Contingent Fees, Signaling and Settlement Authority

Transcription

1 Contingent Fees, Signaling an Settlement Authority SHMUEL LESHEM USC Law School Conventional wisom suggests that uner contingent fee contracts, attorneys have an excessive incentive to settle the case; therefore, a laintiff shoul retain the authority over settlement ecisions. We show, by contrast, that when the laintiff ossesses rivate information about the outcome of a trial an makes a take-it-or-leave-it settlement eman, elegating settlement authority to an attorney uner a contingent fee contract increases the robability of settlement an the laintiff s equilibrium ayoff. We also show that contingent fee contracts with attorney control over settlement are more efficient than hourly fee contracts, as the former involve a higher robability of settlement. The intuition behin these results is that the attorney s greater reluctance to go to trial allows him to more effectively signal the laintiff s tye through the settlement eman. 1. INTRODUCTION Conventional wisom has it that contingent fee contracts rovie the attorney excessive incentives to settle the case to the etriment of the laintiff. Uner a contingent fee contract, the attorney collects a share of either a court awar or settlement, but nothing if the case is lost at trial. 1 Because the attorney incurs litigation costs only if the case rocees to trial but is ai even if the case settles, the attorney woul likely be keen to settle the case. A major concern is, therefore, that an attorney retaine on a contingent fee basis might agree to a settlement lower than that in the best interest of the laintiff. 2 This concern is esecially I woul like to thank Gillian Hafiel, Marcel Kahan, Dan Klerman, Lewis Kornhauser, Geoffrey Miller an Kathryn Sier for their comments an suggestions. 1 Most tort claims in the U.S. are file uner contingent fee arrangements. In ersonal injury cases, contingent fees have become the ominant financing metho (see Rubinfel an Scotchmer, 1998: ). 2 A recent excetion is Polinsky an Rubinfel (2002). A ifferent concern has to o with the attorney s sub-otimal incentive to invest in the case, assuming that the marginal increase in the

2 436 / REVIEW OF LAW AND ECONOMICS 5:1, 2009 acute uner a flat (or unitary) contingent fee, whereby the attorney s share of the settlement is equal to his trial share. 3 The averse effects of attorneys incentives uner contingent fee contracts have long been recognize (see, for examle, Miller, 1987; Gravelle an Waterson, 1993). Recently, Polinsky an Rubinfel (2003) have ut forwar a financial mechanism uner which the attorney is reimburse some of his litigation costs so that his (ercentage) share of litigation costs is equal to his (ercentage) share of a court awar or settlement. This, so the argument goes, will benefit the laintiff by aligning the interests of the laintiff an her attorney regaring settlement of the case. In ractice, laintiffs oftentimes leave major ecisions regaring the conuct of a lawsuit, incluing the ecision of whether to settle the case, to their attorney s goo jugment. 4 For examle, base on an assortment of stuies, Kritzer (1998) reorts that attorneys often control the lawyer-client relationshi. Choi (2003) likewise refers to oft-cite accounts of laintiffs suose aathy regaring settlement an litigation matters once these are hane over to their attorneys. Plaintiffs eference to attorneys iscretion on settlement ecisions is articularly uzzling with resect to contingent fee contracts. Given attorneys interest in settling the case romtly, what o laintiffs gain by letting their attorneys ecie whether to settle the case? This article rovies insight into this question by ointing to the strategic effect of contingent fee contracts in settlement negotiations. The main roosition is that owing to the ifferent ayoff scheules, the attorney is better able to convey the laintiff's rivate information regaring the execte trial awar in the case of contingent fee contracts. This, in turn, increases the robability of settlement comare to the case in which the laintiff negotiates a settlement on her own laintiff s court awar is ecreasing with the attorney s efforts. Note that contingent fee contracts are a secific case of revenue sharing arrangements, whereby the agent woul equate his marginal isutility of effort with his share of marginal rouct rather than, as ictate by efficiency, with total marginal rouct. 3 A flat contingent fee is robably the most common attorney comensation scheme in the U.S. See Rubinfel an Scotchmer (1998:415). 4 Although laintiffs legally have the right to ecie whether to settle or go to trial (see Rule 1.2(a) of the ABA Annotate Moel Rules of Professional Conuct (2003) ( 2003 ABA Moel Rules )), the question as to whether a laintiff can elegate settlement authority to her attorney is a matter of state substantive law. Courts have recognize ifferent means by which a client may elegate settlement authority to her attorney. First, a client may exressly authorize her attorney to settle a case through a rovision in the retainer agreement. Secon, the attorney authority to settle the case may be imlie from the client s instruction. Thir, some courts have recognize the attorney s authority to settle the case base on aarent authority, in cases in which the client's own actions have le a thir arty to believe that the attorney was authorize to enter a settlement agreement. See 2003 ABA Moel Rules, at 33. For a etaile iscussion of attorneys authority to settle cases, see ABA/BNA Lawyers Manual on Professional Conuct, 31:301. Review of Law & Economics, 2009 by beress

3 Contingent Fees, Signaling an Settlement Authority / 437 uner either a contingent fee contract or an hourly fee contract. The laintiff's equilibrium ayoff uner a contingent fee contract is consequently higher when the attorney rather than the laintiff retains the settlement authority. In aition, the laintiff's equilibrium ayoff may be higher uner a contingent fee contract with attorney control over settlement as comare to an hourly fee contract (regarless of the allocation of settlement authority). To substantiate this argument, we stuy the role of the laintiff s attorney in a setting taken from Reinganum an Wile (1986). In this setting, the laintiff ossesses rivate information about the outcome of a trial an the efenant knows the istribution of laintiffs execte court awar but not the laintiff s true tye (that is, the laintiff s court awar). The laintiff then makes a take-itor-leave-it settlement eman to the efenant, which the latter can either accet or reject. Rejection of the settlement eman is followe by a trial where the laintiff s true tye is etermine by the court. Reinganum an Wile show that the outcome of settlement negotiations when the laintiff negotiates irectly with the efenant is a unique searating equilibrium wherein the settlement eman reveals the laintiff s true tye. The efenant s equilibrium strategy, in turn, is to accet lower settlement emans with a higher robability than he woul accet higher emans. Thus, the higher the laintiff s settlement eman, the greater the robability with which the efenant will reject the eman an the case will come to trial. It is the efenant s mixe strategy in resonse to settlement emans the higher the settlement eman, the lower the robability with which the efenant accets the eman that ensures the truthfulness of settlement emans in equilibrium. The essential roerty of this equilibrium can be restate informally as follows. If the laintiff resents a high settlement eman, the likelihoo is greater that the arties will reach a stalemate. If the laintiff s eman is low, by contrast, the chance that a settlement will be reache is greater. This equilibrium outcome thus catures the notion that a settlement eman in itself is a source of information for the efenant. This outcome also has an intuitive aeal in that settlement negotiations are more likely to succee when the laintiff makes a low as comare to a high settlement eman. The rationale behin the searating roerty of this equilibrium is that the cost of negotiations breakown is higher for laintiffs with execte low court awars, who have less to gain from going to trial, than it is for laintiffs with execte high court awars, who gain more from going to trial. This enables laintiffs to signal their tye through the settlement eman. Here we allow the laintiff s attorney to negotiate a settlement on behalf of the laintiff by making a settlement eman to the efenant. We carry out the analysis by comaring the robability of settlement an the laintiff s htt:// DOI: /

4 438 / REVIEW OF LAW AND ECONOMICS 5:1, 2009 equilibrium ayoff uner ifferent fee contracts an ifferent allocations of settlement authority. In articular, we consier the case in which the attorney is assigne an active role of making a take-it-or-leave-it settlement eman to the efenant. In aition, we treat settlement negotiations as a three-layer game in which the laintiff s choice of fee contract an allocation of settlement authority between the laintiff an her attorney affect not only the laintiff an the attorney but the efenant as well. 5 We show that elegating settlement authority to an attorney retaine on a contingent fee benefits the laintiff an that the resulting equilibrium is more efficient than that which is obtaine uner either an hourly fee or a contingent fee contract with laintiff control over settlement. 6 The intuition behin this result is fairly simle. Because he incurs the laintiff s litigation costs but obtains only a fraction of the court awar, the attorney is more reluctant than the laintiff to go to trial. As a result, the efenant is able to inuce truthful revelation of laintiff tyes by threatening to break off negotiations with a lower robability. That is, the attorney s greater reluctance to go to trial enables him to more effectively signal the laintiff s tye through the settlement eman. Thus, the robability of settlement an the laintiff s equilibrium ayoff uner contingent fee contracts with attorney control over settlement are higher comare to both contingent fee contracts with laintiff control over settlement an hourly fee contracts. Notice that the lower the fee rate, the greater the attorney s reluctance to go to trial (because the attorney gains a lower fraction of the court awar but still bears the entire laintiff s litigation costs). Thus, the increase in the robability of settlement that arises from elegating settlement authority to the attorney is ecreasing in the fee rate. It shoul be stresse that settlement emans are revealing uner any fee contract an any allocation of settlement authority; ifferent fee contracts vary only with resect to the robability of settlement an the laintiff s equilibrium ayoff. It shoul also be emhasize that although the moel is restricte to the case in which the laintiff ossesses the entire bargaining ower, its qualitative results woul hol if bargaining ower were allocate ranomly between the laintiff an the efenant (see Section 6.2). A ossible interretation of the robability of settlement in our moel is that it catures the creibility of the settlement eman: the higher the robability of settlement, the more creible the settlement eman is. In evaluating the creibility of a settlement eman, the efenant has to consier the 5 For the sake of simlicity, we treat the efenant an his attorney as one layer, thereby ignoring a otential conflict of interest between them. 6 Signaling effects also lay out in a moel with two-sie information asymmetry (see Daughety an Reinganum, 1994). Our qualitative results therefore survive the introuction of rivate information of the efenant (see also Farmer an Pecorino, 2005). Review of Law & Economics, 2009 by beress

5 Contingent Fees, Signaling an Settlement Authority / 439 consequences of negotiations breakown for the rooser. Since negotiations breakown are more costly for the attorney uner contingent fees than for the laintiff uner either hourly fees or contingent fees, the attorney s settlement eman is more creible than the laintiff s. The remainer of the article is organize as follows. Section 2 reviews the relevant literature. Section 3 sets u a moel with hourly fee contracts. Section 4 introuces flat contingent fees an erives the robability of settlement, the attorney s fee rate an the laintiff s ayoff uner laintiff control over settlement an attorney control over settlement. Section 5 comares the robability of settlement, the laintiff s ayoff an social welfare uner ifferent fee structures an allocations of settlement control. Section 6 consiers imlications an extensions of the analysis. Section 7 conclues. 2. RELATED LITERATURE As note above, this aer buils on Reinganum an Wile s (1986) signaling moel wherein an informe laintiff who bears his own litigation cost makes a take-it-or-leave-it settlement eman to an uninforme efenant. Farmer an Pecorino (2005) exten Reinganum an Wile s moel to examine the effect of contingent fees on settlement rate. Throughout their analysis, however, Farmer an Pecorino assume that laintiffs retain settlement authority. This aer further extens the Reinganum an Wile analysis by comaring hourly fee contracts to contingent fee contracts with laintiff as well as attorney control over settlement. In oing so, this aer refines Miller s (1987) analysis on the conflict of interest between the laintiff an her attorney uner contingent fee arrangements. Whereas Miller emhasizes the agency roblem between the laintiff an her attorney in a symmetric information setting, this aer stresses the avantage of elegation when settlement negotiations are characterize by information asymmetry. To ut our analysis into ersective, it will be helful to survey other relevant literature. One branch of articles exlores the role of the laintiff s attorney as an ineenent layer in settlement negotiations characterize by asymmetric information. Watts (1994) consiers an uninforme laintiff who makes a single take-it-or-leave-it eman to an informe efenant. The laintiff can either hire an exert attorney or negotiate with the efenant on her own. Watts shows that hiring an attorney increases the laintiff s ayoff by allowing the attorney to make a more accurate settlement eman to the efenant. Watts results o not een on the attorney s comensation scheme, but rather on the attorney s exertise in acquiring information about the efenant s tye. Thus, her moel oes not consier the strategic effect of the fee contract on settlement negotiations. htt:// DOI: /

6 440 / REVIEW OF LAW AND ECONOMICS 5:1, 2009 Rickman (1999) examines the strategic effect of a contingent comensation scheme in a ynamic setting in which an attorney hire on a contingent fee basis resons to two consecutive settlement offers mae by an uninforme efenant. One equilibrium outcome is for an attorney reresenting a low-tye laintiff to emloy a mixe strategy whereby a low (first) settlement offer is rejecte with some ositive robability an for an attorney reresenting a hightye laintiff to always reject a low settlement offer. Rickman shows that bearing litigation costs vests the attorney s rejection of the first settlement offer with greater creibility, which, in turn, inuces a high settlement offer in the first stage of negotiation more often. This har bargaining effect is offset by the fact that the resence of litigation costs lowers the attorney s reservation value of settlement, thereby allowing the efenant to lower the settlement offer. The overall effect of increasing litigation costs on the laintiff s equilibrium ayoff when the attorney negotiates a settlement is thus ineterminate. Here, by contrast, the creibility of the laintiff s attorney is measure in the efenant s resonse to a settlement eman. Also, the result that the laintiff refers elegation is unqualifie so long as the laintiff ossesses the entire bargaining ower (see Section 6.2 for an analysis of the case in which the laintiff oes not ossess the entire bargaining ower). Moreover, since it is the attorney who makes the settlement eman, an increase in the laintiff s litigation costs oes not affect the equilibrium settlement amount, but rather increases the robability of settlement. A ifferent stream of research exlores the otimal allocation of settlement authority between the laintiff an the attorney uner contingent fee contracts when there is erfect information as to the outcome of trial. Bebchuk an Guzman (1996) oint to the strategic avantage of retaining settlement authority by the laintiff uner a flat contingent fee contract. In articular, the attorney s commitment to bear legal costs if the case goes to trial makes the laintiff inifferent between settlement an trial (when the laintiff retains settlement authority), an therefore enhances the laintiff s ability to extract a higher settlement when comare to an hourly (or a fixe) fee arrangement. The attorney, because he is more reluctant to go to trial, is lace in a weaker bargaining osition relative to the laintiff. Choi (2003) exlores the otimal allocation of settlement authority uner a bifurcate fee contract. In an attemt to exlain why settlement authority is often lace with the attorney, Choi argues that elegating settlement authority to an attorney ai on a bifurcate contingent fee basis increases the laintiff s ayoff from settlement if bargaining ower shifts to the efenant. The iea is that rewaring the attorney with a high fee rate if the case goes to trial an a low fee rate if the case settles increases the attorney s reservation value for settlement. Review of Law & Economics, 2009 by beress

7 Contingent Fees, Signaling an Settlement Authority / 441 Thus, given that his settlement share is lower than his trial share, the attorney will only agree to a settlement high enough to make him inifferent between settlement an trial. The strategic avantage of elegating settlement authority to the attorney is confine to bifurcate fee contracts. Uner a flat contingent fee contract, by contrast, the laintiff is better off retaining settlement authority because the attorney s reference for settlement lowers his reservation value for settlement, resulting in a lower ayoff for the laintiff. Taken together, Bebchuk an Guzman (1996) an Choi (2003) rovie suort for the view that laintiffs shoul retain settlement authority uner flat contingent fees so as to imrove their bargaining osition vis-à-vis the efenant. This article, in contrast, assumes that the laintiff ossesses the entire bargaining ower, thereby focusing on the role of asymmetric information in settlement negotiations. It thus arrives at the oosite conclusion regaring the otimal allocation of settlement authority uner flat contingent fees. The article iffers from revious analyses in two rimary resects: First, the moel here results in an equilibrium where the settlement eman is ientical uner ifferent fee contracts an ifferent allocations of settlement authority. The ifferent fee contracts iffer by the robability of settlement in equilibrium, which is higher uner contingent fee contracts with attorney control over settlement when comare to other fee arrangements. Secon, the moel here resuoses that the laintiff s contract choice affects the attorney s execte rofit an hence the equilibrium contingent fee as well as the efenant s equilibrium strategy. 3. EQUILIBRIUM WITH HOURLY FEES The basic moel uses the Reinganum an Wile (1986) framework. Assume that a laintiff s execte court awar is istribute on [ j, j], where j > 0, accoring to a ensity function f ( j). The laintiff s rivate information relates either to the robability of revailing at trial or to the actual amages suffere by her or to both. 7 We enote the laintiff s tye (i.e., her execte court awar) by j. 8 Let 7 A note on the information structure is in orer. Although the laintiff has an incentive to reveal favorable rivate information to her oonent rior to trial, she may not o so for two reasons. For one thing, the laintiff may not be able to creibly convey her rivate information rior to trial. For examle, the reliability of witnesses may not be ascertaine outsie the courtroom. For another, the laintiff may hesitate to reveal her rivate information rematurely out of concern that the efenant will be better able to set u a reemtive evientiary strategy if the case eventually roceee to trial. This suggests that information asymmetry regaring the laintiff s rivate information is likely in settlement negotiations. 8 The laintiff s execte court awar is equal to the jugment for the laintiff if the laintiff wins at trial multilie by the robability that the laintiff wins at trial. htt:// DOI: /

8 442 / REVIEW OF LAW AND ECONOMICS 5:1, 2009 c, c > 0 enote the laintiff s an the efenant s litigation costs, resectively. Assume that the laintiff always has a creible threat to go to trial ( j > c ). We further assume that the laintiff can effectively monitor the attorney s investment in the case. This assumtion ignores a otential conflict of interests between the laintiff an the attorney with resect to the level of effort investe in the case by the attorney. We make this assumtion in orer to focus attention on the information asymmetry between the laintiff an the efenant. Finally, we assume that all arties are risk-neutral. Settlement negotiations commence after the laintiff has entere into a fee contract with her attorney. Denote by s the laintiff s settlement eman an let s = j+ c an s = j+ c. We let the laintiff make the settlement eman, thereby avoiing a otential conflict of interest between the laintiff an her attorney as to whether to settle the case or rocee to trial. Note that settlement ecisions uner an hourly fee contract are suscetible to a conflict of interest iametrically ifferent from the one commonly attribute to a contingent fee arrangement. Thus, because the attorney is ai only if the case reaches trial uner an hourly fee contract, the attorney might seek to go to trial whereas the laintiff woul rather settle the case. Relaxing the assumtion that the laintiff controls settlement ecision, however, woul strengthen our results. The laintiff s strategy is a function that secifies the settlement eman, s, that she makes. The efenant s strategy consists of a strategy an a belief. The efenant s strategy is a function, (s), which secifies the robability that the efenant will accet the laintiff s eman base on his belief about the laintiff s tye. The efenant s belief, b (s), efines the laintiff's tye as a function of the settlement eman. As long as the efenant s belief is that the laintiff s eman is equal to the laintiff s true tye lus the efenant s litigation costs the efenant is inifferent between any mixe strategy of acceting or rejecting the settlement eman. In aition, the efenant s best resonse is to reject any settlement eman that the efenant believes excees the laintiff s true tye lus the efenant s litigation costs an to accet any settlement eman that the efenant believes falls short of that amount. The efenant s equilibrium strategy must also be such that the laintiff maximizes her execte rofit given the laintiff s strategy. The laintiff chooses a settlement eman s to solve the following maximization roblem: (1) max ( s) s+ (1 ( s)) ( j c ). S Review of Law & Economics, 2009 by beress

9 The first-orer conition to maximum with resect to the settlement eman s is: (2) ' ( s)( s j+ c ) + ( s) = 0. In a searating equilibrium, the laintiff s eman is truthful; that is, s = j + c. It must therefore be that (3) s) = '( s)( c + c ). ( s ) The general solution to (3) is given by ( ) /( c + s = C e c, where C is a constant of integration. The bounary conition is obtaine by setting the robability that the efenant accets the lowest settlement eman, s = j+, at one. The solution of (3) is therefore c ( ) /( ) (4) s s c ( ) + c s = e. To comlete the characterization of the equilibrium, off-equilibrium strategies an corresoning beliefs nee to be secifie. For s< s, let b ( s) = s c ; for s> s, let b ( s) = s c (note that these off-equilibrium beliefs are not unique). Accoringly, for s< s, ( s) = 1; an for s> s, ( s) = 0. 9 The relevant results are summarize in Lemma 1 LEMMA 1 (Reinganum an Wile, 1986) Uner hourly fee contracts: (a) For s [ s, s], the robability of settlement is ecreasing in the settlement eman an increasing in both arties litigation costs. (b) The laintiff s equilibrium ayoff is (c) The efenant s equilibrium ayoff is j+ c ). Proof. See the Aenix. Contingent Fees, Signaling an Settlement Authority / 443 j + )) c, where s = j+. ( s ) c (1 ( s ( c 9 Note that the efenant s equilibrium strategy is weakly ominate by the same strategy excet that the highest settlement eman, s, is rejecte with robability one. This is because the efenant is inifferent between acceting an rejecting the settlement eman s only if it is mae by laintiff j, but strictly refers to reject s if it is mae by any other laintiff. This can be solve by consiering only settlement emans such that s [ s, s) (see Reinganum an Wile, 1986:561, n. 3). htt:// DOI: /

10 444 / REVIEW OF LAW AND ECONOMICS 5:1, EQUILIBRIA WITH CONTINGENT FEES 4.1. THE FEE ARRANGEMENTS AND THE PLAYERS PAYOFFS Before roceeing to characterizing the equilibrium uner contingent fee contracts, let us make a general note on the effect of the fee arrangement on the layers ayoffs. Since the equilibrium outcome wherein the laintiff makes the settlement eman is revealing (or searating), it follows that uner any fee arrangement between the laintiff an her attorney, the efenant equilibrium ayoff is equal ( j+ c ). That is, whether the efenant accets the settlement eman or goes to trial, the efenant always ays the laintiff s true court awar lus his litigation costs. The efenant s equilibrium ayoff, therefore, is invariant to the fee arrangement between the laintiff an her attorney. It follows that only the robability of settlement an the laintiff s ayoff are taking ifferent values uner ifferent fee arrangements. As will be clear below, these variables are interrelate. Next we consier the effect of the allocation of settlement authority uner contingent fee contracts on settlement negotiations. We consier two tyes of settlement mechanisms: laintiff control over settlement ecision an attorney control over settlement ecision. We rovie the following results. First, uner contingent fee contracts, the robability of settlement an laintiff s equilibrium ayoff are higher with attorney control over settlement when comare to laintiff control over settlement. Secon, the robability of settlement is higher uner contingent fee contracts with attorney control over settlement when comare to hourly fee contracts. Thir, the laintiff s equilibrium ayoff uner contingent fee contracts with attorney control over settlement may be either higher or lower, eening on the laintiff s tye, when comare to hourly fee contracts ASSUMPTIONS AND SEQUENCE OF EVENTS We make the following assumtions about contingent fee contracts: First, we assume that the efenant observes the laintiff s contract choice. In articular, we assume the efenant observes the fee rate between the laintiff an her attorney. This assumtion may be justifie by the fact that attorneys often have reutation for taking cases on hourly fee or contingent fee basis. Secon, we assume that laintiffs observe their tyes only after the attorney have learne the case an informe them on the value of their claim (see, e.g., Miller, 1987; Dana an Sier, 1993). This, in turn, imlies that attorneys are not able to evise a contractual mechanism to searate ifferent tyes of laintiffs. This assumtion also imlies that the efenant cannot uate his information Review of Law & Economics, 2009 by beress

11 about the laintiff s tye by observing the fee contract between the laintiff an her attorney. Last, we assume that attorneys cannot renegotiate the fee rate after observing the laintiff s tye nor can they, after learning the case, ay the laintiff to settle the case for a lower amount instea of going to trial. Reasons for this effect inclue, for examle, attorneys concerns for their reutation. 10 The sequence of events receing settlement negotiations unfols as follows. In the first stage, attorneys announce a fee rate, r. We assume the fee rate is exogenously fixe; we comment in Section 6.3 on the case in which the fee rate is etermine enogenously. In the secon stage, laintiffs ecie whether to hire the attorney. In the thir stage, if the laintiff chooses to hire the attorney, the attorney observes the laintiff s tye. In the fourth stage, the laintiff or her attorney accoring to the allocation of settlement authority makes a settlement eman to the efenant. In the fifth stage, the efenant accets or rejects the settlement eman. The sixth an final stage eens on the outcome of the fifth stage: if the efenant rejects the settlement eman, the case rocees to trial. We next analyze the equilibrium robability of settlement an the laintiff equilibrium ayoff uner ifferent allocations of settlement authority between the laintiff an the attorney EQUILIBRIUM WITH PLAINTIFF CONTROL OVER SETTLEMENT WITH CONTINGENT FEE CONTRACT We begin by consiering the case in which the laintiff controls the settlement ecision uner a contingent fee contract. Consier the laintiff s choice of settlement eman. The laintiff chooses s to solve the following maximization roblem: (5) max(1 r) [ ( s) s+ (1 ( s )) j]. s The first-orer conition to maximum with resect to the settlement eman s is: (6) ( 1 r ) [ '( s )( s j) + ( s)] = 0. Contingent Fees, Signaling an Settlement Authority / 445 In equilibrium, the efenant s belief must be correct, that is, Therefore, it must be that s = j+ c. (7) ( s) = '( s) c. 10 See, for examle, Bebchuk an Guzman (1996) who suggest that reutational constraints may revent attorneys from offering laintiffs a ayment to inuce them to accet a settlement rather than go to trial. htt:// DOI: /

12 446 / REVIEW OF LAW AND ECONOMICS 5:1, 2009 The bounary conition for (7) is obtaine by setting the robability that the lowest settlement eman, s = j+ c, is accete at 1. The solution of (7) is therefore ( s s) / c (8) ( s) = e, c where the subscrit enotes contingent fees with laintiff control over settlement. We summarize the relevant results in Lemma 2 (the efenant s offequilibrium behavior is similar to that uner hourly fee contracts). LEMMA 2 (Farmer an Pecorino, 2005) Uner contingent fees with laintiff control over settlement: (a) For s [ s, s], the robability of settlement is ecreasing in the settlement eman, increasing in the efenant s litigation costs, an is ineenent of the laintiff s litigation costs an the fee rate. (b) The laintiff s equilibrium ayoff is (1 r )( j+ ( s ) ), where s = j+ c (c) The efenant s equilibrium ayoff is j+ c ). Proof. See the Aenix. ( c c EQUILIBRIUM WITH ATTORNEY CONTROL OVER SETTLEMENT WITH CONTINGENT FEE CONTRACT We now turn to the case in which the attorney controls the settlement ecision uner a contingent fee contract. The attorney chooses s to solve the following maximization roblem: (9) max ( s r) rs+ (1 ( s r)( rj c ). s The first-orer conition to maximum with resect to the settlement eman s is: (10) ' ( s r)( rs rj+ c ) + ( s r) r = 0. The efenant s belief is correct in equilibrium, that is, therefore that s = j+ c ; it must be (11) s r) r = '( s r)( rc + c ). ( Review of Law & Economics, 2009 by beress

13 Contingent Fees, Signaling an Settlement Authority / 447 The left-han sie is the attorney s marginal benefit of increasing the settlement eman. This is equal to the attorney s settlement share multilie by the robability that the increase settlement eman will be accete by the efenant. The right-han sie is the attorney s marginal cost of increasing the settlement eman, which results from the lower likelihoo that the efenant will accet the higher settlement eman. Remember that the attorney s costs of going to trial are equal to the attorney s share multilie by the efenant s litigation costs lus the laintiff s litigation costs. This is so because by going to trial, the oortunity to extract the efenant s litigation costs is lost an the attorney has to incur the laintiff s litigation costs. The attorney will reveal the laintiff s true tye through the settlement eman if his marginal benefit of increasing the settlement eman is exactly offset by his marginal cost of oing so. The bounary conition for (11) is obtaine by setting the robability that the lowest settlement eman, s = j+ c, is accete at 1. The solution of (11) is therefore: (12) ca ( s r( s s) /( c + rc ) r) = e, where the subscrit enotes contingent fees with attorney control over settlement. Note that contrary to the case of hourly fees an contingent fees with laintiff control over settlement, the efenant's strategy here eens on both the settlement eman an the attorney s fee rate. We summarize the relevant results in Lemma 3 (the efenant s offequilibrium behavior is similar to that uner hourly fee contracts). LEMMA 3 Uner contingent fees with attorney control over settlement: (a) For s [ s, s], the robability of settlement is ecreasing in the settlement eman an the fee rate, increasing in litigation costs, an is more sensitive to the laintiff s litigation costs than to the efenant s litigation costs. (b) The laintiff s equilibrium ayoff is (1 r )( j+ ( s ) ), where s = j+. (c) The efenant s equilibrium ayoff is j+ c ). Proof. See the Aenix. ( ca c c htt:// DOI: /

14 448 / REVIEW OF LAW AND ECONOMICS 5:1, COMPARISON OF EQUILIBRIA 5.1. COMPARISON OF PROBABILITIES OF SETTLEMENT Proosition 1 below consiers the equilibrium robability of settlement uner contingent fees with attorney control over settlement, laintiff control over settlement an hourly fee contracts. PROPOSITION 1 Proof. (a) The equilibrium robability of settlement is highest uner contingent fee contracts with attorney control over settlement, lowest uner contingent fee contracts with laintiff control over settlement an in-between in hourly fee contracts. (b) Contingent fee contracts with attorney control over settlement are Pareto suerior to hourly fee contracts, which in turn are Pareto suerior to contingent fee contracts with laintiff control over settlement. (a) The equilibrium robabilities of settlement uner contingent fees with attorney control over settlement, hourly fees, an contingent fees with r( s s) /( c ) laintiff control over settlement are + rc ( s s) /( c ) e, + c e, an ( s s) / c e, resectively (see Lemmas 3(a), 1(a) an 2(a), resectively). Note that the function e -x is ecreasing in x. We therefore nee to show that r( s s) /( c + rc ) < ( s s) /( c + c ) < ( s s) / c, for r (0,1). The right inequality is trivial. To rove the left inequality, multily the nominator an the enominator of s s) /( c + c ) by r. ( (b) Social welfare eens on the robability of trial times the amount of litigation costs. Note that the amount of litigation costs oes not een on the fee arrangement between the laintiff an her attorney or the allocation of settlement authority. Since the equilibrium robability of settlement is highest uner contingent fees with attorney control over settlement an lowest uner contingent fees with laintiff control over settlement, it follows that social welfare is lowest uner the former arrangement an highest uner the latter. The intuition behin art (a) is as follows. The robability of settlement eens on the rooser s (i.e., the laintiff or the laintiff s attorney) benefit from settlement the ifference between her settlement eman an the lowest settlement eman an the oortunity cost of trial the ifference between the rooser s settlement ayoff an trial ayoff (note that the cost of trial oes not Review of Law & Economics, 2009 by beress

15 Contingent Fees, Signaling an Settlement Authority / 449 een on the laintiff s tye, but rather on the rooser s ientity, the fee arrangement, an the allocation of settlement authority). The greater the rooser s benefit from the roose settlement, the lower must be the robability of accetance necessary to inuce searation of tyes. In aition, the greater the oortunity cost of trial, the higher the robability of accetance require to inuce searation of tyes. The equilibrium robability of settlement eens on the ratio between the rooser s benefit from settlement an the oortunity cost of trial. The higher this ratio, the greater the robability of settlement require to inuce a truthful settlement eman. This ratio is highest when the attorney controls the settlement ecision uner contingent fee contracts because the attorney receives only a ortion of a settlement recovery but bears all the laintiff s litigation costs if the case goes to trial. As a result, the efenant is able to inuce truthful revelation of the laintiff s tye by resorting to a weaker threat to break off negotiations when the laintiff s attorney makes the settlement eman uner a contingent fee contract, relative to the cases when the laintiff makes the settlement emans uner either a contingent fee or an hourly fee contract. Thus, it is the attorney ifferent ayoff scheule that reners his settlement eman more creible than that of the laintiff. Proosition 1(a) is illustrate in Figure 1: (s) 1 s s s Figure 1: The robability of settlement uner contingent fee contracts versus hourly fee contracts htt:// DOI: /

16 450 / REVIEW OF LAW AND ECONOMICS 5:1, 2009 Figure 1 shows the robability of settlement uner contingent fees with attorney control over settlement (the bol curve), hourly fees (the thin curve) an contingent fees with laintiff control over settlement (the broken curve). Note that the ifferences between the equilibrium robabilities of settlement uner the ifferent fee contracts are eenant on the egree of information asymmetry between the laintiff an the efenant. Secifically, as the suort of the istribution of the laintiff s execte court awars (i.e., [ j, j] ) increases, 11 the greater are the ifferences between the equilibrium robabilities of settlement uner the ifferent fee contracts COMPARISON OF PLAINTIFF S EQUILIBRIUM PAYOFFS UNDER CONTINGENT FEES WITH PLAINTIFF VS. ATTORNEY CONTROL OF SETTLEMENT PROPOSITION 2 The laintiff's benefit from elegating--as comare to retaining--settlement control uner a contingent fee contract is c (1 r)[ ( s ) ( s )], where s = j+. ca Proof. Recall from Lemmas 2(b) an 3(b) that the laintiff s equilibrium ayoffs uner contingent fees with laintiff an attorney control over settlement are (1 r )[ j+ ( s ) ] an (1 r )[ j+ ( s ) ], resectfully. c c c ca c Since ca ( s ) > c ( s ) (by roosition 1(a)), the ifference between the first exression an the secon exression is strictly ositive an thus catures the laintiff's benefit from elegating settlement control. The rationale behin Proosition 2 is as follows. CAs shown in Proosition 1(a), contingent fees with attorney control over settlement involves a higher robability of settlement as comare to contingent fees with laintiff control over settlement. Since the transfer from the efenant to the laintiff is higher if the case is settle, rather than trie (as the settlement transfer also inclues the efenant s litigation costs), the combine execte ayoff of the laintiff an the attorney is higher uner contingent fees with attorney control over settlement versus laintiff control over settlement. It is instructive to comare Proosition 2 with Bebchuk an Guzman (1996), who maintain that the laintiff s retention of her settlement authority uner contingent fee contracts imroves the laintiff s bargaining osition vis-à-vis the efenant relative to hourly fees. Their reasoning is that since going to trial is a costless c 11 For examle, if the robability that the court fins for the laintiff increases. Review of Law & Economics, 2009 by beress

17 alternative for the laintiff uner a contingent fee arrangement, the minimum settlement eman to be accete by the laintiff is higher than the settlement accete in the case of an hourly fee contract. To illustrate this argument, consier a case in which the laintiff oes not have the entire bargaining ower an the efenant oes not incur litigation costs. Whereas uner contingent fees the laintiff s reservation value for settlement is equal to her execte court awar, uner hourly fees the laintiff s reservation value for settlement is equal to her execte court awar minus her litigation costs. The laintiff s reservation value for settlement is therefore higher uner contingent fees than uner hourly fees. This argument assumes away asymmetry of information between the laintiff an the efenant an resuoses that bargaining ower in not ossesse entirely by the laintiff. Proosition 2, in contrast, is base on the assumtions that settlement negotiations are riven by asymmetric information an that bargaining ower is ossesse entirely by the laintiff. When the laintiff enjoys a suerior bargaining osition, elegating settlement authority to the attorney is beneficial to the laintiff because the latter s inifference between settlement an trial forces the efenant to reject the laintiff s settlement eman more often than she might reject the attorney s settlement eman. Thus, shifting the focus of the analysis from the laintiff s relative bargaining ower vis-à-vis the efenant to asymmetry of information between the litigants usets the conclusion that the laintiff shoul retain settlement authority. The next roosition comares the laintiff s equilibrium ayoff uner contingent fees with attorney control over settlement versus hourly fees. PROPOSITION 3 The laintiff s equilibrium ayoff uner contingent fee contracts with attorney control over settlement may be higher or lower than her equilibrium ayoff uner hourly fee contracts. In articular, the laintiff s equilibrium ayoff uner contingent fee contracts with attorney control over settlement is higher (lower) than uner hourly fee contracts if c [(1 r) ( s ) ( s )] > ( < ) rj (1 ( s )) c, where s ( j) = j+. ca Proof. Recall from Lemmas 1(b) an 3(b) that the laintiff s equilibrium ayoffs uner hourly fee contracts an contingent fee contracts with attorney control over settlement are j + ( s ) c (1 ( s )) c an (1 r ) j+ (1 r) ca( s ) c, resectively. Subtracting the latter exression from the former an rearranging terms yiels the inequality state in Proosition 4. The interretation of Proosition 3 is straightforwar. The left han-sie of the inequality is the ifference between the laintiff s shares in settlement uner contingent fees versus hourly fees. Recall from Proosition 1(a) that uner contingent fees with attorney control over settlement the robability of htt:// DOI: / Contingent Fees, Signaling an Settlement Authority / 451 c

18 452 / REVIEW OF LAW AND ECONOMICS 5:1, 2009 settlement is higher relative to hourly fees (that is, ca ( s ) > ( s ) ). The higher the robability of settlement, in turn, the higher the laintiff s execte ayoff from settlement. Uner contingent fees, however, the laintiff has to share the efenant s litigation costs with her attorney. The laintiff s settlement ayoff, therefore, is multilie by ( 1 r). The right-han sie of the inequality in Proosition 3 is the ifference between the laintiff s litigation costs uner contingent fees with attorney control over settlement (i.e., rj ) an the laintiff s litigation costs uner hourly fees (i.e., (1 ( s )) c ). Proosition 3 imlies that although contingent fees with attorney control over settlement are more efficient, they may not always increase the laintiff s execte rofit as comare to hourly fees. Thus, laintiffs who have little to signal those with execte low court awar are better off uner an hourly fee contract, thereby avoiing aying the attorney a settlement rent even at the cost of going to trial more often. Similarly, since the attorney s fee uner contingent fee contracts is a fraction of the laintiff s court awar, legal fees uner contingent fee contracts for high-tye laintiffs may be higher in comarison to hourly fee contracts irresective of the higher robability of settlement uner contingent fee contracts. High-tye laintiffs thus suffer from the information asymmetry between attorneys an laintiffs with resect to the laintiffs tyes. The ecisive factors in comaring the laintiff s execte ayoff uner ifferent fee contracts are total legal fees an total surlus available to the laintiff an her attorney uner contingent fee versus hourly fee contracts IMPLICATIONS AND EXTENSIONS 6.1. CONTINGENT FEES AND STRATEGIC DELEGATION The results of the revious Section can be interrete more broaly against the backgroun of the strategic elegation literature. Strategic elegation refers to a state of affairs in which a rincial is able to imrove his equilibrium ayoff (relative to his ayoff absent elegation) by elegating authority to an agent. The benefits of elegation stem from the ability to commit oneself to a course of action. By conitioning the agent s ayoff uon a certain outcome in an irrevocable an observable fashion, the rincial can inuce a thir arty to rely in a manner that increases the rincial s equilibrium ayoff relative to his noelegation ayoff. The benefits of elegate use in the context of bargaining were 12 For a iscussion on the signaling effect of the laintiff s choice of fee contract, see Section 6.4. Review of Law & Economics, 2009 by beress

19 Contingent Fees, Signaling an Settlement Authority / 453 stresse by Schelling (1960:29): The use of a bargaining agent affects the ower of commitment in at least two ways. First, the agent may be given instructions that are ifficult or imossible to change Secon, an agent may be brought in as a rincial in his own right, with an incentive structure of his own that iffers from the rincial s. To illustrate his oint, Schelling invokes the following examle of settlement negotiation with an auto insurance comany: The rivate citizen, in settling out of court, cannot threaten suit as effectively as the insurance comany since the latter is more consicuously oblige to carry out such threats to maintain its own reutation for subsequent accients. Schelling s ieas about strategic elegation have been extensively exlore an extene in numerous articles (see for examle Fershtman an Gneezy, 2001). This article rooses yet another case of strategic elegation, one that arises uner circumstances involving transmission of rivate information. In such circumstances, an agent s ifferent comensation schemes enable him to communicate rivate information to a thir arty more effectively, which results in a lower robability of negotiations breakown. The savings in transaction costs can be share between the rincial an the agent. The analysis here can therefore be extene to other rincial-agent settings in which the rincial ossesses rivate information an the agent's comensation is conitional on the outcome of a bargaining rocess DELEGATION WHEN THE PLAINTIFF DOES NOT POSSESS THE ENTIRE BARGAINING POWER We restricte the analysis to the case in which the laintiff has the entire bargaining ower. Delegation was valuable in our moel because it hele the attorney maintain creibility when the attorney mae the settlement eman. If the efenant mae the settlement offer an the laintiff's attorney retaine settlement authority, the attorney might accet lower offers than the laintiff woul because the attorney bears litigation costs but only gets a fraction of the jugment at trial. How woul our results change if bargaining ower were not ossesse entirely by the laintiff? Before roceeing to answer this question, note that the attorney s incentive to accet lower settlement offers mae by the efenant eens on the egree of information asymmetry between the laintiff an the efenant as well as the fee rate. An attorney reresenting a high-tye laintiff woul reject a low settlement offer since his ayoff from taking the case to trial is higher than the settlement offer, notwithstaning the costs incurre by the attorney at trial. Thus, the ernicious effect of elegating settlement authority to the attorney when the efenant makes the settlement offer eens on the laintiff s execte court awar. In aition, the attorney is more likely to accet low htt:// DOI: /

20 454 / REVIEW OF LAW AND ECONOMICS 5:1, 2009 settlement offers, the lower is the fee rate. The reason is that the attorney s execte rofit from taking the case to trial is increasing with the fee rate. The higher the fee rate, therefore, the higher the settlement offer require to inuce the attorney to settle the case. Now consier the case in which the two litigants fli a weighte coin to etermine who makes the settlement offer. The esirability of elegation (ex ost) in this case eens on the laintiff s tye. For high-tye laintiffs, the benefit of signaling their tye through elegation of settlement authority to the attorney outweighs the cost associate with the attorney acceting a lower settlement offer than is in the laintiff s interest. Low-tye laintiffs, by contrast, are better of retaining settlement authority since the benefit of elegation is offset by the cost of elegation. Since the laintiff oes not know his tye before the attorney learns the case, the laintiff s ecision of whether to elegate the case eens on his execte court awar. Thus, the laintiff may well refer elegation even in a ranom offeror case because the benefit of elegation (i.e., conveying the laintiff s rivate information an thereby saving litigation cost) excees its cost (i.e., inucing the attorney to accet a lower settlement eman than in the laintiff s interest) ENDOGENOUS FEE RATE We have assume throughout the analysis that attorneys fee rate uner contingent fee contracts is exogenously fixe, but our results woul continue to hol if the fee rate were etermine enogenously. Thus, assume that the market for attorneys is cometitive so that attorneys execte rofit in equilibrium is zero (see Farmer an Pecorino, 2005). 13 Also assume that, rior to settlement negotiations, attorneys incur a cost k to learn the laintiff s tye. 14 Finally, assume that attorneys announce a fee rate base on the istribution of laintiff tyes so that the fee exactly covers their cost of learning the laintiff s tye an their execte litigation costs. As we rove in the Aenix, the equilibrium fee rate uner contingent fee contracts is lower with attorney relative to laintiff control over settlement. To see why, recall that the attorney s equilibrium rofit uner contingent fee contracts, given a truthful settlement eman, is re[ j] + E [ ( s )]( c + c ) c k, j c 13 For ossible justifications of this assumtion, see the iscussion in Miceli an Segerson, 1991: See also Rubinfel an Scotchmer, 1993, an Dana an Sier, Dana an Sier, however, assume that the attorney can ro the case after observing the laintiff s tye. Here, by contrast, we assume that in the absence of settlement, the attorney always goes to trial. 14 This assumtion ensures that the equilibrium fee rate uner contingent fee contracts with attorney control over settlement is ositive. Review of Law & Economics, 2009 by beress