Pretrial Settlement with Imperfect Private Monitoring


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1 Pretrial Settlement wit Imperfect Private Monitoring Mostafa Beskar University of New Hampsire JeeHyeong Park y Seoul National University July 2011 Incomplete, Do Not Circulate Abstract We model pretrial settlement bargaining in te World Trade Organization as a signaling game wit nontransferable utility in wic te defending country knows te likeliood of winning in te court and te complaining country receives only an imperfect signal about te likeliood of te court outcome. We study te consequences of improving te accuracy of te complaining party s private signal on te likeliood and terms of settlement. Among oter results, we nd tat wen private signal is not accurate enoug, an increase in te quality of private signal increases te likeliood of a dispute. 1 Introduction As a major part of te postworldwarii international economic institutions, te World Trade Organization (WTO) as facilitated its member countries Assistant Professor of Economics and Peter Paul Researc Fellow, University of New Hampsire, y Professor of Economics, Seoul National University, 1
2 negotiations for multilateral trade liberalization and te enforcement of te negotiated trade agreements. As a part of its rule enforcement system, te WTO s dispute settlement procedure plays a central role in te multilateral trading system. Wile te WTO s dispute resolution procedure underscores te rule of law by requiring unanimous voting of te WTO member countries to overturn its nal ruling, 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 settlements play in enforcing trade agreements, we develop a simple model of pretrail settlement bargaining. In particular, we introduces an imperfect private signal of a complaining party regarding a potential violation of a defending party into trade disputes. For example, a complaining party may le a petition to te WTO against a defending party s abuse of te escape clause protection, based on its exporting rms allegation tat te defending party s import competing sector s economic situation is not bad enoug to warrant suc protection. Wile te complaining party s information about potential abuse of te escape clause protection can be more accurate tan te judgment of a tird party panel of te WTO due to its closer acquaintance wit te defending party, suc information would still be imperfect and also private in te sense tat public disclosure of suc information can be very costly to te rms of te complaining party. 1 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 salesrelated information despite te fact tat suc nondisclosure often leads to excessive dumping duties based on best information available. 2
3 Te analysis of te pretrial settlement game generates some interesting results. We study te consequences of improving te accuracy of te complaining party s private signal on te likeliood and terms of settlement. Among oter results, we nd tat wen private signal is not accurate enoug, an increase in te quality of private signal increases te likeliood of a dispute. Wile an increase in te quality of private signal would eventually decreases te likeliood of a dispute, te possibility of obtaining pretrial settlement can be seriously treatened wen te quality of private signal becomes iger tan a critical level, especially wen te pretrial consultation possibility among disputing parties is severely limited. A literature review to be added. 2 Basic setup Te basic setup of our model of trade disputes and settlements can be summarized 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,. Eac country s government is subject to its import competing sector s random political pressure for protection, denoted by, wic can be eiter ig () or low (). Tis random domestic pressure for protection is eac government s private information, of wic te oter government receives 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 Dispute Settlement Body (DSB) of te WTO, tat may generate its ruling on a disputed case upon request. DSB s ruling is announcement of its yet anoter imperfect signal of te political pressure for protection. Wile DSB as no coercive power of forcing a defending government to adopt a speci c level of import tari based on its ruling, DSB can allow a complaining government to impose a certain level of retaliatory tari against te defendant government s deviation 3
4 from its ruling. In te absence of eac government s imperfect private signal of te oter government s domestic pressure for protection, Beskar (2010a) caracterizes an optimal dispute settlement mecanism tat induces governments to implement tari combinations tat maximize exante payo s given te incentive constraint for truttelling and te informational constraint of DSB. In te following analysis, we assume tat governments will employ suc an optimal dispute settlement mecanism once tey fail to reac a pretrial settlement. In contrast to Beskar (2010a), our analysis allows a complaining government to receive a signal of a defendant government s potential misrepresentation of its domestic political pressure for protection. Suc a signal can be more accurate tan DSB s signal because trading partners repeated trade relationsip is likely to generate better understanding of eac oter tan a tird party may possess. Despite suc an informational advantage of a complaining government in detecting potential deviation from a trade agreement, utilizing suc information in dispute settlement procedure may face some serious incentive problems as te complaining government may misrepresent its private signal in te procedure. Te focus of our analysis is, tus, on te use of a complaining government s private signal against potential misrepresentation of a defendant government s political pressure for protection, prior to te DSB s ruling. First, we will model te pretrial settlement game as a signaling game in wic a defendant government signals its type (weter it is facing a ig political pressure for protection or a low one) by proposing a speci c tari combination and a complaining government can eiter accept te defendant s tari o er or litigate it, based on its private signal. Suc modeling of te pretrial settlement game is counterfactual as te WTO dispute settlement procedure requires te defendant governments to consult te complaining government potentially for a negotiated pretrial settlement. We plan to analyze te pretrial settlement game wit te pretrial consultation requirement in place, 4
5 comparing te settlement outcomes wit and witout pretrial consultation. Prior to analyzing te pretrial settlement game, we describe a simple and widely used politicaleconomy trade model tat we use, largely replicating te corresponding sections of Beskar (2010a). 2.1 Markets We assume competitive markets wit linear demand and supply functions in wic countries gain from trade due to di erent costs of production. Te trade policy instrument at te governments disposal is import tari s. We also assumed, a la Baldwin (1987), tat eac government maximizes a weigted sum of its producers surplus (), consumers surplus ( ), and tari revenues (T ), wit a relatively iger weigt on te surplus of its importcompeting sector. As demonstrated by Grossman and Helpman (1994), te iger weigt given to te welfare of a sector may be te result of political pressure, troug lobbying for example, tat a government faces. Denoting te political weigt on te welfare of te importcompeting sector by 1, eac government s welfare drawn from its importable sector, m, is given by u (; ) m () + m () + T (), were, is te speci c tari imposed on imports. Te eac government s welfare from its exportable sector, x, is given by v (r) x (r) + x (r). were, r is te foreign country s import tari. Finally, let W D (; r; ) = u (; )+v (r) denote te political welfare of country D s government (denoted by D from now on) as a function of ome and foreign tari s. Te welfare of country C s government (denoted by C from now on), W C (r; ; ), can be de ned in a similar fasion. 5
6 Private political socks To capture uctuations in political economy preferences, we assume tat is subject to random socks, i.e., te weigt tat te ome government gives to te welfare of its importable sector may cange over time. Formally, we assume tat is drawn from a binary set ;, suc tat = wit probability and = wit probability 1. On te oter and, we assume tat te foreign government s political pressure parameter for its importable sector, x, is xed and equal to. Te Role of te DSB Following Beskar (2010b), we assume tat te DSB is an impartial entity tat receives a noisy signal, 2 denoted by DSB, about te state of te world in te defending country and announces tis signal publicly. we assume tat tis signal matces te true state of te world, i.e., by DSB, wit probability 1; namely: 2 Pr ( DSB = j = ) = Pr DSB = j = =. It is important to note tat assuming an informational role for te DSB does not imply any informational advantage on bealf of te DSB over te disputing parties. Te advantage of te DSB over te disputing parties is its impartiality, wic makes its public announcements about its privately observed signal reliable. 2.2 Optimal Dispute Settlement Mecanism wit DSB s ruling Prior to analyzing te pretrial settlement game between C and D in te following section, we describe te optimal settlement mecanism under te auspices of te DSB, and te resulting expected payo s, caracterized by Beskar (2010a). We assume tat te DSB is an impartial entity tat receives 2 Tis signal may be generated troug investigations, court earings, etc. 6
7 a noisy signal (troug investigations or court earings) about te state of te world in te defending country and announces tis signal publicly. Formally, te DSB receives a signal of political pressure, denoted by DSB, tat matces te true state of te world wit probability > 1; i.e., 2 Pr ( DSB = j = ) = Pr DSB = j = =. Now, we consider te problem of designing an incentivecompatible direct revelation mecanism tat maximizes expected joint welfare of te parties. Te sequence of events is as follows: 1. C requests te DSB to generate its ruling on te disputed case, after failing to reac a pretrial settlement wit D. 2. Parties commit to a mecanism. 3. DSB receives a noisy signal, denoted by DSB, about te political pressure in country D and announces it publicly. 4. D makes an announcement, denoted by d, about its political pressure. 5. Te mecanism determines te tari pair (; r) to be adopted by te parties. Prior to DSB s ruling, D would ave already made an announcement of facing a ig political pressure. After te DSB s ruling of a low political pressure, owever, D is allowed to cange its initial position and follow te DSB s ruling for te case of low political pressure, witout incurring any penalty for canging its position. Tus, putting D s announcement after DSB s announcement in te sequence of events does make sense. Te optimal solution is summarized by two entries, namely, ( d ; DSB ) and r ( d ; DSB ) : Tere are four incentive compatibility constraints tat must be satis ed. First, suppose tat D is facing a ig political pressure and te DSB as also observed a signal of ig political pressure, i.e., DSB =. D will report its type trutfully if and only if: W D ; ; r ; ; W D ; ; r ; ; : (1) 7
8 If te true state of te world is =, but te DSB s signal sows a ig political pressure, D will ave te incentive to report a low political pressure if and only if: W D ; ; r ; ; W D ; ; r ; ; : (2) Te remaining two incentive compatibility constraints are for situations were te DSB receives a signal of low political pressure. If tis signal matces te true state of te world, ten te incentive compatibility constraint is given by W D ( (; ) ; r (; ) ; ) W D ; ; r ; ; : (3) Finally, if te DSB s signal of low political pressure di ers from te true state of te world, D as te incentive to report its ig political pressure trutfully if and only if W D ; ; r ; ; W D (; ) ; r (; ) ; : (4) Te expected joint welfare of te governments, wic will be used as to measure te mecanism s performance, can be introduced as follows. 3 First, consider a situation were D is under ig political pressure. Wit probability, te DSB observes a signal of ig political pressure and wit probability 1, te DSB observes a lowpressure signal. Tus, given ig political pressure in te ome country, te expected joint welfare is W D ; ; r ; ; + W C r ; ; ; ; + (1 ) W D ; ; r ; ; + W C r ; ; ; ; : Now consider te case were D is facing low political pressure. Te DSB s 3 Given our focus on countries tat are ex ante symmetric, it is plausible to consider te expected joint welfare as te measure of te mecanism s performance. 8
9 signal in tis case will be a low political pressure wit probability, and a ig political pressure wit probability 1 welfare under low political pressure is. Terefore te expected joint W D ( (; ) ; r (; ) ; ) + W C (r (; ) ; (; ) ; ) + (1 ) W D ; ; r ; ; + W C r ; ; ; ; : Te rst case above, i.e., a ig political pressure, is realized wit probability and te second case occurs wit probability 1. Tus, ex ante, tat is, before te realization of te state of te world, te expected joint welfare of te governments is given by W D ; ; r ; ; + W C r ; ; ; ; + (1 ) W D ; ; r ; ; + W C r ; ; ; ; + (1 ) (1 ) W D ; ; r ; ; + W C r ; ; ; ; + (1 ) W D ( (; ) ; r (; ) ; ) + W C (r (; ) ; (; ) ; ) : (5) Te problem of designing a direct revelation bargaining mecanism will be to maximize (5) subject to incentive compatibility constraints (1 4). 4 In tis gure, points A and A 0 represent te rstbest tari pairs under low and ig political pressures, respectively. Te circular curves centered around A (A 0 ) are te joint political welfare contours wen political pressure at ome is low (ig). Te optimal solution can be demonstrated by four tari pairs, namely, L, L 0, H, and H 0, depicted in Figure (1). Te curves going troug HH 0 and LL 0 are two isowelfare contours of D under low political pressure. If DSB =, ten te equilibrium tari pair is eiter H or H 0, depending on D s true state of te world. Under low political pressure, D will be indif 4 Altoug not modeled explicitly, it is assumed tat te entire mecanism introduced in tis paper is sustainable troug repeated interactions between te parties. In oter words, parties ave te incentive to respect te rules of negotiations (suc as limiting retaliations to wat is speci ed by te mecanism) in order to guarantee a sustainable relationsip in te long run. Interested readers are referred to Beskar (2010b) and Park (2011) for te study of te DSB in a repeated game setting. 9
10 Figure 1: Equilibrium of te DSBassisted bargaining game (L, L 0, H, and H 0 ). ferent between H and H 0, and we assume tat it will coose H to maximize te joint welfare of te governments. Under ig pressure, owever, D will be strictly better o at H 0 tan H, so it will announce a ig political pressure and H 0 will be te outcome of te bargaining game. If te DSB observes a low pressure signal, i.e., DSB =, ten te equilibrium tari pair is eiter L or L 0. Similar to te previous case, D is indi erent between L and L 0 wen it faces low political pressure and we assume it will coose L so tat te joint welfare is maximized. Moreover, if D faces ig pressure, it will be strictly better o by announcing a ig pressure tat results in adopting tari pair L 0. Te DSB s announcements can be interpreted as aving a framing effect on renegotiations. If te DSB rules in favor of D by stating tat D is facing ig political pressure, te subsequent bargaining game between te governments is to mutually agree on eiter H or H 0. In contrast, if te DSB announces a low political pressure in D, te governments bargain over L and L 0. Loosely speaking, D will ave te upper and in renegotiations if te DSB issues an opinion favorable to te defendant. Similarly, if te DSB s 10
11 opinion is against D, C will be in a better bargaining position. As DSB s signal becomes more accurate, tat is wen becomes closer to 1, H H 0 will sift to te rigt and down and L L 0 will sift to te left and up. Tat is because as te DSB becomes more accurate in observing te true state of te world, te cost of making a wrong judgment becomes less of a concern and te DSB can be more aggressive in its rulings in favor or against te ome country. In te extreme case of = 1, L will coincide wit A, wile H 0 will coincide wit A 0, meaning tat bargaining results in te rstbest outcome. For a given value of, an increase in moves bot H H 0 and L L 0 to te rigt and down. Te sift of L L 0 to te rigt and down re ects te fact tat wen a ig pressure is more likely, te DSB wants to reduce te cost of wrong rulings wen te true pressure is ig. Moreover, H H 0 sifts in te same direction because te probability of low pressure is now smaller and te expected cost of a wrong judgment wen a ig pressure signal is observed is reduced. Wen = 1; tere will be no asymmetric information and A 0, H 0, and L 0 will coincide. According to te direct mecanism caracterized above, D as to coose one of te two tari pairs tat are recommended by te DSB. In practice, owever, te DSB cannot restrict D s coice of import tari s. Te DSB can only determine C s permissible retaliatory tari given D s tari. 5 In te ligt of tis real world observation, Beskar (2010a) consider a mecanism in wic D s tari coice is not restricted, but te DSB can impose a cap on te maximum level of retaliation by C. As sown by Beskar (2010a), owever, tis alternative mecanism generates te same secondbest outcome caracterized above. Given te above caracterization te optimal dispute settlement meca 5 Here we can plausibly assume tat te complaining party will not retaliate beyond te level tat is permitted by te court. Tat is because any incentive to adopt extralegal retaliation can be eliminated by autorizing more protection in te original defending country along te appropriate tari pair menus. 11
12 nism wit DSB s ruling, te expected payo s from invoking te DSB ruling process conditional on a realized value of political pressure are given by W D L () = W D ; ; r ; ; + (1 )W D ; ; r ; ; ; W D L () = W D ( (; ) ; r (; ) ; ) + (1 )W D ; ; r ; ; ; W C L () = W C r ; ; ; ; + (1 )W C r ; ; ; ; ; WL C() = W C (r (; ) ; (; ) ; ) + (1 )W C r ; ; ; ; ; (6) were WL i () denotes i s expected payo from invoking DSB ruling process conditional on D s political pressure is, wit (; ) and r (; ) being de ned as te optimal solutions of te above direct mecanism. 3 Pretrial Settlement Game wit a Takeor Leaveit O er Having te dispute settlement mecanism wit te DSB s ruling caracterized as in te preceding section, tis section analyzes te pretrial settlement game between C and D prior to invoking te DSB ruling process. Recall tat C receives a noisy private signal about te political pressure for protection of D. Formally, C receives a signal, denoted by C, tat matces te true state of te world wit probability C > 1; i.e., 2 Pr C = j = = Pr C = j = = C. re ecting a potential informational advantage of C as a trading partner of D, we allow te possibility of C >. As discussed by Beskar (2010a), te disputing parties ave a collective incentive to nd a settlement witout resorting to DSB s ruling since te joint welfare of te disputing parties is a concave function and te DSB rulings are uncertain. Tis incentive to settle is in addition to te desire to avoid 12
13 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 outcome on te pattern of dispute settlement, we assume zero litigation costs and investigate weter C would invoke a formal dispute after observing any positive level of violation by D. In analyzing te pretrial settlement game, we consider te game in wic D makes one takeorleaveit 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), were denotes D s tari in te political sector and r denotes C s retaliatory tari. After observing its noisy signal of D s state of te world, If C accepts tis proposal, tere will be no litigation. Oterwise, te dispute escalates to te DSB and te game will continue as described in Section 2.4. Tis is a signaling game in wic D is te sender and C is te receiver. Te proposed tari pair, t, will be understood as a signal of D s type (i.e., level of political pressure) and te treat of litigation is te cost tat is associated wit tis signal. Te following is te list of new notations tat will be employed in te analysis of tis signaling game: W C (t) : C s welfare under tari pair t: W D (t; ) : D s welfare under tari pair t and political pressure. P : Set of Pareto e cient tari s wen political pressure is 2 ; : We consider ybrid equilibria of tis signaling game, wic include pooling and separating equilibria as special cases. In a ybrid equilibrium, a igtype D as a pure strategy in te equilibrium, wic we denote by t. On te oter and, te strategy of a lowtype D is to randomize between t l and t wit t l t. Let denote te probability tat a lowtype D proposes t instead of t l. C s equilibrium strategy will be 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 =. 13
14 t l ; t ; ; ; is a Perfect Bayesian Equilibrium 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 () (7) (b) if 2 (0; 1), D is indi erent between proposing t l and t, i.e., W D (t l ; ) = W D (t ; ; ; ) C [ 1 W D (t ; ) + W D L ()] (8) + 1 C [ 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 (): (9) 3. C (weakly) prefers settlement to litigation wen t l is proposed, i.e., W C (t l ) > W C L () : (10) 4. Wen D proposes t (a) and C = ; if 2 (0; 1), C is indi erent between settlement and litigation, 14
15 i.e., W C (t ) = W C L ( C = ; ) Pr = j C = ; W C L () (11) + 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 = ; ); were Pr = j C = ; = C (1 ) (1 ) C + (1 C ) : (b) and C = ; if 2 (0; 1), C is indi erent between settlement and litigation, i.e., W C (t ) = WL C ( C = ; ) Pr = j C = ; WL C (12) + 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 = ; = , 0 1, 0 1. C C + (1 ) (1 C ) : 15
16 3.1 Equilibrium conditions In addition to te above conditions 15 for a Perfect Bayesian Equilibrium, we require two additional conditions tat a reasonable equilibrium sould satisfy. Condition 1 Wen = and D decides to reveal its type trutfully, it will propose t l to maximize its payo subject to conditions 7 and 10. Tis maximization problem as a unique solution, wic makes C indifferent between settlement and litigation (see Lemma 2 of Beskar (2010)). Terefore, te equilibrium value of t l, denoted by t max l by Condition 2 Given proposing t 0 6= t for settlement. W C (t max l ) = WL C () and t max l 2 P : is uniquely determined ; ;, a igtype D cannot increase its payo by Lemma 1 Condition 2 rules out equilibria in wic > 0 and t > t min, wit t min being de ned by W D t min ; = WL D and t min 2 P : Proof. On te contrary, assume tat > 0. Tis means tat wen C =, C is indi erent between settlement and litigation given t and. Now suppose tat D proposes t " for settlement. Tis proposal induces te igtype C to strictly prefer settlement to litigation. On te oter and, if t > t min te igtype D is better o by making tis proposal for su ciently small ". Formally, te igtype D is better o under te new proposal if and only if C W D L + 1 W D t ; + 1 C W D L < C W D t "; + 1 X W D L ; or W D t ; W D t "; < W D t ; W D L : 16
17 Te RHS of tis condition is positive for > 0 and t > t min. Te LHS, on te oter and, will be arbitrarily close to zero for "! 0. Terefore, a strategy pro le in wic > 0 and t > t min is not an equilibrium. Lemma 2 Condition 2 rules out equilibria in wic < 1 and t = t min. Proof. On te contrary, suppose tat < 1 and t = t min. < 1 implies tat a lowtype C is indi erent between settlement and litigation, wic in turn implies tat a igtype C strictly prefers settlement and = 1. De ne t ; X as te level of t tat makes igtype C indi erent between settlement and litigation given and X. Condition 2 requires tat X W M ; + 1 X WL M + 1 W M t min ; t min X W M t ; X ; + 1 X W M L : Noting tat W M t min ; = W M L ; tis inequality can be written as wic is not satis ed. QED. X W M t ; X ; W M t min ; 0; Lemma 3 Condition 2 rules out equilibria in wic < 1 and t > t min. Proof. Higtype D s payo under t ; ; < 1; = 0 : C W D t ; + 1 C W D L + 1 W D t ; If D proposes t ", lowtype C will settle as well. Terefore, for (t ; ; < 1; = 0) to be an equilibrium, igtype D sould be worse o by tis proposal C W D t ; + 1 C W D L + 1 W D t ; W D t "; 17
18 or C + 1 C 1 W D t ; + 1 C W D L W D t "; or 1 C W D t ; W D L W D t ; W D t "; : Te RHS of tis inequality is arbitrarily close to zero as "! 0. Tus, tis condition is satis ed only if te LHS is zero, i.e., eiter = 0 or t = t min. Terefore, since in equilibrium we ave > 0, < 1 implies tat t = t min. Lemma 4 In equilibrium, = 1 for all C. Proof. Given tat in te equilibrium we must ave t t min, tis lemma follows directly from te previous two lemmas. 3.2 Equilibrium Properties 1. Lowtype D indi erent between proposing t l and t : (a) If > 0 ten t = t min, and lowtypedindi erence requires: W D (t max l ; ) = C W D L ()+ 1 C W D L () + 1 W D t min ; ; or = W D t min ; W D (t max l ; ) C (1 C ) [W D (t min ; ) W L D ()] (1 C ) (13a) 18
19 On te oter and, igtypecindi erence requires W C t min C = C + (1 ) (1 C ) W L C (1 ) 1 C + C + (1 ) (1 C ) W L C () ; or = Tus, 1 imply tat C (1 ) (1 C ) WL C W C t min W C (t min ) W C L () : (14) and > 0 implies C C 2 1 : (15) 1 + W L C () W C (t min ) W C (t min ) WL C() C < C 1 W D t min ; W D (t max l ; ) W D (t min ; ) W D L () : (16) (b) If = 0; lowtypedindi erence requires: W D (t max l ; ) = C W D L () + 1 C W D (t ; ) ; (17) and igtypecindi erence requires W C (t ) = C C + (1 ) (1 C ) W L C (18) (1 ) 1 C + C + (1 ) (1 C ) W L C () : or = C W C (t ) WL C (1 ) (1 C ) WL C () W C (t ) : (19) For tis to be equilibrium property we need to ave t min 19 t
20 t max, wit t max being de ned by W C (t max ) = WL C and t max 2 P. Tis requires W D t min ; W D (t max l ; ) W D (t min ; ) W L D () C 1 C W D (tmax ; ) W D (t max l ; ) W D (t max ; ) WL D () (20) Also we must ave 1, wic requires C 1 : 1 + W L C () W C (t ) W C (t ) WL C() Given tat C = W D (t ;) W D (t max l ;) W D (t, a necessary and su cient ;) WL D() condition for te last inequality to satisfy is W D (t ; ) W D (t max l ; ) W D (t ; ) WL D () 1 : (21) 1 + W L C () W C (t ) W C (t ) WL C() Tis condition imposes restriction on te coice of t. Tis pro le ( = 0 and lowdindi erent) is an equilibrium if and only if tere is t 2 t min; tmax tat satis es 21 and C 1 C W D (t max ;) W D (t max l ;). W D (t max ;) WL D() 2. Lowtype D prefers proposing t to proposing t l : tis implies = 1 and requires W D (t max l ; ) < C W D L () + 1 C W D L () + 1 W D (t ; ) (a) If > 0 ten t = t min and we must ave W D (t max l ; ) < C WL D ()+ 1 C WL D () + 1 W D t min ; 20
21 (b) If = 0 : W D (t max l ; ) < C W D L () + 1 C W D t ; C ; ; were, igtypecindi erence requires W C (t ) = 3.3 Equilibrium analysis C C + (1 ) (1 C ) W L C (1 ) 1 C + C + (1 ) (1 C ) W L C () ; Rewriting equation 18 for = 1 yields te following relationsip tat we call CC: W C (t ) = C C + (1 ) (1 C ) W L C (1 ) 1 C + C + (1 ) (1 C ) W L C () ; Moreover, call equation 17 te DD relationsip: C 1 (22) W D (t max l ; ) = C W D L () + 1 C W D (t ; ) : (23) Figure 2 depicts CC and DD relationsips grapically, for te case were < C 2. In bot CC and DD relationsips, t is an increasing function of C. Moreover, for any C < 1, te CC curve lies below t = t max and for any t t max te DD curve is to te left of C = 1. Terefore, CC and DD ave eiter no intersection or tere is an even number of intersections. Tis grap sows a case were CC and DD intersect at two points. Tis generates 6 regions of C to be considered for te equilibrium. 1. C < C 1 < C 2 : > 0, t = t min and < 1:Equilibrium conditions for strategy pro le 1.a. above is satis ed. Terefore, is given by 13a and is given by C 1 < C < C 3, ten = 0, < 1, and t is given by te DD curve. 21
22 Figure 2: Equilibrium for Di erent Values of C 22
23 3. C 3 < C < C 4, ten = 1, = 0 and t is given by te CC curve. 4. C 4 < C < C 5, ten 0 < < 1, = 0 and t is given by te DD curve. 5. C 5 < C < 1, tere exists no Perfect Bayesian Equilibrium tat satis es Condition 1 and 2. Proposition 1 For C < min C 1 ; C 2, we ave t = t min in te equilibrium. For min C 1 ; C 2 C C 5, te equilibrium value of t is given by te upperenvelope of te CC and DD curves. For C > C 5, tere is no Perfect Bayesian Equilibrium tat satis es Condition 1 and 2 for te pretrial settlement game. For C < C 2, note tat < 1: On te contrary, assume tat = 1. Ten, igtype C will prefer litigation over settlement if C < C 2, implying = 1, wic in turn implies = 0, tus leading to contradiction. For C < C 1 ;note tat 2 (0; 1) requires > 0 because W D (t max l ; ) < W D (t min ; ; = 1; = 0) wit C < C 1. Tus, C < min C 1 ; C 2 is a su cient condition for strategy pro le 1.a to be te equilibrium strategy pro le. For min C 1 ; C 2 C C 5 ; note tat t is taking te maximum value among possible Perfect Bayesian Equilibrium values of t, an outcome tat is favorable to D. Tis re ects tat D is te rstmover wo makes a takeorleaveit o er on tari s, extracting all te bene t generated by improvement in C s information (iger C ). Te last result in te above proposition is probably te most surprising one: wen te private information of C gets accurate enoug, players may suddenly face a serious problem in obtaining pretrial settlement. Tis problem comes from D s inability of o ering tari s combination wit wic it can avoid playing a complete separating equilibrium strategy of = 0: Wen C s information gets accurate enoug so tat C > C 5, ten lowtype D will strictly prefer o ering t l = t max l 23 over t t max because of te
24 ig likeliood of facing litigation wit C > C 5 (and = 1). If lowtype D indeed plays = 0, ten D s o ering of t > t max l implies tat D is igtype wit probability 1. Tis will induce C to settle wit any t < t max because W C (t < t max ) > WL C, aving = = 0, wic in turn makes = 1 an optimal coice for D. One potential way to avoid tis problem is tat igtype D o ers t = t max (wit = 0), making C indi erent between litigation and settlement (i.e., W C (t max ) = WL C ) so tat = 1 and = 0 can be an equilibrium strategy for C. However, igtype D would not set t = t max wit = 1 and = 0 because it can increase its payo by o ering t = t max ", inducing C to settle wit probability 1. Anoter potential way to avoid no pretrial settlement is tat lowtype D o ers t l < t max l so tat lowtype D becomes indi erent between o ering t l (< t max l ) and t t max even wit C > C 5, tus avoiding playing = 0. Once again, owever, lowtype D would not set t l < t max l because lowtype D can increase its payo by o ering t l = t max l and getting settlement wit W C (t max l ) = WL C (). Te reason for aving no pretrial settlement equilibrium result is similar to te reason for te wellknown antifolk teorem result under imperfect private monitoring, originally sown by Matsusima (1991): "te repetition of te onesot equilibrium is te only reasonable supergame equilibrium, even toug eac player can almost perfectly monitor te oter players coices." Tis antifolk teorem result of Matsusima (1991) comes from its focus on te pure strategy Nas equilibrium: if players play a pure strategy cooperative equilibrium, ten tey will ignore teir imperfect private signals tat indicates potential deviations from te cooperative equilibrium and avoid invoking punisment tat is costly for players, wic in turn would induce players to deviate from te cooperative equilibrium. Recall tat a similar issue arises in te pretrial settlement game for C > C 5 : if lowtype D plays = 0, ten D s o ering of t implies tat D is igtype, inducing C to settle wit any t < t max, aving = = 0, wic in turn makes = 1 an optimal coice for D. 24
25 Tere exists a di erence between te antifolk teorem result of Matsusima (1991) and tis paper s no pretrial settlement equilibrium result: te latter result only arises wen te private signal gets accurate enoug wile te former result arises under any imperfect private monitoring. Note tat no pretrial settlement equilibrium result does not arise for C C 5 because D can o ering tari s combination wit wic it can avoid playing a complete separating equilibrium strategy of = 0. 4 Conclusion to be added. References Baldwin, R. (1987). Politically Realistic Objective Functions and Trade Policy: PROFs and Tari s. Economic Letters 24, Beskar, M. (2010a). TirdPartyAssisted Renegotiation of Trade Agreements. Working Paper. Beskar, M. (2010b). Trade Skirmises and Safeguards: A Teory of te WTO Dispute Settlement Process. Journal of International Economics 82 (1), Grossman, G. and E. Helpman (1994). Protection for Sale. Te American Economic Review 84(4), Matsusima, H. (1991). On te teory of repeated games wit private information* 1:: Part i: antifolk teorem witout communication. Economics Letters 35 (3), Park, J.H. (2011). Enforcing International Trade Agreements wit Imperfect Private Monitoring. Review of Economic Studies 78(3),
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