Pretrial Settlement wit Imperfect Private Monitoring Mostafa Beskar Indiana University Jee-Hyeong Park y Seoul National University April, 2016 Extremely Preliminary; Please Do Not Circulate. Abstract We model pretrial settlement bargaining in te WTO trade disputes as a signaling game wit nontransferable utility. In tis pretrial bargaining wit te DSB s judgement being subject to errors, a defendant government knows te probability of winning te DSB ruling by observing te realized contingency tat determines protection desirability, but a complainant government only receives an imperfect private signal of te contingency. A trut-telling equilibrium arises regardless of te accuracy of te complainant s private signal: te defendant never exaggerates its desirability for protection. Despite tis trut-telling beavior, te complainant assigns a positive probability for litigation (no settlement), wic decreases in its signal s accuracy but remains positive even wen te signal becomes almost perfect. Wen te accuracy of te complainant s signal improves, te defendant s take-it-or-leave-it tari combination o er decreases toward a Pareto e cient tari combination. Assistant Professor of Economics, Indiana University, mbeskar@indiana.edu y Professor of Economics, Seoul National University, j-park@snu.ac.kr 1
1 Introduction As a part of te post-world-war-ii international economic institutions, te General Agreement on Tari s and Trade (GATT), wic later became te World Trade Organization (WTO) in 1995, as facilitated its member countries negotiating multilateral trade liberalization and enforcing te negotiated trade agreements. In enforcing te commitments under te WTO, its dispute settlement procedure (DSP) plays a central role. Any member government may le a petition to te WTO s Dispute Settlement Body (DSB) against its trading partner s measures tat are suspected of voilating anticipated commitments under te WTO. Altoug te WTO s DSP underscores te rule of law by requiring unanimous voting of all member countries to overturn te recommendation of a tird-party panel (and possibly te report of te Appellate Body on te appealed recommendation of a panel), te WTO strongly empasizes settling disputes troug consultations among disputing parties. As stated in te WTO s o cial website, "..., te point is not to pass judgement. Te priority is to settle disputes, troug consultations if possible. By January 2008, only about 136 of te nearly 369 cases ad reaced te full panel process. Most of te rest ave eiter been noti ed as settled "out of court" or remain in a prolonged consultation pase - some since 1995." To understand te role tat pretrial settlement plays in enforcing trade agreements, we develop a simple model of pretrial bargaining in wic a defendant government proposes a take-it-or-leave-it tari combtination o er after observing te realized contingency tat determines te desirability of protection. In particular, we analyze te role of a complainant government s imperfect private signal about a potential violation by a defendant government in trade disputes. For example, te complainant government may le a petition to DSB of te WTO against te defending government s potential abuse of escape-clause protection, based on its exporting rms allegation tat te defendant government s import competing sector is not su ciently injured by imports to warrant suc protection. Te complainant govern- 2
ment s information about te potential abuse of escape-clause protection can be more accurate tan te judgment of a tird-party panel of te WTO because of its (exporting sectors ) repeated economic and political interactions wit te defendant country. Suc information, owever, is still imperfect and also private in te sense tat public disclosure of suc information can be igly costly to te exporting rms of te complainant country. 1 Our analysis of a pre-trial settlement game wit suc an imperfect private signal of a potential violation generates te following results, particularly about te consequence of improving te accuracy of te complaining government s signal on te likeliood of violations and terms of settlement. Surprisingly, a trut-telling equilibrium arises as te outcome of te game regardless of te accuracy of te complainant government s signal: te defendant government never exaggerates its desirability for protection as an attempt to abuse te escape-clause protection. Despite tis trut-telling beavior of te defendant government, te complainant government assigns a positive probability to its litigation (no settlement) against te denfendant government s claim for escape-clause protection (i.e., a tari combination o er tat signals suc claim). Wen its signal s accuracy improves, te litigation probability of te complainant government decreases but remains positive even wen te signal becomes almost perfect. In response to te improvement of te complainant government s signal, te defendant government s pretial tari combination o er decreases toward a Pareto e cient tari combination, in wic te complainant government is indi erent between litigation and settlement. "A literature review to be added." 1 It is easy to nd examples tat rms coose not to reveal teir private information even in te situation tat suc nondisclosure would lead to a costly consequence. For example, tere exist many U.S. antidumping cases in wic foreign companies under investigation decide not to provide private costs- and sales-related information despite te fact tat suc nondisclosure often leads to excessive dumping duties based on best information available. 3
2 Basic setup Te basic setup of our model of trade disputes and settlement is as follows. Tere are two countries, country C and country D, tat trade two products, x and y, on wic eac country may impose an import tari. Country D s government is subject to its import competing sector s pressure for protection, denoted by, wic can be eiter ig () or low (). Tis random domestic pressure for protection is te private information of country D s government (denoted by D, encefort), of wic te government of country C (denoted by C) receives an imperfect private signal, denoted by C, wic can be eiter ig () or low (). In addition to C and D, tere is a tird party, namely DSB of te WTO, tat may generate its ruling on a disputed case upon request. Te DSB ruling is an announcement of its yet anoter imperfect signal of D s domestic pressure for protection. As discussed later in more details, we introduce a minimum speci cation for te DSB ruling: we assume tat C and D can obtain iger expected payo s wit DSB tan te ones witout DSB given tat C as no information about D s contingency on its pressure for protection. 2 Te focus of our analysis is on te use of C s imperfect private signal against D s potential misrepresentation of its domestic pressure for protection before te DSB ruling. We model te pretrial settlement game as a signaling game in wic D signals its type (weter its domestic protection pressure is ig or low) by proposing a take-it-or-leave-it tari combination o er, wic 2 In te absence of C s signal of D s domestic pressure for protection, Beskar (fortcoming) caracterizes an optimal dispute settlement mecanism tat induces te governments to implement tari combinations tat maximize te ex-ante joint payo given te incentive constraint for trut-telling and te informational constraint of DSB. Suc an optimal dispute settlement mecanism enables te governments to obtain iger expected payo s tan te ones tat te governments can attain by temselves wit C aving no information about D s political pressure for protection. Wile our assumption allows a less-tan optimal dispute settlement mecanism, we do assume tat te DSB ruling and te resulting outcome of litigation neiter depend on te accuracy of C s private signal nor depend on te governments pretrial beaviors. 4
C can eiter accept (and settle) or litigate based on its imperfect private signal. 2.1 Markets Prior to analyzing te pretrial settlement game, we describe a simple and widely-used political-economy trade model, wic can generate te carateristics of governments payo functions tat we assume in our analysis. We assume competitive markets in wic countries gain from trade because of di erent costs of production. Te trade policy instrument at eac governments disposal is its import tari. We also assume, à la Baldwin (1987), tat eac government maximizes a weigted sum of its producers surplus (), consumers surplus ( ), and tari revenues (T ), possibly wit a iger weigt on te surplus of its import-competing sector. As demonstrated by Grossman and Helpman (1994), te iger weigt given to te import-competing sector may be te result of political pressure, troug lobbying for example, tat a government faces. Denoting te political weigt on te import-competing sector by 1, eac government s payo drawn from its import-competing sector, m, is given as follows: u (; ) m () + m () + T (), were, is te speci c tari on imports. Te eac government s payo from its export sector, x, is given by v (r) x (r) + x (r). were, r is te oter government s import tari. Finally, let W D (t; ) W D (; r; ) = u (; ) + v (r). 5
denote te total payo of D as a function of t (; r). Te total payo of C, W C (t; ), can be de ned in a similar manner. Private political socks To capture uctuations in political economy preferences, we assume tat is subject to random socks, i.e., te weigt tat D places on its importcompeting sector may cange over time. Formally, we assume tat is drawn from a binary set ;, suc tat = wit probability and = wit probability 1. For simplicity, we assume tat C s political pressure parameter for its import-competing sector is xed and equal to, tereby denotes only te contingency of D s domestic pressure for protection. 2.2 DSB s ruling We assume tat disputing parties could resort to te tird-party ruling by DSB if tey fail to reac a mutually accepted solution in te consultation stage. We treat te DSB ruling process, if used, as a black box tat will result in outcomes tat satisfy a set of conditions to be laid out below. Let T denote te set of Pareto e cient tari pairs and WL i () denote te expected payo of a government i = fd; Cg from litigation if te true state of te world is (of D). Moreover, de ne t min l ; t max l 2 T and t min ; tmax 2 T suc tat W D W D t min l ; W D L () ; W C (t max l ) W C L () ; t min ; W D L ; W C (t max ) W C L : We assume tat te DSB ruling satis es te following conditions: 1. C will strictly prefer an expected court ruling wen = to an expected 6
court DSB wen =. In oter words, W C L (l) > W C L, or t max l C t max : (1) 2. C of any type will strictly prefer an expected court ruling wen = to an expected DSB ruling wen =. In oter words, t min l t min l D t min ; (2) Dl t min : 3. Consider any incentive-compatible mecanism wit t() suc tat t() Dl t(); wic C and D can emply wit no DSB and no information of C. Te expected joint payo under litigation is greater tan te expected payo under any suc mecanism. Namely, (1 ) W C L () + W D L () + W C L () + W D L () > (1 ) W C (t()) + W D (t(); ) + W C (t()) + W D (t(); ) : (3) Moreover, we assume tat tere is joint surplus from settlement under = ; i.e., as well as under =, i.e., t min l t max l ^ t min l t max l ; (4) Dl C t min t max ^ t min t max : (5) D C Proposition 1 Conditions (1)-(5) imply te following preference ranking wit regard to te four extreme-value tari combinations associated wit te DSB ruling. 7
t min l t max l t min t max ; D D D t min l C t max l C t min C t max : Proof. To be added: [Sketc of te proof] We rst sow tat conditions 3-5 imply t max l t min ^ t max l Dl t min ^ t max l t min : D C Te remaining relationsips are directly implied from te oter conditions. 3 Pre-trial Settlement Game wit a Take-or- Leave-it O er Having te DSB ruling caracterized as in te preceding section, tis section analyzes te pretrial settlement game between C and D before te DSB ruling. Recall tat C receives a noisy private signal about D s domestic pressure for protection. Formally, C receives a signal, denoted by C, tat matces te true state of te world wit probability > 1; i.e., 2 Pr C = j = = Pr C = j = =. As discussed by Beskar (fortcoming), te disputing parties ave a collective incentive to settle witout resorting to DSB s ruling because te joint payo of te disputing parties is a concave function in t and te DSB ruling is uncertain. In addition to tis incentive to settle because of te concavity of te joint payo function, tere may exist an additional incentive for settle- 8
ment to avoid te transaction cost of litigation, wic may include attorney fees, cost of gatering information, etc. In order to igligt te e ect of uncertain DSB outcomes on te pattern of dispute settlement, we assume zero litigation cost and investigate weter C would invoke a formal dispute after observing certain tari -setting beaviors by D. In analyzing te pretrial settlement game, we consider te game in wic D makes a take-it-or-leave-it o er on tari s prior to te DSB ruling process. More speci cally, we study te following pretrial settlement game. Assume tat after te realization of te state of te world, D proposes a tari pair t = (; r). If C accepts tis proposal after observing its noisy signal of te state of te world, tere will be no litigation. Oterwise, te dispute escalates to te DSB, leading to te DSb outcome described in Section 2.2. Tis is a signaling game in wic D is te sender and C is te receiver. Te proposed tari pair, t, is D s signaling of its type (i.e., level of its domestic pressure for protection) and te treat of litigation is te cost associated wit tis signaling. We consider ybrid equilibria of tis signaling game, wic includes pooling and separating equilibria as special cases. On te one and, a ig-type D as a pure strategy of proposing t in te equilibrium. On te oter and, te strategy of a low-type D is to randomize between t l and t wit t l t. Let denote te probability tat a low-type D proposes t instead of t l. C s equilibrium strategy is to accept a settlement proposal wen t = t l, to reject t = t wit probability if C =, and to reject t = t wit probability if C =. ; ; ; t l ; t is a Perfect Bayesian Equilibrium (PBE) if and only if: 1. Wen =, (a) D prefers to settle at t l tan to litigate, i.e., W D (t l ; ) W D L () (6) 9
(b) if 2 (0; 1), D is indi erent between proposing t l and t, i.e., W D (t l ; ) = W D (t ; ; ; ) [ 1 W D (t ; ) + W D L ()] (7) + (1 ) [ 1 W D (t ; ) + W D L ()]; if = 1, W D (t l ; ) W D (t ; ; ; ), and if = 0, W D (t l ; ) W D (t ; ; ; ). 2. Wen =, D (weakly) prefers to settle at t tan to litigate, i.e., W D t ; W D L (): (8) 3. C (weakly) prefers settlement to litigation wen t l is proposed, i.e., W C (t l ) > W C L () : (9) 4. Wen D proposes t (a) and C = ; if 2 (0; 1), C is indi erent between litigation and settlement, i.e., W C (t ) = W C L ( C = ; ) Pr = j C = ; W C L () (10) + 1 Pr = j C = ; W C L (); if = 1, W C (t ) W C L (C = ; ); if = 0, W C (t ) W C L (C = ; ); 10
were Pr = j C = ; = (1 ) (1 ) + (1 ) : (b) and C = ; if 2 (0; 1), C is indi erent between litigation and settlement, i.e., W C (t ) = WL C ( C = ; ) Pr = j C = ; WL C (11) + 1 Pr = j C = ; WL C (); if = 1, W C (t ) W C L (C = ; ), and if = 0, W C (t ) W C L (C = ; ); were Pr = j C = ; = 5. 0 1, 0 1, 0 1. + (1 ) (1 ) : Lemma 1 Tere exists te following two types of mutually exclusive equilibria: Type I equilibrium wit te low-type C ( C = ) being indi erent between litigation and settlement, aving = 0 and 2 (0; 1]; Type II equilibrium wit te ig-type C ( C = ) being indi erent between litigation and settlement, aving 2 (0; 1] and = 1: Proof. "to be added." We can rule out = = 0 and = = 1 from equilibrium values of our interest. If = = 0, te low-type D will always o er t (tus, = 1), generating a pooling equilibrium, strictly dominated by an equilibrium wit 11
an informative DSB ruling. If = = 1, ten it will be identical to te litigation case wit no information of C. Tus, we can focus on te two types of equilibrium speci ed in Lemma 1. 3.1 Divine PBE As in oter signaling games, tere exists multiple Perfect Bayesian equilibria tat satisfy te above conditions 1-5. As re nement, we use te solution concept of "divine equilibrum," developed by Banks and Sobel (1987): De nition 2 "to be added." By applying tis equilibrium concept, we can sow te following lemmas about te divine PBE of te signal game speci ed above: Lemma 2 Te divine PBE value of t l is t max l uniquely determined by Proof. "to be added." W C (t max l ) = WL C () and t max l 2 T : Given Lemma 2, now we need to caracterize divine PBE values of ; ; ; t max l ; t tat depend on te value of : Lemma 3 Te only divine PBE, ; ; ; t max l ; t, is te one tat maximizes te expected payo of te ig-type D. Proof. A complete proof to be added: Let ; ; ; t max l ; t denote te PBE under wic te expected welfare of te ig-type D is te igest among all PBE. Now consider a PBE, ; ; ; t max l ; t 6= ; ; ; t max l ; t To prove tis lemma, we need to sow tat a PBE wit ; ; ; t max l ; t does not satisfy te divinity criterion, but ; ; ; t max l ; t does. : 12
To sow tat ; ; ; t max l ; t does not satisfy te divinity criterion, we rst sow tat D(l; ; t )[ D (l; ; t ) D(; ; t );tus, (t ) = fg: Because te expected payo of te ig-type D under ; ; ; t max l ; t is strictly lower tan its expected payo under ; ; ; t max l ; t by de nition: < (1 )(1 ) + (1 ) W D (t ; ) + (1 ) + WL D () i i (1 )(1 ) + (1 ) W D (t ; ) + (1 ) + WL D (); ( = ; = ) tat satis es i (1 = )(1 ) + (1 = ) W D (t ; ) + = (1 i ) + = WL D () = (1 )(1 ) + (1 ) W D (t ; ) + (1 ) + W D L () is greater tan ( ; ) wit W D (t ; ) > W D L (). Tis implies tat D (; ; t ) = f( = ; = )g and D(; ; t ) = f(; ) j 0 < = and 0 < = wit at least one of te weak inequalities olds wit a strong inequalityg: Because te expected payo of te low-type D under expected payo under ; ; ; t max l ; t : ; ; ; t max l ; t is identical its = (1 ) + (1 )(1 ) W D (t ; l) + + (1 ) WL D (l) i i (1 ) + (1 )(1 ) W D (t ; l) + + (1 ) WL D (l) = W D (t max l ; l); ( = ; = ) tat satis es i (1 = ) + (1 ) W D (t ; l) + = WL D (l) = (1 ) + (1 ) W D (t ; l) + W D L (l) is identical to ( ; ): Tis implies tat D (l; ; t ) = f( ; )g and D(l; ; t ) = f(; ) j 0 < and 0 < wit at least one of te weak inequal- 13
ities olds wit a strong inequalityg: Terefore, D (l; ; t ) [ D(l; ; t ) = f j 0 < and 0 < g D(; ; t ) = f(; ) j 0 < = and 0 < = wit at least one of te weak inequalities olds wit a strong inequalityg wit ( ; ) < ( = ; = ): Tis implies tat (t ) = fg: If te deviation message from ; ; ; t max l ; t is t, ten te receiver (C) would believe tat suc a deviation is done by a ig-type D by te divinity criterion. Given tis belief te optimal action of C is settlement ( = 0 and = 0), aving and min (1 ) + (1 )(1 ) W D (t ; l) + + (1 ) W D (;)2A ( (t );t ) L (l) = W D (t ; l) > W D (t max l ; l); min (1 )(1 ) + (1 ) W D (t ; ) + (1 ) + W D (;)2A ( (t );t ) L () i i = W D (t ; ) > (1 )(1 ) + (1 ) W D (t ; ) + (1 ) + WL D () > (1 )(1 ) + (1 ) W D (t ; ) + (1 ) + W D L (): Tus, a PBE wit ; ; ; t max l ; t does not satisfy te divinity criterion. On te oter and, te equilibrium ; ; ; t max l ; t satis es te divinity criterion. To see tis, consider a situation were D proposes an o equilibrium tari pair t 0 6= t were t= 2 T c : Let (= ; = ) denote (; ) tat togeter wit t = constitutes a PBE. By de nition of t we know tat te expected payo of te ig type D under (t = ; = ; = ) is strictly lower tan its expected payo under t ; ;. Neverteless, te low-type D is indi erent between (t = ; = ; = ) and t ; ; : Terefore, due to te continuity of D s expected payo wit respect to (; ) and t ; tere must exist ( == ; == ) > ( = ; = ) for wic te low-type D strictly prefers te deviation outcome, (t = ; == ; == ); to te equilibrium, t ; ; ; wile te 14
ig-type D is strictly worse o by te deviation. Terefore, D(; ; t = )[ D (; ; t = ) D(l; ; t= );tus, (t = ) = flg: Tis means tat wen a deviation from te equilibrium ; ; ; t max l ; t is observed, C would tink tat suc a deviation is carried out by a low-type D. Given tis belief, te optimal action of C is litigation ( = 1 and = 1), aving and min (1 ) + (1 )(1 ) W D (t 0 ; l) + + (1 ) W D (;)2A ( (t 0 );t0 ) L (l) = WL D (l) < W D (t max l ; l); min (1 )(1 ) + (1 ) W D (t 0 ; ) + (1 ) + W D (;)2A ( (t 0 );t0 ) L () i i = WL D () < (1 )(1 ) + (1 ) W D (t ; ) + (1 ) + WL D (): Terefore, a PBE wit ; ; ; t max l ; t does satisfy te divinity criterion. Note tat te above proof focuses on te PBE in wic > 0 so tat te low-type D is indi erent between o ering t max l te PBE in wic = 0, tus t = t max. and o ering t : Now, consider Note tat Lemma 2 and 3 come from te assumption tat D makes a take-it-or-leave-it o er on tari s prior to te DSB ruling process, wic in turn provide D wit all te bargaining power in te pretrial settlement game. 3.2 Caracterization of Divine PBE Proposition 3 For all values of 2 [0:5; 1), te divine PBE entails a truttelling equilibrium wit = 0, aving t belong to ft j W C (t) = W C (t max ) WL C g and (; ) be de ned by te following 15
LD condition tat makes a low-type D be indi erent between t max l and t W D (t max l ; ) = + (1 ) W D L () + (1 )(1 )W D (t ; ) ; were 2 (0; 1) implies = 0; and 2 (0; 1) implies = 1: Proof. "to be added" Figure 1 can grapically demonstrate te above proposition. According to Proposition 3, te divine PBE is on C s indi erence curve, on wic C is indi erent between litigation and settlement given tat D s type is ig wit W C (t) = W C L. Tese tari combinations de ne te settlement o ers tat are least favorable to C among te potentially acceptable o ers: C would be willing to accept suc tari combination o ers if C knows tat D is under a ig domestic pressure for protection. Also note tat a igtype D s indi erence curve wit W D t; = WL D () in Figure 1 de nes te settlement o ers tat are least favorable to a ig-type D. Tus, te equilibrium settlement o er must entail a tari combination tat belongs to te oval-saped area in-between tese two extreme-value indi erence curves. Tere is anoter indi erence curve tat is important in caracterizing te divine PBE in Figure 1: a low-type D s indi erence curve, on wic it is indi erent between revealing its type by o ering t max l and exaggerating its domestic pressure for protection by o ering t wit W D (t; ) = W D (t max l ; ) : If te settlement o er is on tis indi erence curve, ten a low-type D would be indi erent between t max l and t (even) wen = = 0: te only values of and tat satisfy te LD condition in Proposition 1 are zero wen t is on tis indi erence curve. For a given value of 2 [0:5; 1), note tat te tari combinations on a low-type D s iger indi erent curve wit W D (t; ) > W D (t max l ; ) uniquely de nes and wit a positive probability of litigation troug te LD condition. Also note tat te iger a low-type D s indi erence curve is, te iger te probability tat C assigns for litigation. 16
Now, consider te problem of coosing a settlement o er (t ) tat maximizes te expected payo of a ig-type D (te criterion for divine PBE) among tari combinations on a low-type D s indi erence curve wit W D (t; ) = W D (t max l ; ). Because = = 0 for any settlement o er on tis indi erence curve, a ig-type D simply needs to coose t tat maximizes W D t;. Also note tat te indi erence curve of a ig-type D always cuts te indi erence curve of a low-type D from below, wic in turn implies tat t tat maximizes W D t; on te low-type D s indi erence curve wit W D (t; ) = W D (t max l ; ) is t O max as any tari o er tat goes beyond tis will be rejected (tus litigated) by C. Tis proves tat only t O max on te C s indifference curve wit W C (t) = WL C is a possible candidate for a divine PBE for te case wit = = 0: For any oter values of and, tere exists a corresponding indi erence curve of a low-type D tat satis es te LD condition. Given tese speci c values for and, once again, one simply needs to coose t tat maximizes W D t; on te corresponding indi erence curve to nd t tat maximizes te expected payo of a ig-type D. On suc a corresponding indi erence curve, t tat maximizes W D t; is te one tat intersects wit te C s indi erence curve wit W C (t) = WL C : Tis proves tat te divine PBE is on C s indi erence curve wit W C (t) = WL C. W C L Given tat te divine PBE is on C s indi erence curve wit W C (t) =, it is easy understand wy te divine PBE entails a trut-telling equilibrium wit = 0: If aving > 0 wit a settlement o er being on C s indi erence curve wit W C (t) = WL C litigating over settling., will make C strictly prefer Proposition 4 D s settlement o er, t, declines toward a more e cient one as C s signal improves wit t! t max as! 1: Proof. "to be added" To understand te above proposition, one needs to know te trade-o tat a ig-type D faces wen it coose t on C s indi erence curve wit 17
W C (t) = WL C. As D s settlement o er, t, declines toward t max along C s indi erence curve wit W C (t) = WL C, te settlement payo for a igtype D, W D t ;, strictly increases. However, a lower tari combination on tis C s indi erence curve also implies a iger probability of litigation wit a iger value for eiter or, tat is determined by te LD condition in Proposition 3. To maximize te expected payo of a ig-type D, tus one needs to balance te bene t of lowering te settlement tari o er toward t max against te cost of raising te probability of litigation associated wit lowering te tari combination o er. As C s signal improves wit a iger value for ; te probability of litigation associated wit any tari combination o er decreases, canging te above mentioned trade-o in favor of lowering te settlement tari o er furter toward t max. Proposition 5 Te divine PBE entails only a type I equilibrium wit = 0 and 2 (0; 1) for > I wit: I = [W D (t max ; ) W D (t max l ; )]=[W D (t max ; ) WL D ()] < 1; were te last inequality comes from W D (t max l ; ) > W D L () : Proof. "to be added" Figure 2 grapically illustrates te above proposition. On te vertical axis of Figure 2, we ave t on C s indi erence curve wit W C (t) = WL C wit a sligt abuse of te notation t : altoug t is (; r) instead of being a variable wit a single value, bot and r moves in te same direction along te C s indi erence curve wit W C (t) = WL C. Tis enable us to represent a cange in t by a cange in a single variable, for example, suc as a corresponding cange in in t = (; r): On te orizontal axis, we ave te accuracy of C imperfect private signal,. Altoug Figure 2 sows for te values from 0 to 1, te only relevant range of is [0:5; 1): Eac LD curve in Figure 2 corresponds to a speci c value pair of and, wit a lower LD curve being associated wit a iger probability of litigation. 18
Also note tat eac LD curve decreases in, implying tat a lower settlement tari o er is compatible wit a iger value for, keeping a low-type D to be indi erent between o ering t and o ering t max l : For > I, only a type I equilibrium wit = 0 and 2 (0; 1) is possible for t tat is greater tan t max, as sown in Figure 2. Corollary 6 Even wen C s private signal is almost accurate wit! 1, te probability tat C assigns for litigation remains strictly positive wit = max > 0. 4 Conclusion "to be added." 19
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Pre-trial settlement: Domain of t. r W C ( t) W C L ( θ) W C ( t max ) O max r min r max r max r l W D ( t; θ) W D ( t max ; θ) l max t l max t W O max t D D ( t; θ) W ( θ) β β L 0 β 0 & β 0 W D ( t; θ) W D ( t max ; θ) l t T θ t T θ max τl min τ max τ Figure1 O max τ τ
t t Omax LD ; =0, =0) t max LD ; min (0,1), =0)) LD ; =1, max (0,1)) LD ; =1, =0) LD ; =1, >0) 0 1/2 I 1 Figure 2