrespective of since this is optima whether the buyer is informed or uninformed (In other words, offering 2 is the dominant strategy for the unnformed seer. Remember that Q( Q) is maximized at 2 ). However, we know that the informed seer woud aso quote 2 for some vaues reported by his bank. To be precise, the informed seer s strategy is 2 if V [0, ( ) 2 ] V if V [( ) 2 Q i =, 2 ] 2 if V [ 2, 2 ] V if V [ 2, ] It shoud be cear now that the uninformed buyer, when offered 2 must aso take into account that it maybe the informed seer offering him 2 after finding out that V [0, ( ) 2 ] or V [ 2, 2 ]. This is what restricts the vaue of to be a specific number if = 2 25

26 [ 2, 0.54] 2 [, ] 2 if V [0, ( )] Q i = V if V [( ), ] if V [, ] p s = (2 )( ) ( + 2) [, 0.54] if V [0, ( )] V if V [( ), ] Q i = if V [, ] V if V [, ] (2 ) ( + ) p s = ( p 3 b ) (p2 b + )( ) For proof, see Appendix E. For pots of the possibe vaues of and in equiibria, see Figure The seer s cost of hiring the advisor For the seer to mix between hiring an advisor and not hiring one, his payoffs from the two have to be equa. For equiibria of the form if V [0, ( )] V if V [( ), ] Q i = if V [, ] V if V [, ] the seer s cost of hiring the advisor is given by c s = 2 2 p 2 b + 2 ( pb ) 2 For equiibria of the form if V [0, ( )] Q i = V if V [( ), ] if V [, ] 26

27 Figure 9: Range of and in a equiibria The figure shows the ranges of, the maximum offer accepted by the uninformed seer, and, the probabiity of the buyer hiring a bank, for a possibe equiibria. Areas and 2 correspond to equiibria of the form V V. Area 3 corresponds to equiibria of the form V. 27

28 the seer s cost of hiring the advisor is given by c s = 2 2 p 2 b For proof, see Appendix F. Note that for any, c s is increasing in. 5.8 The buyer s cost of hiring the advisor For the buyer to mix between hiring an advisor and not hiring one, his payoffs from the two have to be equa. Since he has no bargaining power, both have to be equa to zero. We have aready considered the case of the uninformed buyer above. In this section, we focus on the informed buyer to get a condition on the buyer s cost of hiring the advisor. For equiibria of the form if V [0, ( )] V if V [( ), ] Q i = if V [, ] V if V [, ] the buyer s cost of hiring the advisor is given by c b = 2 ( )2 + ( 2 2 p s ( ) 2) + 2 For equiibria of the form if V [0, ( )] Q i = V if V [( ), ] if V [, ] the buyer s cost of hiring the advisor is given by c b = ( )2 2 For proof, see Appendix G. What are the range of payments to the advisor we see in equiibrium? Figure 0 pots how increasing and affects c s and c b which support the equiibrium for region in Figure 9. The graphs are reminiscent of indifference curves. Changing corresponds to a shift of the curve outwards, whie changing eads to a movement upwards aong the curve. Hence, given any pair (c s, c b ) in this range, there is a unique and and, by extension, a unique p s. Figure pots a vaues of c s and c b for which equiibria exist. Note that at this stage, neither of these are exogenous. Rather, they depend on the true exogenous parameter, the advisor s cost of effort, and the information rents on top of that which the advisors may or may not be abe to extract in the optima contract. I endogenize the payment to the advisors as a function of these exogenous parameters next. 28

29 Figure 0: Existence of a unique mapping from (c s, c b ) to (,, p s ). The figure shows how the buyer s and seer s cost of hiring an advisor change as and increase for equiibria corresponding to region in Figure 9. Increasing eads to a shift of the curve outwards, whie increasing eads to a movement upwards aong the curve. There is a unique mapping between any (c s, c b ) and (,, p s ). 29

30 Figure : The seer s and buyer s costs of hiring an advisor for which a mixed equiibrium exists The figure shows a possibe vaues of the buyer s and seer s cost of hiring an advisor for which a mixed equiibrium exists. Note that neither of these costs is exogenous. They depend on the advisor cost of effort, which is the true exogenous parameter, and aso on any information rents extracted by the advisors. The bue and red areas correspond to VV equiibria and the green to V equibria 30

31 6 Part III - Optima contracts when both the buyer and seer hire banks 6. Seer s contract with the advisor So far, we have assumed that the cost c s is exogenous. However, c s is the outcome of a contract between the seer and the advisor. Now, we turn to the issue of how c s is reated to c, the cost of effort the advisor incurs. It turns out that the the seer s abiity to hod the advisor to an information rent of zero depends on which equiibrium is reaised. Start by considering equibria of the form if V [0, ( )] V if V [( ), ] Q i = if V [, ] V if V [, ] Let us consider the various options avaiabe to the advisor if he decides to report a vaue without exerting any effort. If the seer s offers are the same for two or more reported vaues, the corresponding wages have to be the same. If the wages are different, the advisor woud aways report that vaue for which the wage is the highest. This doesn t affect the probabiity of the transaction going through, but increases the wage conditiona on it going through. If the advisor reports a vaue in either of the intervas [0, ( )] or[, ] without putting in effort, the seer offers the buyer. The uninformed seer accepts it and the informed seer accepts it if the reaized vaue, i.e. with probabiity. so the transaction goes through with probabiity ( ) + ( ) or. So, the intermediary gets an expected payoff of w()( ) without exerting effort. If the advisor reports a vaue V in the interva [( ), ] without putting in effort, the seer offers the vaue reported. In this range, the vaue is ess than, so the uninformed seer woud accept the offer. The transaction goes through with probabiity ( ) + ( V ) or V. So, the intermediary can secure himsef an expected payoff of w(v )( V ) without exerting effort for a V [( ), ] The option eft is to report a vaue V in the interva [, ] without putting in effort. The seer offers the vaue reported. In this range, the vaue is greater than, so the uninformed seer woud reject the offer. The offer wi ony go through if the buyer is informed and the actua vaue is ess than the vaue reported, i.e. with probabiity ( V ). So, the intermediary can secure himsef an expected payoff of ( V )w(v ) without exerting effort for a V [, ] To motivate the advisor to exert effort, his payoff on exerting effort and reporting the vaue truthfuy must be greater than 0. If he exerts effort and the vaue V [0, ( )], 3

32 the seer offers. Since the actua vaue is ess than, the transaction goes through ony if the buyer is uninformed i.e. with probabiity. So, expected payoff conditiona on the vaue being in this range is ( )w(). If he exerts effort and the vaue V [( ), ], the seer offers V. The transaction aways goes through since V. If he exerts effort and the vaue V [, ], the seer offers. Since the vaue is greater than, the transaction aways goes through. So, expected payoff conditiona on the vaue being in this range is w(). If he exerts effort and the vaue V [, ], the seer offers V. Since V, the transaction ony goes through if the seer is informed i.e. with probabiity. Hence, the expected payoff if he exerts effort is ( )( )w() + ( ) ( ) w(v ) dv + w() + w(v ) dv c Simpifying this expression and equating the payoff from exerting effort to be greater than any payoff from not exerting effort gives the seer s probem and the famiy of constraints he faces. Minimise the expected payment to the advisor (p 2b 2 + pb ) w() + w(v ) dv + w(v ) dv c subject to the constraints (p 2b 2 + pb ) w() + ( ) w(v ) dv + w(v ) dv c ( )w() (p 2b 2 + pb ) w() + (p 2b 2 + pb ) w() + ( ) ( ) ( ) w(v ) dv + w(v ) dv + w(v ) dv c ( V )w(v ) if V [( ), ] w(v ) dv c ( V )w(v ) if V [ We sove this for the modified uniform distribution U ɛ introduced in Section 4.3. The optima contract is given by k c p w(v, ) = b if V [( p V b ), ] k c if V [ ( V ), ɛ] where k is a constant. The payment made to the advisor is given by c( + k ). As ɛ 0, the payment is just the cost of effort c, so the advisor extracts no information rents. The proof is in Appendix H., ] 32

33 Figure 2 shows the wage paid to the seer s advisor as a function of the vaue reported by the advisor. Remember that in these equiibria, the vaue at which the transaction takes pace is not necessariy the vaue reported by the advisor because there are intervas in which the seer undercharges or overcharges the buyer. The incentives to the advisor are determined by the seer s offer and not his report since the seer s offer determines the probabiity of the transaction happening. For reports of ow vaues and vaues in the interva above,, the advisor offers so that the wage corresponds to w(, ). This is why the wage is not monotonicay increasing in the vaue reported by the advisor. Figure 2: Optima contract with the seer s advisor for = 0.8 and = 0.3 The figure shows the wage paid to the seer s advisor as a function of the vaue reported by the advisor. This corresponds to the equiibrium where the buyer hires an advisor with probabiity = 0.8 and accepts any offer ess than or equa to = 0.3 if he hasn t hired an advisor. The vaue reported b the advisor is not the same as the vaue at which the transaction takes pace since there are intervas where the seer undercharges or overcharges. The wage is increasing monotonicay in the transaction vaue. Some of the wages are off the equiibrium path and wi not be observed in equiibrium (The wages have been scaed by ck where c is the advisor s cost of exerting effort and k is a constant). We sti have to check whether the advisor has an incentive to misreport the vaue after exerting the effort. We need to check this for misreporting from each of the intervas to each of the other 3 intervas. I iustrate this for one interva beow. 33

34 If the advisor finds that V [0, ( )] and reports the vaue truthfuy to the seer, the seer makes the buyer an offer of. The advisor gets w() ony if the buyer is uninformed. If instead, the advisor misreports the vaue to V [( ), ], the seer offers V. Since V <, the transaction sti goes through ony if the buyer is uninformed and the bank gets w(v ) < w() if it goes through. So, the advisor has no incentive to do this. Misreporting to V [, ] is pointess since the seer offers in that range, same as without misreporting, which changes neither the fee nor the probabiity of the transaction going through. Lasty, misreporting to V [, ] eads to the seer offering V. In this case, the transaction fais for sure because both the informed and uninformed seer wi reject the offer since V > V and V > respectivey. So, there is no incentive to misreport to this range Hence, there is no incentive to misreport from V [0, ( )] to any of the other three intervas. Simiary, it can be shown that the contract is misreporting-proof i.e. the advisor has no incentive to misreport the vaue after discovering that the true vaue ies in each of the other three intervas as we. The proof is given in Appendix I. The contract is potted in Figure 3 for = 0.3 and = 0.8 Now consider equibria of the form if V [0, ( )] Q i = V if V [( ), ] if V [, ] The optima contract is given by w(v, ) = k c V if V [( ), ] where k is a constant. The payment the intermediary is given by c(+k ). The payment is aways greater the cost of effort c, so the advisor extracts information rents in this range. Aso, this contract is misreporting-proof. These resuts are proved in Appendix J 6.2 Buyer s contract with the advisor The buyer s advisor reports a vaue to the buyer. His contract can ony depend on whether the offer corresponding to the vaue he reports is equa to the actua offer made by the seer. 34

35 Figure 3: Optima contract with the seer s advisor for = 0.8 and = 0.3 The figure shows the wage paid to the seer s bank as a function of the transaction vaue. This corresponds to the equiibrium where the buyer hires a bank with probabiity = 0.8 and accepts any offer ess than or equa to = 0.3 if he hasn t hired a bank. The wage is increasing monotonicay in the transaction vaue. Some of the wages are off the equiibrium path and wi not be observed in equiibrium ( The wages have been scaed by ck where c is the bank s cost of exerting effort and k is a constant). First, consider equiibria are of the form if V [0, ( )] V if V [( ), ] Q i = if V [, ] V if V [, ] It is cear that the buyer has no way of distinguishing between the ower and upper intervas since the seer offers in both cases. So the wage in these two intervas has to be the same. Ese, the buyer s advisor woud never report a vaue in the interva corresponding to the ower wage. Let this wage be w(, ). If V [( ), ] or V [, ], the seer offers V. If the buyer s advisor does not exert any effort, he guesses V right with probabiity 0. So, not putting effort and reporting a vaue in either of these intervas gives him zero utiity. The ony case in which the buyer s advisor can get an expected utiity greater than 0 35

36 without exerting effort is if he reports V [0, ( )] or V [, ]. In both these cases, he gets paid w() if the seer offers. The seer offers w() if he is uninformed [ or if he is informed and the vaue fas into those intervas i.e. with probabiity p s + p s ( ] ). So, the buyer s advisor can get ( p s + p s ( ))w(, ) without putting in any effort. If the advisor does exert effort, he discovers V [0, ( )] or V [, ] with probabiity ( ). The seer offers whether he is informed or uninformed. So, with probabiity ( ), the bank gets w(, ). If V [( ), ] or V [, ], his reported vaue matches the seer s offer ony if the seer is informed. The buyer tries to minimize the expected payment to the bank ( )w(, ) + p s ( ) w(v, )dv + subject to the advisor s IC constraint for exerting effort ( )w(, ) + p s which simpifies to p s ( ) ( ) w(v, )dv + w(v, )dv + w(v, )dv w(v, )dv w(v, )dv c [ p s + p s ( ) [ c [ p s] ( ] ) w(, ) Decreasing w(, ) decreases the objective function and stricty oosens the constraint. So, the optima contract sets w(, ) to 0. The constraint thus binds. The expected payment to the advisor is aways c. This means that the advisor extracts no informationa rents. In genera, the buyer s optima contract can take various forms. However, a contracts are subject to two restrictions. First, the wage corresponding to a report of i.e. the threshod that the buyer woud have used had he not hired the advisor, must be zero. 9 Second, the advisor makes the cost of effort c in expectation and gets no information rents. Subject to these constraints, the contract can be fat, increasing or decreasing. One way to impement this is through a fat fee = c p s( + ) in V [( ), ] or 9 Intuitivey, hiring the advisor has not reay heped the buyer in this case and so the advisor is paid zero. ] w(v, ) 36

37 V [, ]. In genera, any wage structure w(v, ) which satisfies ( ) w(v, )dv + w(, ) = 0 w(v, )dv = c p s and wi work. It is easy to verify that the advisor wi not misreport once he has been incentivized to put in the effort. If the advisor misreports from V [0, ( )] orv [, ], where the seer offers, to V [( ), ] or V [, ], where the seer offers V, he has zero probabiity of getting the vaue right. Hence, he wi not report a vaue in this range uness he finds the vaue to be in the range. If instead, the advisor misreports from V [( ), ] or V [, ], where the seer offers V, to V [0, ( )] orv [, ], he gets paid w(, ) i.e. 0 at best. There is no incentive to do this either. Hence, this contract is misreporting-proof. Figure 4 shows 3 possibe optima contracts. Since the contract is not uniquey pinned down, there are many others. For equiibria of of the form if V [0, ( )] Q i = V if V [( ), ] if V [, ] it is apparent by arguments amost exacty the same as above that the optima contract sets ( ) w(v, )dv = c p s and w(, ) = 0 Once again, the advisor is paid c in expectation, i.e. extracts no information rents, and the contract is misreporting-proof. 6.3 The range of c for which the mixing equiibria exist We have demonstrated that the buyer s advisor never gets information rents and the seer s advisor doesn t for the V V equiibria. For the rest of the paper, I consider ony equiibria where the cost of effort c is the same for both the buyer s advisor and the seer s advisor. Figure makes it cear that the V equiibria cannot have both the 37

38 Figure 4: Optima contract with the buyer s advisor The figure shows the wage paid to the buyer s bank as a function of the transaction vaue. In genera, the buyer s optima contract can take various forms subject to two restrictions. First, the wage corresponding to a report of i.e. the threshod that the buyer woud have used had he not hired the bank, must be zero. Second, the bank makes the cost of effort c in expectation and gets no information rents. Subject to these, the contract can be fat, increasing or decreasing. Three such contracts- the soid, dotted and dashed ines are given in the figure. advisors costs of effort equa to c. This is because for these equiibria, c b = c and c s > c since the seer s advisor extracts information rents. However, from the graph, we see that this is not possibe. By the same ogic, the V V corresponding to the areas shaded red can aso be ignored. We are eft ony with the bue area of the graph.this is shown in Figure 5 7 Compete characterization of the Equiibria I fuy characterise the buyer s and seer s strategies in equiibria given the cost of effort c of their advisors. A strategy is described beow in terms of the ordered tripe (,, p s ) given c. In keeping with the requirements of a Perfect Bayesian Equiibrium, the beiefs 38

39 Figure 5: Equiibria and the advisor cost of effort The figure shows the ranges of the advisors cost of effort for which mixed equiibria exist under the assumptions that both the advisors have the same cost of effort c. The set of equibria correspond to the intresection of the region in Figure with the x = y ine. We ony need to consider the bue region in Figure because the ine doesn t intersect the green or red regions. In the equiibria, both advisors get paid the effort cost. As can be seen from the figure, equiibria exist for a wide range of c. of either party are consistent with the strategy of the other. I aso describe the contracts between both parties and their advisors. The advisors exert effort and report truthfuy in a the equiibria. Buyer s strategy If uninformed, the buyer accepts any offer ess than or equa to a threshod. If informed, the buyer accepts any offer ess than or equa to the vaue V. The buyer becomes informed i.e. hires an advisor with probabiity. The buyer s contract with his bank is given by, for eg, A fat fee = Seer s strategy If uninformed, the seer offers. c p s( + ) in V [( ), ] or V [, ] and w(, ) = 0 39