PRETRIAL NEGOTIATION, LITIGATION, AND PROCEDURAL …

PRETRIAL NEGOTIATION, LITIGATION, ANDPROCEDURAL RULES

JIONG GONG AND R. PRESTON MCAFEE*

We model the ci�il dispute resolution process as a two-stage game with the partiesbargaining to reach a settlement in the first stage and then playing a litigationexpenditure game at trial in the second stage. We find that the English rule shifts thesettlement away from the interim fair and unbiased settlement in most circumstances.O�erall welfare changes are in fa�or of the party who makes the offer in the pretrialnegotiation stage. Lawyers howe�er, always benefit from the English rule, because feeshifting increases the stake of the trial and thus intensifies the use of the legal ser�ice.Ž .JEL K40

I. INTRODUCTION

Newt Gingrich, in the Contract with Amer-� �ica 1994, 145 , calls for ‘‘common sense legal

reforms,’’ including a ‘‘so-called loser-paysŽrule’’ in which the unsuccessful party in a

suit pays the attorneys’ fees of the prevailing. Žparty . The ‘‘loser-pays rule’’ hereafter fee-

.shifting or English rule , Gingrich argues,‘‘strongly discourages the filing of weak casesas well as encourages the pursuit of strongcases, since claimants can get their court

� �costs reimbursed if they win’’ 1994, 146 . Avoluminous literature, discussed below, sup-ports Gingrich’s view. However, by and large,this literature neglects two important consid-erations in analyzing the English rule.

*This paper was completed while Jiong Gong wasdoing graduate study at the University of Texas atAustin, and the opinions expressed do not reflect thoseof Telcordia. We are also grateful to Dr. Phil Reny,David Sibley, Dale Stahl, Steve Bronars, John Zheng,other faculty members, and graduate students of theUniversity of Texas at Austin economics department forhelpful comments. We are also grateful to three anony-mous referees for helpful suggestions.Gong: Research Scientist, Telcordia Technologies, Mor-

ristown, N.J. 07960. E-mail [email protected]: Murray S. Johnson Professor of Economics,

Department of Economics, University of Texas atAustin, Austin, TX 78712. E-mail [email protected]. Other names are also used, like the British rule,

the Continental rule, and the European rule. In thelegal profession, this kind of practice is termed indem-nity, or fee shifting. We will use fee shifting most of thetime in this article.

2. We have been unable to find an example ofanother nation that uses the American rule for legalfees. Western European nations do not use the Ameri-can rule.

First, the English rule increases the stakeof the litigating parties. Thus, although aswitch to the English rule may reduce thenumber of lawsuits, the lawsuits that get tocourt should involve higher legal expenses.Consequently, the overall effect on legalexpenses is unclear. Second, the literatureneglects the fairness of the outcome. Doplaintiffs obtain an award justified by theevidence? We provide some theoreticalevidence that the English rule distortsoutcomes away from a fair outcome.

The judicial procedural systems in mostnations follow the English rule, which allowsfor some degree of fee shifting, or the re-warding of legal fees to the winner of legalbattles.1 It is an old British doctrine of ‘‘thecosts follow the event.’’ The United States isa remarkable exception.2 The American ruledeveloped gradually. In the early days of thecolonies, the procedural system inherited theEnglish rule, allowing attorneys to recoverfees from the losing party. Gradually, attor-neys found it more lucrative to sign privatecontingency agreements with their clients andpaid less attention to redemption from thelosing party. The court in the meantimegradually relaxed enforcement of fee shiftingand ceased monitoring legal costs, until the

ABBREVIATIONS

F-K: Froeb and Kobayashi

218Economic InquiryŽ .ISSN 0095-2583Vol. 38, No. 2, April 2000, 218�238 �Western Economic Association International

GONG & MCAFEE: NEGOTIATION, LITIGATION, RULES 219

American rule became part of the statutorylaw.3

We develop a model that permits us toaddress the question of the effects of feeshifting on fairness and expenditure at trial.Since pretrial settlement occurs in a signifi-cant portion of legal disputes, pretrial nego-tiation appears empirically important. Inenvironments with symmetrically informedcontestants, costly trials will be avoided bysettling, because there are no deviating viewsas to the outcome of the trial. Howevermany disputes do go to trial. Thus, incom-plete information also appears to be empiri-cally significant. We allow for incompleteinformation about the fundamental facts ofthe case as well as the costs of prevailing attrial. The actual likelihood of prevailing attrial is itself endogenous.

We also endogenize expenditure at trial,which is obviously necessary to answer anyquestion about the effects of fee shifting onlegal expenditures. Orley Ashenfelter and

� �David Bloom 1993 provided empirical evi-dence that legal expenditures have a pris-oner’s dilemma nature, thus appearing to besocially wasteful. Since fee shifting workslike a subsidy to winning and a tax on losing,one might reasonably expect fee shifting toincrease the stake of the trial and thus toencourage greater legal expenditures, thanunder the U.S. system.

We model a trial as a dispute over a fixedamount of money. This captures a variety oflegal contests, including tort liability for in-juries and death and private antitrust suits.4

Our model employs the endogenous legalexpenditure model of Luke Froeb and Bruce

� � Ž .Kobayashi 1993 F.K as a subgame to theanalysis. In this model, there is a probabilityP that any given piece of evidence favors theplaintiff and evidence that does not favorplaintiff favors the defendant. At trial, both

3. The Supreme Court’s first recognition of theAmerican rule was its 1796 ruling on Arcambel �. Wise-man. In 1848, the Field Code of Civil Procedure elimi-nated all provisions regulating the fees of attorneys andleft the measure of fee compensation to the client-attor-

� �ney agreement. See John Leubsdorf 1984 , for a de-tailed account of the history of American rule.

4. The model is perhaps more appropriate for civilcases than criminal cases. It is most applicable to situa-tions where the defendant’s behavior is readily ob-served, but the legality of the behavior is disputed. Thissituation commonly arises with mergers, predatory pric-ing, resale price maintenance, and many liability suits.

the plaintiff and the defendant choose theamount of evidence they collect. It is as-sumed that neither side presents evidenceunfavorable to its cause.5 Thus, a low valueof P means that the plaintiff must expend alarge amount of resources to collect rela-tively little evidence in favor of himself. Thedecision of the court is stochastic but is morelikely to favor the defendant the more theevidence favors the defendant.

We model the dispute resolution processas a simple two-stage extensive form gamewith the parties bargaining in the first stageand choosing the amount of trial effort incourt in the second stage. We consider thecase of symmetric information first, to pro-vide a comparison to the more realistic caseof asymmetric information. Since the funda-mental facts of the case are represented bythe probability of sampling a unit of favor-able evidence, it is natural to define a fair orunbiased settlement to be the product of theclaim and the probability of evidence beingfavorable to the plaintiff. When this proba-bility is commonly known in the negotiationstage as in the case of symmetric informa-tion, not surprisingly we find that both par-ties prefer a settlement. Under the Amer-ican rule, the settlement is unbiased, butunder the English rule the settlement favorsthe party that has a higher probability ofobtaining favorable evidence, thus tilting theoutcome away from a fair allocation.

We then consider the case of asymmetricinformation, where the equilibrium and theresulting outcome for the two parties dependcrucially on who makes the offer in the firststage. To phase out the effect of the first-move advantage, we let each party make atake-it-or-leave-it offer once and then takethe average payoff of the two cases.6 Nowthat the probability of evidence being favor-able to the plaintiff is not observed ex ante,

5. This assumption is a reflection of the adversarialsystem, a defining feature of the Anglo-American proce-dure. See F-K for a more detailed discussion. It involvesan issue of ethics that is beyond the scope of this article�should lawyers present all the information to thecourt even though some of the information is not in theinterest of their clients? The current governing lawrequires only that the attorney make accessible all thewritten documents. Although we do not mean to implythat lawyers are not scrupulous, casual observation indi-cate that lawyers seldom voluntarily present informationthat is detrimental to their clients.

ECONOMIC INQUIRY220

the idea of a fair or unbiased settlement ismodified to be the expectation of the prod-uct of this probability and the claim condi-tional on the information available. The ap-propriate terminology in light of Bengt

� �Holmstrom and Roger Myerson 1983 wouldbe the interim fair settlement, where fairnessmeans as fair as possible given all the avail-able information�the signals received by theplaintiff and the defendant. We identify thesituations where the parties reach a settle-ment or go to trial by constructing a uniqueseparating equilibrium. It is only when bothsides receive signals that their case is strongthat a trial results. The American rule ren-ders an interim fair allocation of the claimexcept when a trial results. In that case, bothparties are worse off than the interim fairallocation, with the difference going towardthe attorneys for legal services. With smallamount of fee shifting, the legal cost willincrease further. When signals for both par-ties are the same and are indicative of asmall P, fee shifting penalizes the plaintiffand benefits the defendant compared withthe interim fair allocation. When both sig-nals are indicative of a large P, fee shiftingdoes exactly the opposite. Finally, we investi-gate the overall ex ante welfare changes inthe presence of fee shifting for all the partiesinvolved in the lawsuit, the plaintiff, the de-fendant, and the lawyers. The result muchresembles that of the symmetric informationcase�it tilts toward the party who has ahigher probability of obtaining favorable evi-dence. However, lawyers always benefit fromfee shifting, because it increases the stake ofthe trial and thus intensifies the use of legalrepresentation.

The rest of the article is arranged as fol-lows. Since the literature is voluminous, dis-cussion of the paper’s relation to the previ-ous studies is relegated to the next section.Section III presents the model of equilib-rium trial effort under symmetric informa-tion. Section IV analyzes the bargaining and

6. This approach was mentioned in Martin J. Os-� �borne and Ariel Rubinstein 1990 . Although the ap-

proach is justified for simplicity, it is quite common thatthe defendant retains much of the bargaining power in

� �the first stage. As Spier 1992 pointed out, the defen-dant always prefers to pay as late as possible, and as aresult discounting alone does not cause the delay topermit signaling by the defendant. It is likely that thedefendant would reject any offer made by the plaintiff,provided that the some offer will be acceptable later.

trial behavior under the asymmetric informa-tion. The welfare impact of fee shifting onthe three parties is investigated in Section V.The paper is concluded with a brief discus-sion of the policy implications. All proofs arerelegated to the appendix.

II. LITERATURE REVIEW

Litigation and pretrial negotiation hasbeen studied extensively by many authors.The voluminous literature on fee shifting isprimarily focused on the effects of fee shift-ing on the probability of settlement. Existingtheoretical results are controversial and de-pend on how the dispute resolution processis modeled. The early models of William

� � � �Landes 1971 , Richard Posner 1973 , and� � Ž .John Gould 1973 P-L-G model concluded

that the risk attitude of litigants plays themajor role in determining settlement. Thegreater risk associated with the English ruleleads risk-averse litigants to settle morecases. However, in a more general version of

� �P-L-G, Steven Shavell 1982 showed thatunder certain circumstances the English ruleleads to fewer out of court settlement. Avery

� �Katz 1987, 1990 further showed that En-glish rule increases litigation expenditure as

� �well. John Hause 1989 , on the other hand,found that the English rule is more likely tolead to settlement than the American rule ina model with assumptions inconsistent with

7 � �rational beliefs. Kathryn Spier 1994 re-cently found that the direct-revelation mech-anism that maximizes the probability of set-tlement is one that resembles Rule 68 of theFederal Rules of Civil Procedure, a variantof the fee-shift rule. Jennifer Reinganum &

� �Louis wilde 1986 argued that the equilib-rium probability of trial is independent ofthe extent of fee shifting, because the trialprobability is only a function of the totallitigation costs, which were exogenous in that

� �study. John Donohue 1991, a,b also pre-dicted that both rules would have identicaleffects. Applying the ‘‘Coase theorem,’’ heargued that the procedural rules are irrele-vant as long as the involved parties are freeto sign a private contract specifying thePareto optimal rule applicable to the court.

� �7. Among other things, Hause 1989 assumed thatthe defendant believes the plaintiff is less likely toprevail than the plaintiff believes.


� �Thomas Rowe 1984 and RonaldBraeutigam, Ball Owen, and John Panzar� �1984 argued that it is impossible to predictin general whether more or fewer claimswould be settled under the English rule asopposed to the American rule. In a literaturereview on the subject matter, Robert Cooter

� �and Daniel Rubinfeld 1989 wrote that theoverall effect of different rules cannot bedetermined from theory alone.

Empirical studies have not reached a con-sensus on the effects of fee shifting on theprobability of settlement. Gary Fournier and

� �Thomas Zuehlke 1989 provided evidencethat as the stakes in a trial are increasedbecause of fee shifting, parties intensify theirefforts to reach a settlement and are morelikely to succeed. But Edward Snyder and

� �James Hughes 1990 found empirical sup-port for the prediction that fee shifting en-courages parties to litigate rather than settletheir claims. Finally, it might be worthwhileto point out that among lawyers it is com-monly believed that fewer lawsuits will occurwhen the loser pays more of the legal costs,although this belief has never been rigor-

Žously addressed at a theoretical level Cooter� �.and Rubinfeld 1989 .

Different theoretical opinions about theeffects of pretrial negotiation arise from dif-ferent models employed by distinct authors.8Extant theory can be usefully classified intotwo categories. The first category involvesmodels with disagreement over the likeli-hood of prevailing at trial. The second cate-gory improves on the first by employing pri-vate information to create disagreements,thus allowing for rational beliefs.

� �The P-L-G model and Shavell 1982 ex-plained costly litigation as the result of devi-ating views on the likelihood of prevailing attrial. Under this framework, if the plaintiff’sexpected gain in court is smaller than the

8. The entire litigation process is very complex, in-volving many decisions made by the parties to the dis-pute at several stages. Much of the litigation efforts andexpenses are incurred in the pretrial discovery phasewhere relevant information about facts is discoveredand expert consultants are deposed. The parties can stillexchange offers for a settlement along the way. Anexact model of this process would be extraordinarilycomplex. Therefore, we will follow the framework of theprevious studies all of which assume that the negotia-tion only takes place before any litigation expenses areincurred, i.e., before the discovery process. Nalebuff� �1987 suggested that prediscovery negotiation would bea better terminology.

defendant’s expected loss, there must exist avalue in between that the two parties canagree on for settlement. If the plaintiff per-ceives the probability of winning at trial tobe sufficiently greater than the defendant’sbelief about the same probability, then theplaintiff’s expected gain could well be higherthan the defendant’s expected loss. In thiscase, settlement terms would not exist thatboth parties were willing to accept, and theywould end up in court. This type of modelhas been criticized for suffering from twodrawbacks. First, the trial expenditure shouldbe an important choice variable instead ofbeing treated as fixed, and the parties’ prob-abilities of prevailing in court ought to be afunction of these trial expenditures. Bothparties to the dispute typically know muchmore than the court about the facts, andcollecting supporting evidence and transmit-ting the information to the court is costly. Inother words, the trial stage is like a war ofattrition, because the parties have differentbeliefs about prevailing in court and hencefail to reach an agreement in the negotiationstage. Recognizing this problem, Braeutigam,

� �Owen, and Panzar 1984 , Charles Plott� � � �1987 , Cooter and Rubinfeld 1989 , and,

� �more recently, Froeb and Kobayashi 1993improved on P-L-G model by incorporatingthe equilibrium level of trial expenditures,should a trial take place.

The second drawback of the model ofdeviating views, which none of the abovestudies addressed, is the unrealistic assump-tion that the probabilities of prevailing attrial are both different and common knowl-edge. At most, one of the parties has correctbeliefs. Common knowledge of the beliefsshould lead to agreement. Rationally deviat-ing assessments should be attributed to par-ties holding private information on the mer-its of the case, prescribing the setting of themodel to be a game of incomplete informa-tion where strategic interaction, includingtransmission of private information, is takeninto account.

The second category of litigation modelsemploys private information to create dis-agreements, allowing for rational beliefs.Members of this class include I.P.L. P’Ng� � � �1983 Lucian Bebchuk 1984 , Reinganum

� � � �and Wilde 1986 , Barry Nalebuff 1987 ,� �Urs Schweizer 1989 , and, more recently,

� �Kathryn Spier 1992, 1994 . All but Schweizer

ECONOMIC INQUIRY222

� � � �1989 and Spier 1994 modeled the pretrialnegotiation stage as a standard bargaininggame with one-sided private information. Theone-sided private information studies may befurther distinguished according to whetherthe informed party moves first to allow fortransmitting of private information and ac-cording to the features of the environmentthat is privately observed.9 However, thesestudies do not endogenize expenditures attrial and thus are silent on issues concerningeffects of any parameters on the cost oftrials.

Another feature that distinguishes ourwork from the existing literature is the waywe model private information. Previousstudies usually treat the parties’ probabilityestimates of prevailing at trial as privateinformation, conditional on whether thedefendant is guilty or not. In reality, civillawsuits such as product liability, patent in-fringement, contract dispute, antitrust law-suit, and defamation cases are usually verycomplex and often even the defendant doesnot know whether he has done anything ille-gal. Rarely can the jury identify an action onthe part of the defendant that proves liabil-ity, nor can it rule out all actions that willexonerate him. Consider a private antitrustsuit brought to block a proposed merger.The law is concerned with the ‘‘likely’’ harmto competition of the merger, which is hardlya precisely formulated standard. Conse-quently, both plaintiff and defendant canoffer evidence, none of which is disputative,and about which reasonable people mightdisagree.

Similarly, the standard in liability casesconcerns reasonable use of the product, andthis standard has not even been constant

Žover time see Andrew Daughety and Jen-� �.nifer Reinganum 1993, 1995 . But this un-

certainty does not imply that the two partiespossess no information at all about theirrespective strength in court. What deter-

9. P’Ng, Reinganum and Wilde, and Nalebuff hadthe informed party move first. Bebchuck had the in-formed party move last. Reinganum & Wilde’s privateinformation is the plaintiff’s amount of damage. Be-bchuck and Nalebuff treated the defendant’s probabilityassessment of prevailing at trial as private information.P’Ng has the defendant’s knowledge of whether he hasviolated the law or not as private information.Schweizer’s private information is the parties’ signalsthat link stochastically to the probabilities of prevailingat trial, and thus is closest to our model.

mines whether the party is likely to win incourt is the probability that the fundamentalfacts or evidence turn out to favor his side.The population of the potential evidence ispartly the consequence of the defendant’saction. Hence, the probability distribution ofevidence ought to be conditional on his ac-tion, giving the defendant some informationabout the potential sample of evidence. Onthe other hand, the plaintiff, after havingused the product and incurred the damage,should also have information as to the likelyoutcome of evidence collection. In light ofthe above considerations, we let the privateinformation be signals the two parties havereceived before the negotiation, and thesesignals are correlated with the fundamentalfacts of the case, which are not observeduntil trial. Note the subtle difference be-tween our treatment of private information

� �with Schweizer’s 1989 . In his model, theprivate signals are correlated with the par-ties’ estimates of the likelihood of prevailingat trial, while our privates signals are corre-lated with the probability that a randomsample evidence from the fundamentalfacts will turn out to be in one party’s favor.Thus, in the present study, private informa-tion is actually about the costs of prevailingat trial, and the probability of prevailing isendogenous.

III. THE CASE OF SYMMETRICINFORMATION

In this section, we consider the case ofsymmetric information, where the facts ofthe suit represented by the probability ofobtaining favorable evidence are commonknowledge. To capture the impact of feeshifting, we suppose that the prevailing party

� .can recover a certain percentage � � 0,1 ofhis own litigation costs from the losing party.Under the American rule, � � 0, and underthe English rule, � � 0. For practical pur-poses, we may think of � as quite small. Onemay question whether a small � representsthe true English rule. Werner Pfennigstorf� �1984 implies that a pure form of the En-glish rule is a rarity on the books for thefollowing reasons. In Europe, not all litiga-tion costs are reimbursable and even thereimbursable costs are limited and regulated.For example in England and Canada, thecosts to be reimbursed are defined as includ-


ing only ‘‘necessary and proper’’ costs. Inpractice, the court officials, called taxingmasters, decide the amount, and it is usuallyabsurdly small compared with the totalamount charged by the attorney.10

Suppose that the plaintiff claims that theplaintiff has incurred a loss and demands acompensation of a certain amount. Withoutloss of generality, the damage is assumed tobe one dollar. Let P denote the probabilitythat a randomly sampled unit of evidence isfavorable to the plaintiff. Since the defen-dant has contrary interest against the plain-tiff, the probability that evidence is favorableto the defendant is 1 � P.11 Both the defen-dant and the plaintiff pay the litigation costc for each unit of evidence obtained. Thelitigation costs can be thought of as the costsof investigating the case, deposing witnesses,hiring experts, and attorney fees.

Because the proportion of evidence favor-ing the plaintiff is P, we define a fair settle-ment to be a payment to the plaintiff of P.There are two justifications for this assump-tion. One may think of the evidence col-lected as implying that plaintiffs in identicalcircumstances were actually injured withprobability P, so the defendant’s averageliability was P. Alternatively, one could con-sider P to be the proportion of the claimeddamage that the plaintiff actually suffered.

As the standard approach of analyzing atwo-stage extensive form game, we first lookat the subgame of litigation expenditures attrial. The subgame is essentially a reduced

� � Ž .form of Froeb and Kobayashi’s 1993 F-Kgame of the search for evidence, which mod-els trial expenditures behavior in an econom-ical and tractable manner. Both plaintiff anddefendant are risk neutral. The choice vari-able for both parties is the amount of evi-dence to collect. Since P is known when the

� �10. See Kritzer 1984 . McAfee had a personal cor-roboration in Canda. Litigation costs expressly excludecontingent fees. There is substantial agreement in Eu-rope that contingent fee agreements between the attor-ney and the client are unethical. Regarding the fact thatcontingent fee practice is so widely accepted and in-volves a substantial amount of money in the UnitedStates, it is reasonable to expect that only a smallportion of the litigation costs would be recovered by theprevailing party had the English rule been written intothe American judicial procedural statutes.

11. This is without loss of generality, for if a fraction� of the evidence favors neither side, we may adjust thecost to be the cost of obtaining relevant evidence bydividing by 1 � �.

two parties enter into the trial and the par-ties only display to the judge the evidencefavorable to themselves, it is equivalent toletting the amount of the favorable evidencebe the choice variable, which is denoted byE for the plaintiff and E for the defen-p ddant. The costs of collecting E and E willp d

Ž .be cE �P and cE � 1 � P , on average.p pEach party’s probability assessment of the

likelihood of prevailing at trial should be anincreasing function of the favorable evidencepresented by himself and a decreasing func-tion of the unfavorable evidence presentedby his opponent. We follow F-K and assumethe judge or the jury uses a simple rule basedentirely on presented evidence by both par-ties to decide the case, such that the proba-bility of ith party’s prevailing at trial is

Ž . 12E � E � E , i � j, i, j � p, d. When bothi i jterms in the quotient are zero, we assumethe probability to be 1�2, although E � 0 isinot equilibrium behavior for at least oneparty regardless of the posited probability.13

Given the environment, the parties face thefollowing objective functions in the subgame

Ž .1Ep� Ž .� � � maxp E � EEp p d

E Ep p� c 1 � �ž /P E � Ep d

E Ed d� � c1 � P E � Ep d

Ep� Ž .� � � mind E � EEd p d

E Ed d� c 1 � �ž /1 � P E � Ep d

E Ep p� � cP E � Ep d

Ž .The first equation in 1 is the plaintiff’sexpected gain from the trial. It is the ex-

12. U.S judges typically instruct juries to consideronly the evidence presented at trial.This jury technology

� �is a special form used by Plott 1987 .13. The nature of the trial can be broadened to cases

Ž .where the jury may choose the reward E � E � Ep p dfor the plaintiff, because of the posited risk neutrality.

ECONOMIC INQUIRY224

pected award by the jury minus his ownlitigation costs, plus the recovery of a per-centage of it if he wins, and minus a percent-age of the expected litigation costs spent byhis opponent if he loses. The second equa-tion represents the expected payment by thedefendant. We assume that the two partiesplay the unique pure strategy Nash equilib-rium to this game. The appendix shows that

Ž .the solution to 1 is

Proposition 1: The Nash equilibrium ofthe litigation expenditure game has aunique solution that

Ž .21

� Ž .E � P 1 � Pp 2c

Ž .'� � 1 � 2� P�

Ž .'� 2 P � 1 �

1� Ž .E � P 1 � Pd 2c

Ž . '1 � 2� 1 � P � �� ,

Ž .'� 2 P � 1 �

where

Ž . Ž .� � 1 � 2 � � 4� P 1 � P � 0.

Several observations immediately follow.Ž .First it is obvious from 1 that the defen-

dant’s equilibrium expected payment alwaysexceeds the plaintiff’s expected gain, result-ing in the existence of the cooperative sur-plus to be distributed between the twoparties. Therefore, a settlement is alwayspreferred to a trial. How the surplus is splitis also straightforward. Since both parties aresymmetrically informed about P, no strate-gic action is possible. Under this context, noform of bargaining is more natural than theNash bargaining concept, evenly dividing

Žgains from settlement for a justification, see� �.Ariel Rubinstein 1982 . Cooter and Rubin-

Ž .feld’s 1989 model of symmetric informationalso uses the Nash bargaining concept.

Ž .It can be verified from 2 that in thespecial case of � � 0,

2 Ž .P 1 � P�Ž .3 E �p c

2Ž .P 1 � P�E �d c

Ž . � 2 � 24 � � P � � 2 P � P ,p d

while in the limiting case of � � 1, theydepend on whether P is less, equal or greaterthan 1�2:

0, if P � 1�2Ž .1�8c 1 � a , if P � 1�2� Ž .5 E �p Ž . Ž .P 1 � P �c 2 P � 1 ,� if P � 1�2

Ž . Ž .P 1 � P �c 1 � 2 P ,if P � 1�2� E �d Ž .1�8c 1 � � , if P � 1�2�0, if P � 1�2

Ž .�P� 1 � 2 P , if P � 1�2Ž . Ž .1 � 2� �4 1 � � ,� Ž .6 � �p if P � 1�2� 1, if P � 1�2

0, if P � 1�2Ž . Ž .3 � 2� �4 1 � � ,� � �d if P � 1�2� Ž .P� 2 P � 1 , if P � 1�2

Thus, under the American rule where �Ž� 0, the expected award by the jury, E � Ep p

.� E is exactly P, the probability that evi-ddence turns out to be favorable to the plain-tiff. When � � 1, which is an extreme caseof the English rule, the award goes to 0, 1�2,or 1, depending on whether P is less than,equal to or greater than 1�2.

Note that the Nash bargaining result un-der � � 0 also yields a settlement of theamount P, which is an unbiased and fairallocation of the claim. Hence, we concludethat under symmetric information the Amer-ican rule generates the fair settlement. Alsonote that if the parties do go to trial, underthe American rule the plaintiff wins the trial


with probability P and receives an averagecompensation of P from the defendant. Thesimple jury technology specified thus deliversa fair allocation of the claim under theAmerican rule, a result proved by F-K. Inthe case of symmetric information, costlycourt battles can be avoided by resorting tomutually beneficial negotiations. Trials, how-ever, have the prisoner’s dilemma nature

� �suggested by Ashenfelter and Bloom 1993 ,in that parties expend resources to obtainthe commonly known fair division.

Now consider the impact of switching to-ward the English rule. Denote the Nash bar-gaining settlement as a function of � byŽ . � � Ž . � Ž .�S � � � � � � � �2. First observep d

that when P � 1�2, in the limiting case ofŽ . Ž .� � 1, S � � �P�2 1 � 2 P is negative.

In general, for � large enough, a plaintiffwith a weak case will encounter negativegains from the pretrial negotiation, whichwill certainly prevent him from initiating thelawsuit in the first place.14 As a result, in thefull-information case, fee shifting tends todiscourage frivolous lawsuits, supportingNewt Gingrich’s claim.

Whether a settlement favors the plaintiffor defendant is determined by the sign ofŽ .S� � . If it is positive, then the settlement is

said to favor the plaintiff. If it is negative,the settlement favors the defendant. First,we establish a lemma. It says that, as �increases, the party that spends more on

Ž � �.attorney fees cE �P and cE � 1 � P , de-p dpends on whether P is greater or less than1�2. When P is greater than 1�2, meaningthat the plaintiff has a stronger case, hislegal expenditure will exceed that of the de-fendant. When P is less than 1�2, the oppo-site is true. Furthermore, the gap is an in-creasing function of � .

Ž .7 Lemma 1:

� E� E�p d�ž /�� P 1 � P

� 0, if P � 1�2� 0, if P � 1�2�� 0, if P � 1�2

Ž .14. For sufficiently small P, S� � is negative if andŽ . � Ž .only if � � 2�3. That is �S � ��P � 2 � 3� �2.P� 0

Ž .Now consider the sign of S� � . Upondifferentiating with respect to � and usinglemma 2, we show in the appendix that

� 0, if P � 1�2Ž . Ž . � 0, if P � 1�28 S� � �� 0, if P � 1�2

Thus, as � deviates away from zero, theamount of the settlement increases if theprobability of the randomly sampled evi-dence being favorable to the plaintiff ishigher than being favorable to the defen-

Ž .dant. Figure 1 plots S � against P for sev-Ž .eral values of � . As � increases, S � shifts

downward for P less than 1�2 but upwardfor P greater than 1�2. In other words, asthe American rule switches toward the En-glish rule, the settlement rewards more theparty who has a higher probability of obtain-ing favorable facts supporting the case or,equivalently, a lower cost of presenting astronger case. We summarize the main re-sults of this section in the following proposi-tion.

Proposition 2: In the case of symmetricinformation, the parties to the disputealways prefer the settlement to the trial.Under the American rule, the Nashbargaining solution generates the fairsettlement. As the procedural ruleswitches toward the English rule, thesettlement rewards the party with a

FIGURE 1Equilibrium Settlement with Symmetric

Information

ECONOMIC INQUIRY226

higher probability of obtaining support-ive evidence.

Proposition 2 is very intuitive. When thefacts of the case are clear to the plaintiff andthe defendant, and they play equilibriumstrategies of trial expenditures, they shouldhave the same probability assessment of thecompensation payment ordered by the judge.As � increases, the relative gain to winningincreases and parties increase expendituresat trial, with the side more likely to win inequilibrium more heavily subsidized. At thebargaining table before the trial, the partyless likely to win has a disadvantage becausehis opponent knows he is going to pay alarge amount at trial. Therefore, as � in-creases, the settlement favors more the partywho has an advantage in terms of findingsupportive evidence. This point can be read-ily enforced by the previous observation thatwhen � � 1, the jury award goes to 0, 1�2,or 1, depending on whether P is less than,equal to, or greater than 1�2, suggesting thatwhen P � 1�2, the plaintiff’s share falls andwhen P � 1�2, the plaintiff’s share rises.

The symmetric case where settlement isalways successful is unrealistic, because notrials occur. Difference of beliefs about pre-vailing at trial can prevent the parties fromreaching a settlement. If they do not differon assessments of prevailing at trial as in thecase of symmetric information, they shouldreach an agreement easily. To model thefailure of pretrial negotiation, we now con-sider asymmetries of information.

VI. THE CASE OF ASYMMETRICINFORMATION

Asymmetries of information may causethe parties to go to trial rather than settle.We examine the simplest model with two-sided asymmetric information. In this model,the likelihood that evidence favors the plain-tiff, P, is known to neither party and is

� �viewed ex ante as a uniform draw from 0,1 .Both parties privately and independently ob-serve a single draw from the evidence. Evi-dence favors the plaintiff with probability P,and we denote this outcome by 1 and evi-dence favoring the defendant by 0. TheBernoulli random variables for the plaintiffand defendant are denoted by X and Y,

respectively.15 The environment is commonknowledge to the parties, who are only un-certain about their opponent’s information.From the plaintiff’s perspective, 1 is a strongsignal because it brings the good news that ahigher P is likely, whereas 0 is a weak signal.For the defendant, 1 signals a weak casebecause a higher P is bad news to the defen-dant, whereas 0 signals a strong case.

The pretrial negotiation game can takedifferent extensive forms. In our case, theequilibrium depends on who makes the offerin the negotiation stage. We first assumethat the defendant makes a take-it-or-leave-itoffer and, if the plaintiff rejects, a trial re-sults.16 The case where the plaintiff makesthe offer is similar in nature. It is quitecommon that the defendant retains much ofthe bargaining power in the first stage.

The timing of negotiation is as follows.Both parties receive their private signals firstand then negotiate. Should the parties fail tosettle, legal expenses will be incurred as bothparties prepare for trial. In the process, P isrevealed, and thus the trial outcome corre-sponds to the full-information case modeledin the previous section. This model has theadvantage of simplicity and the disadvantagethat parties would actually prefer to settleonce P is revealed. We consider that ourmodel captures many of the salient aspectsof the legal system, including the endoge-nous legal expenditure and interim disagree-ments about the likelihood of prevailing attrial, in an internally consistent framework.The model fails to capture the effect oflitigants learning about the likelihood of pre-

15. This model is closely related to that of Schweizer� �1989 , although Schweizer’s model did not endogenizeeffort at trial. It would obviously be desirable to endoge-nize the prenegotiation evidence collection, althoughthe resulting complexity is daunting.

� �16. Hause 1989 criticized the idea of one partymaking a take-it-or-leave-it offer, arguing that it is in-consistent with general rule that settlements can beoffered or accepted at any point in the negotiation

� �process. However, as Spier 1992 pointed out, the de-fendant always prefers to pay as late as possible, and asa result discounting alone does not cause the delay topermit signaling by the defendant. That is, the defen-dant would reject any offer made by the plaintiff, pro-vided that the same offer will be acceptable later.Therefore cases are likely to be settled in the last

Ž .minute on the courthouse steps the ‘‘deadline effect’’ .� �In fact, Williams 1983 found than 70% of all civil cases

in Arizona are settled in the last 30 days before thetrial, and 13% were settled on the day of the trial.


vailing at trial through the course of evi-dence collection, an effect ruled out by posit-ing the common knowledge of P at trial. Thesignificance of such learning is left for futureresearch.

When the party decides what offer tomake and similarly when the other partydecides whether to accept or reject the offer,they must consider the expected equilibriumoutcome in the trial subgame. It is straight-forward to compute the expected equilib-rium outcome for the two parties under dif-ferent signal configurations when � is closeto or equal to 0.17 These values are presentedin Table I.

We first consider the equilibrium underthe American rule. The payoff under theAmerican rule corresponds to the payoff inthe above table by setting � � 0. Because Pis assumed to be uniform, the posteriorprobability of a party that the opponent hasa different signal is 1�3 and the probabilityof same signal is 2�3. We now consider theequilibrium of this two-stage game. The nat-ural equilibrium concept for games with in-complete information is David Kreps and

Ž .Robert Wilson’s 1982 notion of sequentialequilibrium. In the more realistic scenariowhere the defendant makes the offer, thesequential equilibrium is a set of strategiesand beliefs such that, at the beginning of thefirst stage of the game, the defendant’s offeris optimal and, at the beginning of the sec-ond stage, the plaintiff reacts optimally giventhe beliefs of the defendant’s signal type,

17. To derive the payoffs when � � 0, it is reason-able to approximate those payoffs using the first-order

Ž � Ž . � . Ž � Ž . � .Taylor expansion E � � x, y � E � � � 0 x, yi i�d� � Ž Ž . � .� 4� � E � � x , y �� 0 . Using Mathematica, itid� � Ž . � Žcan then be shown that d� � �d� � �P 1 �� 0p

.Ž 2 . � Ž . � ŽP 1 � 3P � 6P and d� � �d� � �P 1 �� 0d

.Ž 2 .P 2 � 9P � 6P . It is straightforward to compute thepayoffs using the appropriate conditional density func-tions of P. Note that the conditional density functions

Ž � . Ž .2 Ž � . Ž .of P are f P 0, 0 � 3 1 � P , f P 0, 1 � 6P 1 � PŽ � . 2and f P 1, 1 � 3P .

and the beliefs are obtained from equilib-rium strategies and the observed offer usingBayes’ rule. In other words, the defendant’soffer takes into account the effect of hisoffer on the plaintiff’s belief and action, andthe plaintiff’s decision whether to acceptis also optimal given his signal and the pos-terior belief about the defendant’s signaltype. We restrict attention to pure strategyequilibria.

With only two types of private informa-tion, pure strategy sequential equilibria willbe either fully separating or pooling. A sepa-rating equilibrium is an equilibrium in whichthe two types of the defendant choose twodifferent offers in the negotiation stage. In apooling equilibrium, the defendant’s offerwill be the same regardless of the signal. Thepooling equilibrium is rather simple. Sincethe defendant’s offer does not transmit anyinformation, it turns out that the poolingequilibrium is for the defendant to offer 1�2,and the plaintiff always accepts this offer.18

We will concentrate on the separating equi-librium where the case will end up in courtwith positive probability, which better ac-counts for actual trial experience.

In a separating equilibrium, for each valuey of the two possible signals, the defendant

Ž .makes an offer S y . Several authors havedshown that in a bargaining game of two-sidedinformation, the receiver of the offer uses a

Žcut-off strategy see, for example, Peter� �.Cramton 1984 . If his cut-off value exceeds

the offer, he will accept it and reject it ifotherwise. In the context of our model, the

Ž .plaintiff adopts this cut-off strategy S x, S ,p dwhich maps his private signal and the offer

18. Such an equilibrium where the parties can alwaysreach an agreement is called the ‘‘efficient equilibrium’’

� �by Schweizer 1989 . He further showed that the effi-cient pooling equilibrium does not survive Jeffrey Banks

� �and Joel Sobel’s 1987 ‘‘universal divinity’’ refinement� �concept. Reinganum and Wilde 1986 ruled out the

pooling equilibrium in their model using the same con-cept.

TABLE IEquilibrium Outcome When � Is Small

� �( ( ) � ) ( ( ) � )X Y E � � x, y E � � x, yp d

0 0 1�10 � 6��35 2�5 � 3��1400 1 3�10 � 11��70 7�10 � 11��701 0 3�10 � 11��70 7�10 � 11��701 1 3�5 � 3��140 9�10 � 6��35

ECONOMIC INQUIRY228

� �by the defendant to 0,1 . Because of the firstorder stochastic dominance property of Pand the incentive compatibility constraint,we show in the appendix that both parties’strategies are strictly increasing in their re-ceived signals in a separating equilibrium:

Lemma 2: In a separating equilibrium,Ž Ž .. Ž Ž ..S 1, S y � S 0, s y , y � 0,1, andp d p dŽ . Ž .S 1 � S 0 .d d

Lemma 2 is helpful with constructing theseparating equilibrium. Since there are onlytwo types for the defendant, his signal is fullyrevealed to the plaintiff. Thus, the Bayesianupdate for the plaintiff is trivial. The plain-tiff’s cut-off value will be the expected payoffat trial conditional on his signal and thedefendant’s signal. In the model, the plain-tiff’s belief after observing an offer is thatany offer higher than the equilibrium offerfrom a strong defendant reveals that thedefendant is weak. We will show later thatsuch belief is consistent with the plaintiff’soptimal strategy. Having observed that, westate the following proposition.

Proposition 3: Under the American ruleand when the defendant makes the of-fer, the separating equilibrium is forthe defendant to offer a tough settle-ment of 1�10 when he receives a strongsignal and offer a generous settlementof 3�5 when he receives a weak signal.Seeing a tough offer from the defen-dant, the plaintiff accepts it if he re-ceives a weak signal, and goes to trial ifhe also receives a strong signal. Seeinga generous offer, the plaintiff alwaysaccepts the settlement regardless of thesignals. Furthermore, the separatingequilibrium is unique.

Proposition 3 is quite intuitive. In orderfor the defendant to separate on type, theoffer from the strong defendant, which islower, must be rejected by the strong plain-tiff. Thus, the strong defendant makes theminimal offer acceptable to the weak plain-tiff. The weak defendant, in contrast, makesan offer just acceptable to the strong plain-tiff so that it is always accepted. When theplaintiff makes the offer, the equilibrium hasthe same flavor:

Proposition 4: Under the American ruleand when the plaintiff makes the offer,

the separating equilibrium is for theplaintiff to demand a large settlementof 9�10 when he receives a strong sig-nal and demand a small settlement of2�5 when he receives a weak signal.Seeing a large demand from the plain-tiff, the defendant accepts it if he re-ceives a weak signal, and goes to trial ifhe also receives a strong signal. Seeinga small offer, the defendant always ac-cepts the settlement regardless of thesignals. Furthermore, the separatingequilibrium is unique.

Next we consider the equilibrium underthe switch toward the English rule. Here wewill resort to exact numerical computationsin our investigation. The difficulty that arisesis that the conditional expectation of theequilibrium payoff at trial when � � 0 is a

Ž � �.complicated function of � see eq. 2 .Applying the same logic used in the proof

Ž .of proposition 3 , it is shown in the appendixthat the separating equilibrium of proposi-

Ž .tion 3 is entirely robust to the perturbationof the equilibrium payoff at trial caused bythe switch toward the English rule. The max-imal level of fee shifting that supports theseparating equilibrium is � � 0.82, a sub-stantial amount of indemnity that is typicallyunrealistic under most judiciary systems. For� exceeding 0.82, the weak plaintiff will findit unprofitable to initiate the lawsuit. Theseparating equilibrium is without surprisesimilar to the case under American rule wehave shown in that it is only when the bothsides feel they have a strong case that a trialresults.

Proposition 4 is also robust to large �close to 1, when the procedural rule movestoward the English rule. In fact, it is morerobust than the case when the defendantmakes the offer, because we do not evenhave to consider the rationality constraintthat the plaintiff is willing to file a lawsuit.The nature of fee shifting is that it amplifiesthe first move advantage, so as long as theplaintiff is willing to sue for � � 0, which isobviously true, he will file a lawsuit for all � .We document the results under the Englishrule in the next proposition.

Proposition 5: Under the English rulewhere the extent of fee shifting is lessthan 82% and when the defendant


makes the offer, the separating equilib-rium is for the defendant to offer a

Ž � Ž . � .tough settlement of E � � 0, 0 ,pwhen he receives a strong signal andoffer a generous settlement ofŽ � Ž . � .E � � 1, 1 when he receives a weakp

signal. Seeing a tough offer from thedefendant, the plaintiff accepts it if hereceives a weak signal and goes to trialif he also receives a strong signal. See-ing a generous offer, the plaintiff al-ways accepts the settlement regardlessof the signals. When the plaintiff makesthe offer, the separating equilibrium isfor the plaintiff to demand a large set-

Ž � Ž . � .tlement of E � � 1, 1 , when he re-dceives a strong signal and demand a

Ž � Ž . � .small settlement of E � � 0, 0 whendhe receives a weak signal. Seeing alarge demand from the plaintiff, thedefendant accepts it if he receives aweak signal and goes to trial if he alsoreceives a strong signal. Seeing a smalldemand, the defendant always acceptsthe settlement regardless of the signals.Furthermore the separating equilib-rium in each case is unique.

V. WELFARE EFFECT OF FEE SHIFTING

Based on the results in the previous sec-tion, we are now able to investigate the im-pact of the fee shifting on the pattern of thesettlement. We compare the results underthe English rule with a small extent of feeshifting to the fair allocation in the followingtables. The outcome in the following tablesare based on who makes the offer and areinterim, meaning that the expectation of thepayoffs should be taken conditional on theknown signals they received respectively. Astrong signal received by the plaintiff is onerepresented by 1, while a strong signal re-ceived by the defendant is one representedby 0. The last row of each table representsthe ex ante expectation, prior to the realiza-tion of the signals. Table IV takes the aver-age of the results in Table II and Table III,with the interpretation that half of the timethe defendant makes the offer and half ofthe time the plaintiff makes the offer.

In terms of the pattern of the settlement,we can see from Table IV that under theAmerican rule where � � 0, both parties geta fair payoff for all signal configurationsexcept when both parties receive signals in-

TABLE IIInterim Equilibrium Outcome When the Defendant Makes the Offer

x y Fair P Plaintiff’s Earning Defendant’s Payment Legal Costs

0 0 1�4 1�10 � 6��35 1�10 � 6��35 00 1 1�2 3�5 � 3��140 3�5 � 3��140 01 0 1�2 3�10 � 11��70 7�10 � 11��70 2�5 � 11��351 1 3�4 3�5 � 3��140 3�5 � 3��140 0

Average 1�2 23�60 � 79��840 9�20 � ��24 1�15 � 11��210

TABLE IIIInterim Equilibrium Outcome When the Plaintiff Makes the Offer


0 0 1�4 2�5 � 3��140 2�5 � 3��140 00 1 1�2 2�5 � 3��140 2�5 � 3��140 01 0 1�2 3�10 � 11��70 7�10 � 11��70 2�5 � 11��351 1 3�4 9�10 � 6��35 9�10 � 6��35 0

Average 1�2 11�20 � ��24 37�60 � 79��840 1�15 � 11��210

ECONOMIC INQUIRY230

TABLE IVAverage Interim Equilibrium Outcome


0 0 1�4 1�4 � 3��40 1�4 � 3��40 00 1 1�2 1�2 1�2 01 0 1�2 3�10 � 11��70 7�10 � 11��70 2�5 � 11��351 1 3�4 3�4 � 3��40 3�4 � 3��40 0

Average 1�2 7�15 � 11��420 8�15 � 11��420 1�15 � 11��210

dicative of a strong case, in which instancethey go to trial. The impact of the fee shift-ing is much like that in the symmetric infor-mation case�it tends to shift each party’swelfare away from the fair allocation whileincreasing the legal cost. In two cases wherethe parties receive the same signals, the En-glish rule shifts the settlement away from thefair allocation. When these same signals allindicate that a small P is likely, fee shiftingfurther penalizes the plaintiff and favors thedefendant. The opposite is true when bothsignals indicate otherwise. In one instancewhere both parties receive strong signals andgo to trial, the English rule results in anunambiguous increase in legal fees, furthermoving both parties’ welfare in court awayfrom the fair allocation. This is summarizedin the next proposition.

Proposition 6: The American rule ren-ders an interim fair allocation exceptwhen a trial results. When both parties’signals favor the defendant, the in-finitesimal move toward the Englishrule further shifts the settlement awayfrom the interim fair allocation in favorof the defendant. When both parties’signals favor the plaintiff, the switchtoward the English rule shifts the set-tlement away from the interim fair al-location in favor of the plaintiff. Whenboth parties receive strong signals inwhich case they go to trial, the in-finitesimal move toward the Englishrule increases the legal fees.

The likelihood of both litigants obtaining0 is 1�3, similarly for both obtaining 1, while

Ž . Ž .either a 0, 1 or 1, 0 combination has aprobability of 1�6. This allows us to computean overall average, presented in the final rowof each table. The assignment of the bargain-ing power to the defendant as in Table II, in

the form of a take-it-or-leave-it offer, resultsin an advantage, in that, for � � 0, the de-fendant on average pays less than the fairallocation. However, when averaging over thetwo cases where each one has a chance tomake the offer, both parties are worse offthan the interim fair allocation, because theyhave to pay for legal services for all signalconfiguration. The difference between thetwo outcomes is split between the attorneysrepresenting each party.

Suppose that plaintiffs face a fixed costŽ .which varies across plaintiffs of initiating alawsuit. This fixed cost is paid after theplaintiff learns his signal but before the de-fendant learns his signal. A small increase in� , starting at the American rule, benefits

Ž .strong X � 1 plaintiffs. Thus, we wouldexpect more lawsuits to be brought by plain-tiffs with strong cases. In addition, the ex-pected payoff for weak plaintiffs, which is1�3 � ��20, is decreasing in � . Thus, we

� �find support for Gingrich’s 1994 claim thatthe loser-pays system will discouragefrivolous lawsuits while encouraging seriousones.

Next we consider the overall ex ante wel-fare impact of fee-shifting on all the relevantparties in a lawsuit, the plaintiff, the defen-dant and the representing attorneys. Againwe first consider the case where the defen-dant makes the offer. Figure 2 is a plot of

Ž .the ex ante payoff to the plaintiff U � , P ,pŽ .the ex ante payoff to the defendant U � , P ,d

and expenditures at trial against P whenŽ . Ž .� � 0. U � , P and U � , P are computedp d

conditional on P but averaged over the sig-nals that can arise, using the correct proba-

Ž Ž . . 19bility e.g. Prob X � 1 � P .

Ž . Ž .2 Ž .19. Conditional on P, U � , p � 1 � P S 0 �p dŽ . Ž . Ž . Ž � Ž . � . 2 Ž .P 1 � P S 1 � P 1 � P E � � 0, 1 � P S 1 ,d p d

Ž . Ž .2 Ž . Ž . Ž . Žand U � , P � 1 � P S 0 � P 1 � P S 1 � P 1d d d. Ž � Ž . � . 2 Ž .�P E � � 0, 1 � p S 1 .d d


FIGURE 2Equilibrium with Asymmetric

Ž .Information Defendent Makes Offer

In Figure 2, the two top curves representŽ . Ž .U 0, P and U 0, P respectively. Naturally,p dŽ . Ž .U 0, P is above U 0, P . The differenced p

between them is the legal costs, which arerepresented by the lower parabola. The dif-ference is widest as P gets close to 1�2. Thisis the best scenario for lawyers as a group,since no party has a dominant case and bothsides spend heavily on legal service. As Papproaches 0 or 1, the two curves of thelitigating parties intersect, indicating the lim-iting situation of settlement. The reason isstraightforward. When P approaches 0, theprobability that the plaintiff receives a strongsignal goes to 0. So it is almost sure that theplaintiff will accept the settlement. When Papproaches 1, the probability that the defen-dant receives a strong signal goes to 0. Thenit is almost sure that the defendant will al-ways offer a sufficiently high offer to securea settlement. Recall that the ex ante fairallocation of the claim should be P, repre-sented by the 45 line in Figure 2. Roughlyspeaking, the plaintiff gets more than heshould when P is small but less than hedeserves when P is large. Similarly, the de-fendant pays more than he should for smallP but less than he should for large P. Inaddition, the interval of P in which theplaintiff enjoys a surplus over the fair alloca-tion is substantially smaller than that of P inwhich the defendant enjoys a surplus. There-fore, without fee shifting, the defendant is ina relatively advantageous position. The ad-

vantage stems from the fact that the defen-dant is assumed to be the first mover inoffering a settlement in the negotiation stage.

As a function of P, our computation showsthat fee shifting benefits the defendant mostof the time and increases legal fees whilealways hurting the plaintiff. As argued above,since the defendant makes the offer, he is inan advantageous position in the absence offee-shifting. When fee-shifting is introduced,it essentially amplifies this effect, making theplaintiff even worse off with the surplus splitbetween the defendant and the plaintiff at-torneys. Figure 3 plots the equilibrium out-come changes as � increases to 0.1. Figure 3also presents the effect of fee shifting on thetotal litigation costs, which increases as �increases. Provided that � is not increased

Žbeyond 0.82 at which point the separating.equilibrium breaks down , a move toward

the English rule increases legal expenditures.Within the context of the model, there is nochange in the probability of a trial, given theassumed discrete nature of informationavailable to the parties.

In the case where the plaintiff makes theoffer, similar graphs can be drawn. Figure 4is a plot of the ex ante payoffs for the threeparties under American rule. Figure 5records the changes as a result of fee shiftingof � � 0.1. This time the plaintiff gains mostof the time, and the defendant incurs loss.The combined legal fees still increase, paidmostly by the defendant.

FIGURE 3Equilibrium Changes When � � 0.1

Ž .Defendent Makes Offer

ECONOMIC INQUIRY232

FIGURE 4Equilibrium with Asymmetric

Ž .Information Plaintiff Makes Offer

FIGURE 5Equilibrium Changes When � � 0.1

Ž .Plantiff Makes Offer

Finally, we take the average ex ante out-come when half of the time the defendantmakes the offer and half of the time theplaintiff makes the offer. Figure 6 gives theoutcome for each party as a function of P.Figure 7 represents the change when �moves to 0.1. Clearly, the defendant gainsfor small P, and the plaintiff gains for largeP. However, there exists an interval of P inwhich both the litigating parties incur loss.Attorneys, on the other hand, enjoy a win-winsituation. The total legal cost will increase asa result of fee shifting. If plaintiffs also faceda fixed cost of bringing suit that varied acrossplaintiffs, then an increase in fee shiftingwould reduce the number of suits, while in-creasing average legal expenditures on thesuits that were brought, resulting in an over-all ambiguous effect on the total expendi-

FIGURE 6Equilibrium When Plaintiff or

Defendant Makes Offer Half of theTime

FIGURE 7Equilibrium Changes When � � 0.1Ž .Each Makes Offer Half of the Time

tures on legal services and the demand forattorneys. To summarize, we have

Proposition 7: A small increase in feeshifting reduces the plaintiffs’ ex anteearnings for small P, increases the de-fendants’ expected payment for largeP, and increases the total legal fees forall P.

VI. CONCLUDING REMARKS

We investigated the effects of charginglosers at trial with a portion of the winner’slegal costs, or fee shifting, on the pattern ofsettlement, in a model with endogenous ex-penditure at trial. In particular, we com-pared the American rule, where parties paytheir own legal costs, to the English rule,where the loser pays a portion of the winner’scost. Unlike much of the large literature onthis topic, we are concerned with the fairness


of the outcome and the expenditures em-ployed to achieve that outcome.

Under complete information, the adver-sarial system without fee shifting produces areasonable outcome in the following sense.The fair award exceeds the amount that theplaintiff receives from trial but is less thanthe amount that the defendant pays. More-over, the outcome is such that Nash bargain-ing with trial as a threat produces exactly thefair allocation. Consequently, the pattern ofsettlements under complete information andwithout fee shifting is as good as it canpossibly be. It is no surprise, then, that feeshifting distorts the outcome away from thefair outcome, and that fee shifting favors theparty with the strong case, that is, the partywith the lower cost of providing evidence tothe court. Not surprisingly, when the facts ofthe case are the most uncertain, both partiesexpend the greatest resources at trial,and these expenditures are increased by feeshifting.

Many authors have noted that completeinformation appears to be inconsistent withthe fact that many lawsuits are actually set-tled in court. Because trials are costly, ifthere is agreement about the underlying factsof the case, there should always be a mutu-ally advantageous settlement. Consequently,asymmetries of information appear to play asignificant role in legal disputes, with theresult that pretrial negotiation does not in-variably lead to settlement.

Asymmetries of information tend to favorthe party with the weak case so that theplaintiff receives more than the fair alloca-tion when randomly selected evidence favorsthe defendant and less when randomly se-lected evidence favors the plaintiff. Thus, theremarkable virtue of the American rule inpromoting a fair outcome under completeinformation is lost when the adversaries areasymmetrically informed. In this circum-stance, fee shifting can either enhance ordetract from the fairness of the allocation,although on balance it makes the party whomakes offers better off at the expense of hisopponent. By amplifying the stake of thetrial and thus the payoff of the litigatingparties, fee shifting helps the offerer. How-ever, legal expenditures rise with fee shifting,at least until the fee shifting becomes soextreme that the parties settle rather than

risk ruinous legal expenditures at trial. Ournumerical computation with a uniform distri-bution shows such event only occurs when� � 0.82, a rare level of fee shifting in real-ity. To balance the first mover advantage, wetake the average payoff of the two caseswhere each party has a chance to make theoffer. In that case, fee shifting functionsmuch like under the symmetric information�it penalizes the party with a weak case andsubsidizes the party with a strong case. How-ever, the difference lies in the fact that, forborder-line cases where P is around 0.5,both parties lose with the increased cost oflitigation.

The model has two undesirable features.First, the information available to the partiesat the time that settlement is discussedshould be endogenous. That the informationavailable prior to trial is not endogenous isdefensible on the grounds that discovery isan expensive process and that legal costs arealready sunk at the point that the partiesbegin to collect information. However, theassumption of two signals is clearly inade-quate to answer questions about the likeli-hood of settlement, as a separating equilib-rium will generally entail going to court whenboth parties perceive themselves to havestrong cases. Further refinement of the sig-nal space would permit an analysis of theeffect of fee shifting on the likelihood ofsettlement.

The second undesirable feature of themodel is the take-it-or-leave-it offer made bythe litigating parties, although a justification

� �of this assumption is provided by Spier 1992 .It would be preferable to have a more com-plicated model in which standing offers aremade by plaintiff and defendant as a func-tion of the information they have discoveredto date. The complexity of such a model isdaunting, and it would be reasonable, per-haps, to ignore the endogeneity of legal ex-penditures in a first attempt to solve such amodel, which is inconsistent with our goal ofcharacterizing the effect of fee shifting onthe pattern of settlement but of interest inits own right.

APPENDIX

( )Proof of Proposition 1 . The first-order condition un-Ž .der 1 yields that the pair of equilibrium trial efforts is

ECONOMIC INQUIRY234

governed by the following system of equations

Ž .A1E cd �2 PŽ .E � Ep d

21 E 1 1d� � c � �ž /ž /P E � E P 1 � Pp d

� 0

�E cp �2 1 � PŽ .E � Ep d

2E1 1 1p� � c � �ž /ž /1 � P E � E 1 � P Pp d

� 0.

A few manipulations should solve the above system.First, adding up the two equations and multiplying bothsided by E � E , we getp d

1 1Ž . Ž .1 � 1 � � c � E � Ep dž /P 1 � P

1 1Ž .� � c � E � E � 0.p dž /P 1 � P

1 Ž .Multiplying both sides by P 1 � P and arrangingcterms, we have one linear equation

Ž . � Ž .� Ž .A2 1 � 2� 1 � P E � 1 � 2� P Ep d

1Ž .� P 1 � P .

c

Ž .Moving second terms of the two equations in A1 tothe right-hand side and then dividing the first equation

Ž .of A1 by the second one, we have

1 2Ž .E � � c E � Ed p dP

1 12�� cE �d ž /P 1 � P

1 2Ž .� E � � c E � Ep p d1 � P

1 12�� cE �p ž /1 � P P

1 � P� .

P

Arranging terms gives

Ž .A31

Ž . � Ž . �P 1 � P PE � 1 � P Ed pc

2 2Ž . Ž . Ž .Ž .� � 1 � 2 P P E � 1 � P E .d p

Ž . Ž .Plugging A2 into A3 yields

2 2Ž . Ž .Ž .Ž . Ž . Ž .A4 1 � � 1 � P E � 1 � � P Ep d

Ž .� 2 P � 1 E E � 0.p d

Ž .Solving for the positive E in terms of E in A4 givesp danother linear equation

Ž .2 P � 1 � �'Ž .A5 E � E ,p dŽ .Ž .2 1 � � 1 � P

Ž .where � � 1 � 8� P 1 � P

2 Ž .� 4� P 1 � P .

Ž . Ž .Now A2 and A5 constitute a linear system of twoequations in two unknowns. Using the usual method of

Ž .substitution yields 2 .To show the necessary conditions are also sufficient,

Ž . Ž .2multiply �� E by a positive term E � E top p p dŽ .Ž .2 2Žobtain E � c�P 1 � � E � E � � cE 1�P �d p d d

.1�1 � P . This term is obviously decreasing in E , andpnegative if E is sufficiently large. Thus, eitherpŽ Ž . . Ž Ž . . �� E � 0 for all E where �� E E �0p p p p p p

Ž Ž . .� 0, or �� E � 0 at E � 0, and positive up top p psome point where it satisfies the first-order condition

Ž .and after which is negative. Thus, �� E can onlyp pchange signs from positive to negative, and eventuallynegative. A similar result holds for E . Therefore thedsolution to the first-order conditions is an equilibrium.

To show it is also the unique equilibrium, we alsoneed to check possible boundary solutions where Epand E might be zero. But first note that from first-orderdconditions only one of them can be zero. Now suppose

Ž .E � 0. From the cost function in 1 , we can see thatpthe defendant can spend a minimum amount, say E �d, where is a arbitrarily small positive number. But ifE � , E � 0 can not be an equilibrium strategy. Thisd pis because plugging E � 0 and E � back intop d

Ž . Ž . ŽŽ . Ž ..�� E gives 1� � c 1�P � � 1�1 � P ,p pwhich is always positive if � � 1, as is close to 0.Therefore, the plaintiff can increase profits by spendingmore. So it can not be an equilibrium. The same can be

Ž .said about E � 0 and E � . As a result, 2 is thed punique equilibrium.

Ž . Ž .Using lim � � 1�� 4P 1 � P , it is'� � 0Ž . Ž . �straightforward to verify 3 and 4 . Since E can ded

derived similarly, we only derive E� when � � 1. IfpP � 1�2,

Ž .P 1 � P 1 � 2 P � 1 � 2 P�lim E � � 0.p Ž .2c 2 P � 1 1 � 2 P��1


If P � 1�2,

Ž .P 1 � P 2 P � 1 � 1 � 2 P�lim E �p Ž .2c 2 P � 1 2 P � 1��1

Ž .P 1 � P� .

Ž .c 2 P � 1

If P � 1�2,

1� �1�2� Ž .Žlim E � lim P 1 � P 1 � �p 2cP�1�2 P�1�2

�1 �2 .� Ž .�2� P� �� 2 P � 1

1�1 �2�Ž .Ž� lim 1 � 2 P 1 � �

2c P�1�2

�1 �2 . Ž .Ž �3 �2�2� P� � P 1 � P �

�3 �2 .Ž 2 .Ž .� Ž .�� P� �4� � 2� 1 � 2 P � 2�

Ž . �1 �21 2� P 1 � P �� lim

2c 2�P�1�2

Ž . �1 �21 2� P 1 � P �� lim

2c 2�P�1�2

1� .

Ž .8c 1 � �

The second equality above used L’Hopital rule. E� andˆ p� Ž . Ž .E are derived, 6 follows naturally from 1 .d

( )Proof of Lemma 1 :

E� �� Ep dc � cž /�� P 1 � P

c�

Ž .2 2 P � 1

Ž .� � � 1 � 4� P 1 � P'�

�� 'c 1

�2Ž .2 2 P � 1 � � �'

1 �� 2 Ž .� � � � � � � � 2� P 1 � P'

2 ��

c 1�

2Ž .2 2 P � 1 � � �'� Ž . Ž .� � � � � � 4� 1 � �' '

Ž . � Ž .�4�P 1 � P 1 � 4� P 1 � P .

When P � 1�2, the lemma is true if the last term is notŽ .negative. But since � � 1, and � � 1 � 4� P 1 � P ,'

we thus have

Ž . Ž . Ž .� � � � � 4� 1 � � P 1 � P' '� Ž .�� 1 � 4� P 1 � P

� Ž .� � Ž . �� 1 � 4� P 1 � P 1 � 4� P 1 � P � �

Ž . Ž . � Ž .�� 4� 1 � � P 1 � P 1 � 4� P 1 � P

� 0.

When P � 1�2, using L’Hopital’s rule, we haveˆ

� Ž .Lim c � � � �' 'P�1�2

Ž . Ž .�4� 1 � � P 1 � P

� Ž .�4� 1 � 4� P 1 � P

2� Ž . �� 2 2 P � 1 � � �'�� 3

� Lim c 1 � �'½ ž /�P 2P�1�2

Ž . �Ž .�4� 1 � � 1 � 2 P

Ž Ž . Ž . Ž .�� 1 � 4� P 1 � P � 4� 1 � 2 P P 1 � P 522 Ž .Ž .� 2� 2� � � 6� 2 � � 2 P � 1 �' '� 4

� 0.

Q.E.D.

( ) Ž .Proof of Proposition 2 : We only to prove 8 . ByŽ .Envelope theorem, S� �

� Ž . � Ž .d� �1 d� �p d� �ž /2 d� d�

2 2� �Ž . Ž .Ec Ep d� �� E � E P 1 � Pp d

� �� Ž . Ž .�� E1 �E �� p pd d� �� 2 �E �� E ��d p

2 2� �Ž . Ž .Ec Ep d� �� E � E P 1 � Pp d

�� cE1 � cE �Epd d� Ž .� � � � �d�½2 �E 1 � P P ��d

� �� cE �E� cE p pd� Ž .� � � � �p��E 1 � P P ��p

2 2� �Ž . Ž .Ec Ep d� �� E � E P 1 � Pp d

� ��E1 c c �Ep d� � .2 P �� 1 � P ��

ECONOMIC INQUIRY236

Now the sign of the second part already depends on P,as shown in Lemma 1. The first part,

2 2� �Ž . Ž .Ec Ep d�� E � E P 1 � Pp d

2c 1

� � �E � E Ž .2� c 2 P � 1 �'p d

2Ž . Ž . � Ž .�� P 1 � P 1 � P � � 1 � 2� P'�2� Ž . ��P 1 � 2� 1 � P � �' 4

2c 1

� � �E � E Ž .2� c 2 P � 1 �'p d

Ž .Ž . �� P 1 � P 1 � 2 P � � 2 � � 1'2 Ž .��4� P 1 � P .

The first four terms of the above product are alwayspositive, but the last term is nonpositive. To see why,substituting the definition of �, it is sufficient to prove

2'Ž . Ž . Ž .1 � 4� P 1 � P 1 � 8� P 1 � P � 4� P 1 � P .

Since the left side is always positive because � � 1,Ž .squaring both sides of the inequality gives 4P 1 � P

1, which certainly holds for all P. Then the sign ofŽ .S� � is decided entirely by 1 � 2 P.

Q.E.D.

( )Proof of Lemma 2 : The cut-off value for the plaintiffis simply the expected equilibrium payoff at trail condi-tional on his signal and the plaintiff’s signal. SoŽ Ž .. Ž � Ž . � . Ž Ž ..S 1, S y � E � � � 0 1, y , and S 0, S y �p d p p dŽ � Ž . � .E � � � 0 0, y . Then the first part is proved follow-p

ing Table 1.Ž . Ž . Ž � Ž . � .Let u y � 1�3 E � � � 0 y, x � y �d d

Ž . Ž � Ž . � .2�3 E � � � 0 y, x � y denote the defendant’s ex-dpected payment at trial conditional on his signal being

�Ž .y. Let V �, denote the defendant’s expected payoff�when his signal is and he uses strategy *. Now suppose

Ž . Ž .S 1 � S 0 . Consider a type 0 defendant who usesd pŽ . Ž .S 1 instead of S 0 . Thend d

Ž Ž . .V S 1 , 0d

� Ž Ž . .� Ž .� 1 � Pr S 1 rejected S 1d d

Ž Ž . . Ž . Ž .�Pr S 1 rejected u 0 �S 0d d d

�Ž . Ž Ž .� 1�3 Pr S 1d

Ž Ž .. Ž . Ž Ž .� S 0, S 1 � 2�3 Pr S 1p d d

Ž Ž ..� � Ž . Ž .� Ž .� S 1, S 1 u 0 � S 0 � S 0p d d d d

�Ž . Ž Ž . Ž Ž ..� 1�3 Pr S 0 � S 1, S 0d p d

Ž . Ž Ž . Ž Ž ..�� 2�3 Pr S 0 � S 0, S 0d p d

� Ž . Ž .�� u 0 � S 0d d

� Ž Ž . .� Ž .� 1 � Pr S 0 rejected S 0d d

Ž Ž . . Ž .� Pr S 0 rejected u 0d d

Ž Ž . .� V S 0 , 0 ,d

which violates the definition of equilibrium strategywhen the defendant’s signal is 0. Note that the firstinequality follows from hypothesis. The second inequal-

Ž Ž .. Ž Ž ..ity holds because S 1, S 1 � S 0, S 1 �p d p dŽ Ž .. Ž Ž ..S 1, S 0 � S 0, S 0 following the first part of thep d p d

Ž . Ž .proof, and u 0 � S 0 , that is, the defendant neverd doffers anything higher than his expected payment attrial. Therefore, the defendant’s strategy must be atleast weakly increasing. But since we are consideringseparating equilibrium, it must further be strictly in-creasing.

Q.E.D.

( ) ( )Proof of Proposition 3 and 4 : First consider theŽ .defendant’s strategy of proposition 2 when his signal is

1. Given the belief of the plaintiff that anything higherthan the equilibrium offer from a strong defendantreveals that the defendant is weak, he could either offerŽ � Ž . � .E � � � 0 0, 0 � 1�10, which is only going to bep

Ž � Ž . � .accepted by the weak plaintiff, or E � � � 0 1, 1 �p3�5, which assures a settlement regardless of the plain-tiff’s signal. Now suppose 1�10 is offered. It has a 1�3probability of being accepted and 2�3 probability ofbeing rejected, resulting in an expected payment ofŽ .Ž . Ž . Ž � Ž . � .1�3 1�10 � 2�3 E � � � 0 1, 1 � 19�30, whichdis greater than 3�5. Thus, offering 3�5 to secure asettlement is the only optimal strategy for the defendantwhen his signal is 1. When the defendant receives 0, he

Ž � Ž . � . Ž � Žcould still offer E � � � 0 0, 0 � 1�10 or E � �p p. � .� 0 1,1 � 3�5. If he offers 1�10, his expected pay-

Ž .Ž . Ž . Ž � Ž . � .ment will be 2�3 1�10 � 1�3 E � � � 0 0, 1 �dŽ � Ž . � .3�10, which is less than E � � � 0 1, 1 � 3�5, thep

offer than can always secure a settlement. Therefore, we� Ž . Ž . 4have verified that S 0 � 1�10, S 1 � 3�5 is thed d

only optimal strategy for the defendant, given the beliefof the plaintiff. When these offers are made, the actualtype of the defendant is exactly the plaintiff’s belief,showing consistency with his cut-off strategy. The proof

Ž .of proposition 4.3 where the plaintiff makes the offeris similar, using exactly the same logic.

Q.E.D.

( ) Ž .Proof of Proposition 5 : According to proposition 3 ,the separating equilibrium essentially needs to satisfy aseries of inequalities. First there are the willingness tooffer and accept conditions:

Ž . Ž . Ž � Ž . � .A6 S 0 E � � 0, 0d d

Ž . Ž � Ž . � . Ž . Ž � Ž . � .A7 E � � 0, 0 S 0 E � � 0, 1 ,p d p

and

Ž . Ž � Ž . � . Ž .A8 E � � 1, 1 S 1p d

Ž . Ž � Ž . � . 1�3 E � � 0, 1d

Ž . Ž � Ž . � .� 2�3 E � � 1,1 .d

The incentive constraints require that

Ž . Ž . Ž . Ž . Ž � Ž . � .A9 1�3 S 0 � 2�3 E � � 1, 1d d

Ž � Ž . � .� E � � 1, 1p


and

Ž . Ž . Ž . Ž . Ž � Ž . � .A10 2�3 S 0 � 1�3 E � � 0, 1d d

Ž � Ž . � . E � � 1, 1 .p

Ž . Ž .By the nature of the equilibrium, A6 , A7 , and theŽ .first part of A8 automatically hold. Note that theŽ . Ž .second part of A8 is implied by A9 , which fortunately

holds for all � as Figure 8 shows. Figure 9 is a plot ofŽ .the right-hand side minus the left-hand side of A10 . It

is positive when � � 0.98. Finally we need to assure thatthe plaintiff’s expected payoff is positive at least for theweak type so that he is willing to file the lawsuit. That is,Ž . Ž . Ž . Ž .2�3 S 0 � 1�3 S 1 � 0. The numerical computa-d dtion shows that this inequality holds for all � less than0.82.

The proof of the second half is very similar. LetŽ . Ž .S 0 and S 1 denote the plaintiff’s offer when he getsp p

signal 0 and 1, respectively. We need to verify the rangeof � for which the following inequalities hold:

Ž . Ž . Ž � Ž . � .A11 S 0 � E � � 1, 1 ,p p

Ž . Ž � Ž . � . Ž . Ž � Ž . � .A12 E � � 1, 1 � S 1 � E � � 0, 1 ,d p d

FIGURE 8

FIGURE 9

Ž . Ž � Ž . � .A13 E � � 0, 0d

Ž . Ž . Ž � Ž . � .� S 0 � 1�3 E � � 0, 1p p

Ž . Ž � Ž . � .� 2�3 E � � 0, 0 ,p

Ž . Ž . Ž . Ž . Ž � Ž . � .A14 1�3 S 1 � 2�3 E � � 0, 0p p

Ž � Ž . � . E � � 0, 0 ,p

and

Ž . Ž . Ž . Ž . Ž � Ž . � .A15 2�3 S 1 � 1�3 E � � 0, 1p p

Ž � Ž . � .� E � � 0, 0 .d

Ž . Ž . Ž .A11 , A12 , and the first par of A13 are straightfor-ward, according to the definition of the equilibrium.Figure 10 plots the right-hand side minus the left-hand

Ž . Ž .side of A14 . Note that A14 also implies the secondŽ .part of A13 . A similar plot in Figure 11 shows that

Ž .A15 holds for almost all � except when it is very closeto 1.

Q.E.D.

FIGURE 10

FIGURE 11

ECONOMIC INQUIRY238

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