THE LAW AND ECONOMICS

Transcription

1 THE LAW AND ECONOMICS OF LITIGATION Bruce H. Kobayashi, George Mason University School of Law George Mason University Law and Economics Research Paper Series This paper is available on the Social Science Research Network at

2 The Law and Economics of Litigation Bruce H. Kobayashi Professor of Law George Mason Law School REVISED June 15, 2015 I. Introduction This chapter examines the basic model of the law and economics of litigation. Because the Rules of Civil Procedure and the Economics of the Litigation/Settlement decision are covered in separate chapters of this volume, this chapter will focus on private civil litigation, in particular the litigation value of a lawsuit and the incentives generated for filing a suit. The chapter begins with the simple one- stage single plaintiff/single defendant investment model of litigation, and sets out the conditions for filing, default, settlement, and litigation. The analysis then examines the effects of litigation cost and fee- shifting as well as the effects of percentage contingency fee arrangements within the standard one- stage model. The model is then modified to take into account sequencing and option value. We show how litigation with multiple stages and the revelation of information alter the investment value of litigation, as well as the effects of litigation reform proposals such as fee- shifting. Finally, the chapter discusses third party or external effects. We examine how these additional complications affect the outcome of litigation, the viability of a lawsuit and the predictions of the standard model of litigation. This chapter is not intended to be a comprehensive overview of economic analyses of litigation and civil procedure (See Cooter & Rubinfeld (1989), Kobayashi & Parker (2000), Spier (2007)). Rather, this aim of this chapter is to set out the basic mechanics of the law and economics of private civil litigation, and examine how a more robust examination of sequential decision- making in litigation alters some of the basic predictions of the simple model. II. The Basic One Stage Model of Litigation A. One-Stage Models and NEV Suits a. Litigation Payoffs in a Single Stage Model We begin the analysis with the standard one- stage expected value model of litigation (Landes (1971), Gould (1973)). In this model, a risk neutral plaintiff (P) has a claim against a risk neutral defendant (D). The plaintiff estimates that the suit will result in a favorable judgment with probability pp. When judgment is entered

3 for the plaintiff, the defendant is ordered to pay the plaintiff an amount J. The plaintiff s cost of litigating a case to judgment equals CP. 1 The standard model assumes that the plaintiff seeks to maximize the payoff at trial TP equal to the expected judgment net of litigation costs: (1) T! = p! J C! The risk neutral defendant (D) estimates that the probability of a judgment for the plaintiff equals pd, and seeks to minimize his exposure at trial TD equal to the expected judgment plus litigation costs CD: 2 (2) T! = p! J + C! b. The NEV/PEV Threshold In the standard model of litigation, the condition that a suit has positive expected value (PEV) is used as a threshold condition for filing a lawsuit: 3 (3) T! > 0, or p! > p! =!!! Use of the NEV/PEV threshold as a threshold condition for filing a lawsuit requires some additional assumptions about the structure of litigation. Figure 1 illustrates a simple structure that is consistent with use of the NEV/PEV threshold as a filing threshold. In the figure, the plaintiff offers a settlement S, which is either accepted or rejected by the defendant. If the offer is rejected, the plaintiff then must 1 In this chapter, the costs of litigation are assumed to be exogenous. Thus we abstract away from the issue of endogenous litigation expenditures, including signaling and screening models based on litigation expenditures. For a recent in depth review of this literature, see Spier (2007). 2 The defendant is better off paying the judgment (or defaulting) rather than litigating if: T! > J, or p! > p! = 1!!. However, under the simple structure assumed in Figure 1, default is not an option.! For a discussion of the strategic use of default, see Hunter (). 3 One U.S. Appellate Court suggested use of the NEV condition to determine whether a patent lawsuit could be subject to the sham exception to Noerr Pennington antitrust immunity, thus subjecting the filing of a lawsuit to scrutiny under the U.S. antitrust laws. Posner, writing for the Seventh Circuit, would deny immunity for the pursuit of valid but negative expected value claim: But we are not prepared to rule that the difficulty of distinguishing lawful from unlawful purpose in litigation between competitors is so acute that such litigation can never be considered an actionable restraint of trade, provided it has some, though perhaps only threadbare, basis in law. Many claims not wholly groundless would never be sued on for their own sake; the stakes, discounted by the probability of winning, would be too low to repay the investment in litigation (emphasis added) Grip-Pak Inc. v. Illinois Tool Works., 694 F.2d 466 (1982), cert denied, 461 U.S. 958 (1983), overruled by Professional Real Estate Investors, Inc., v. Columbia Pictures 113 S.Ct (1993) 2

4 choose to file and litigate the case to judgment, or drop the case. The payoff to file and litigate is higher than the payoff from dropping the case when TP > 0. Thus, with the simple structure of litigation illustrated in Figure 1, and under the assumptions that: (i) the plaintiff is maximizing the expected judgment net of litigation costs; and (ii) all costs are incurred simultaneously at the trial stage, the plaintiff will rationally choose to file PEV claims, and will not file NEV claims. 4 Plain&ff(Offers( S( Defendant( Rejects(Offer( Defendant( Accepts(Offer( (S,7S)( Plain&ff( Li&gates( ((T P,(T D )( Plain&ff(Does( not(file( (0,0)( Figure 1 The Structure of Litigation Simple One- Stage Model c. Litigation and Settlement The expected litigation payoffs determine the litigants threat points at settlement. That is, the plaintiff s litigation payoff determines the minimum acceptable settlement, and the defendant s litigation exposure determines the maximum he will offer. Thus, the any feasible settlement S will satisfy: (4) T! S T! The absence of a feasible settlement is a sufficient but not necessary condition for litigation, and occurs when: (5) T! > T!, or p! p! > (!!!!! ), or! p! > p! + (!!!!! ).! 4 See, e.g., Bone (2003), Chapter 1, at 34. The effects of altering the structure of litigation are examined below. 3

5 Condition (5) is known as the optimism condition for litigation, as the plaintiff s estimate of the probability of a judgment for the plaintiff, p!, must be greater than the defendant s estimate of the same probability, p!. p P $ 1" 0.9" Li.gated$ 0.8" 0.7" Se2led$ 0.6" 0.5" p P *$ 0.4" 0.3" 0.2" NEV$ $Not$Filed$ 0.1" 0" 0" 0.1" 0.2" 0.3" 0.4" 0.5" 0.6" 0.7" 0.8" 0.9" 1" p D $ Figure 2 Filing, Litigation and Settlement Low- Stakes (200K) Figure 2 depicts in pp, pd space the conditions that give rise to cases being filed, defaulted, settled, and litigated. 5 In the figure, J = 200K, and CP = CD = 70K. Along the 45 degree line are cases in which the two sides agree on the probability of a judgment for the plaintiff. For these cases, a mutually beneficial settlement exists, as condition (4) is never satisfied. The absence of a bargaining range requires an optimistic difference p! p! >.7. Thus, condition (4) is satisfied when the parties divergent and optimistic expectations lie in the Litigated triangle in the upper left hand corner of Figure 2. The NEV/PEV threshold occurs at pp * =.35. p P $ 1" 0.9" 0.8" 0.7" Li.gated$ 0.6" 0.5" Se2led$ 0.4" 0.3" p P *$ 0.2" 0.1" NEV$ $Not$Filed$ 0" 0" 0.1" 0.2" 0.3" 0.4" 0.5" 0.6" 0.7" 0.8" 0.9" 1" p D $ 5 This useful diagram was introduced by Gelbach (2014) to examine the selection of cases for litigation. 4

6 Figure 3 Filing, Litigation and Settlement High- Stakes (600K) The optimism model of litigation predicts that higher stakes relative to costs increase both the probability a suit will be filed and the probability that filed suits will be litigated. Figure 3 shows the conditions when the size of the judgment J is tripled to 600K, holding all of the other parameters constant. The higher stakes relative to costs of litigation increases the expected value of the suit, and shifts the NEV/PEV threshold to pp * = The higher stakes also moves the litigation/settlement line toward the 45- degree line, increasing the set of cases that will be litigated due to the absence of a bargaining range relative to the low- stakes case. B. Effect of Fee Shifting The standard model of litigation assumes that each side bears its own costs and fees. However, the award of costs and/or fees to the prevailing party is provided for in numerous statutes, and is a popular litigation reform proposal. This section examines the effects of fee shifting on the incentives of the parties to file, litigate and settle. 6 a. Two Way Fee and Cost Shifting Use of a system of loser pays or a two way cost and fee shifting system is a popular litigation reform proposal. The basic intuition for its use is that use of a loser pays system raises (lowers) the expected cost of litigation to parties whose probability of prevailing is less than (greater than).5. Thus, use of such cost and fee shifting systems are designed to deter the filing of lawsuits with low probabilities of obtaining a judgment, and to encourage lawsuits with high probabilities of obtaining a judgment (Shavell (1982), Polinsky & Rubinfeld (1998)). To see this, note that under two way cost and fee shifting: (1 ) T! = p! J (1 p! )(C! + C! ) Comparing (1 ) to (1), the expected judgment is unaffected, and the plaintiff s expected litigation costs are greater under two- way fee and cost shifting when (1 p! )(C! + C! ) > C!, or when p! <!!!!!!!. If litigation costs are symmetric, so that C! = C!, the plaintiff s expected litigation costs rise (fall) for p! < >. 5. The NEV/PEV threshold increases, and is given by: (1 *) p! > p! =!!!!!!!!!!!! 6 Other analyses have examined the effect of fee shifting on broader measures of activity, such as compliance with legal standards. See, e.g., Hylton (1993). 5

7 Similarly, the defendant s litigation exposure under two- way fee and cost shifting is: (2 ) T! = p! (J + C! + C! ) Comparing (2 ) and (2), the defendant s expected litigation costs are greater under two- way fee and cost shifting when p! <!!!!!!!. If litigation costs are symmetric, two- way fee and cost shifting increases (decreases) the expected litigation costs of the defendant when pd >.5. Finally, the litigation settlement condition is given by: (5 ) p! p! > (!!!!! ) (!!!!!!! ), or p! > p! + (!!!!! ) (!!!!!!! ) Comparing (5 ) to (5), the effect of two- way fee and cost shifting effectively increases the stakes relative to the costs of litigation. Specifically, with two- way cost and fee shifting, the effective stakes for the litigants now includes both the judgment J and the sum of the parties litigation costs. Figure 4 shows the effect of two- way fee and cost shifting using the same parameters as Figure 2. Because the expected litigation costs are increased for suits where pp <.5, two way cost- and fee shifting increases pp * to.411 and expands the set of cases that result in NEV suits. Under the assumption that NEV suits will not be filed, two way fee shifting will reduce the number of suits filed. However, two- way fee shifting increase the set of filed cases that are litigated. Similar to the effect depicted in Figure 3, the increase in the effective stakes shifts the litigation settlement line toward the 45- degree line resulting in an expanded set of cases that result in litigation due to the absence of a bargaining range. 6

8 p P $ 1" 0.9" 0.8" Li0gated$ 0.7" 0.6" Se.led$ 0.5" p P *$ 0.4" 0.3" 0.2" NEV$ $Not$Filed$ 0.1" 0" 0" 0.1" 0.2" 0.3" 0.4" 0.5" 0.6" 0.7" 0.8" 0.9" 1" p D $ Figure 4 The Effect of Two- Way Cost and Fee- Shifting b. One-Way and Rule 68 Many existing fee- shifting statutes operate asymmetrically. For example, the antitrust laws 7 and civil rights 8 laws feature statutory fee shifting that shift fees and costs to prevailing plaintiffs. In contrast to the proposals for two- way fee shifting, which are intended to deter low probability lawsuits, the intended effect of one- way fee shifting to prevailing plaintiffs is to yield stronger incentives for plaintiffs and their lawyers to file lawsuits with low net value. Ironically, even fee shifting systems designed as two- way cost and fee shifting systems may operate as de facto one- way systems because of systematic wealth constraints, and encourage rather than discourage plaintiffs on the margin. 9 Thus, rather than operating as designed as a mechanism to deter low value lawsuits, the actual effect may be to serve as a litigation subsidy. Under one- way cost and fee- shifting, the litigation payoffs are: (1 ) T! = p! J (1 p! )C! (2 ) T! = p! (J + C! ) + C! 7 15 U.S.C. 15(a) USC 1988(b), Hensley v. Eckerhart, 461 U.S. 424 (interpreting 42 USC 1988(b) as creating a presumption in favor of awarding fees to a prevailing plaintiff, but as not allowing a prevailing defendant to get his attorneys fees reimbursed unless the suit was frivolous); 42 U.S.C. 2000(k). 9 See Snyder & Hughes (1990, 1995) examining the use of two way fee and cost shifting for Florida medical malpractice claims between 1980 and Shepherd (2010) examines a broader set of fee shifting and offer of judgment policies in Florida over a longer time period. 7

9 p P $ 1" 0.9" 0.8" Li0gated$ 0.7" 0.6" Se.led$ 0.5" 0.4" p P *$ 0.3" 0.2" 0.1" NEV$ $Not$Filed$ 0" 0" 0.1" 0.2" 0.3" 0.4" 0.5" 0.6" 0.7" 0.8" 0.9" 1" p D $ Figure 5 The Effect of One- Way Fee Shifting Figure 5 illustrates the effect of one- way cost and fee- shifting in favor of prevailing plaintiffs, under the parameters set out in Figure 1. The NEV/PEV threshold probability is given by: (3 ) p! =!!!!!! Unsurprisingly, given the goals of one- way cost and fee shifting, the pro- plaintiff one- way cost and fee shifting lowers the NEV threshold and induces litigation on the margin. One- way cost and fee- shifting also expands the set of litigated claims, but not as much as two- way cost and fee- shifting. In the latter case, the effective states were equal to the judgment plus both litigants costs and fees. In the case of one way cost and fee shifting, the litigants now face effective stakes equal to the judgment plus the plaintiff s costs and fees. The litigation/settlement threshold is given by: (5 ) p! > p! + (!!!!! ) (!!!! ) It is also possible to have one- way or asymmetric cost or fee- shifting rules that benefit defendants. One example is Federal Rule of Civil Procedure 68. This rule shifts the defendant s post- offer costs when the defendant makes a Rule 68 offer of judgment, and the judgment for the plaintiff that is less favorable than the rejected offer. Notably, Rule 68 shifts only post- offer costs, and is designed as a mechanism to encourage settlement rather than as a simple litigation tax/subsidy (But see Miller (1986)). Thus pre- offer costs and pre and post offer attorney s fees 8

10 are not shifted through the rule. 10 Moreover, it applies only when the party favored by the cost- shifting rule (the defendant) loses. 11 C. The Effect of Contingency Fees The standard model of litigation can be modified to address the use of legal professionals and the generation of lawyer- client agency costs (Miller (1967)). For example, suppose the plaintiff hires a lawyer using a standard contingency fee arrangement with a contingency percentage α =.3. Under such an arrangement, the lawyer bears the costs of litigation, and is given 30% of any judgment or settlement as compensation. The client keeps the remaining 70% of any judgment or settlement. The litigation payoff for the defendant is unchanged. The litigation payoffs for the contingent plaintiff and his lawyer are given by: (1cc) T! = (1 α)p! J (1cl) T!" = αp! J C! Under the assumption that the lawyer bears all of the costs of litigation (including the opportunity cost of his time), the NEV/PEV thresholds for the lawyer and client are: (3cc) p! = 0 (3cl) p!" =!!!" Under the assumption that the client does not bear any of the costs of litigation, the client will rationally pursue all suits. However, because the contingent lawyer only receives 30% of any judgment or settlement, his threshold for agreeing to represent a client is higher than the NEV/PEV threshold of a vertically integrated client/lawyer. 10 Under Federal Rule of Civil Procedure 54(d), costs other than attorneys fees shall be allowed as of course to the prevailing party unless the court otherwise directs. Thus, the costs, which are often a small fraction of litigation costs, follow the English Rule in U.S. Federal civil litigation. Attorneys fees are distinct from costs under the rule. For an example of the interplay between Rule 68 and one-way fee shifting statutes that shift costs including attorneys fees to prevailing plaintiffs, see Marek v. Chesny, 720 F.2d 474 (1985), Rev'd 473 U.S. 1 (1985). 11 Delta Airlines v. August, 450 U.S. 346 (1981) (finding that Rule 68 offer was not triggered when defendant prevailed). 9

11 p P % 1" 0.9" 0.8" Con$ngent( Lawyer(Li$ga$on/ Se1lement( Threshold( 0.7" 0.6" 0.5" Con$ngent(Client( Li$ga$on/ Se1lement( Threshold( p CL *% 0.4" 0.3" 0.2" 0.1" p P *=%0% 0" 0" 0.1" 0.2" 0.3" 0.4" 0.5" 0.6" 0.7" 0.8" 0.9" 1" p D % Figure 6 The Effect of a Contingency Fee Arrangement High Stakes Note that when J = 200K, the lawsuit is an NEV suit for the contingent lawyer even when recovery is certain. Under these conditions, the lawyer will recover 60K, but must spend 70K to obtain the judgment. Figure 6 shows the effect of a standard percentage contingency contract on the incentives to file and litigate a lawsuit. Because the conditions depicted in Figure 2 will generate a corner solution for the lawyer, we use the underlying parameters from Figure 3 (i.e., where J = 600K) to illustrate the effects of contingency contracts. While contingent clients will rationally pursue all cases where recovery is possible, contingent lawyers will only represent clients when pcl * >.39. (Miceli (1994)). There is also a divergence in the lawyer s and client s decisions to litigate or settle the case. The litigation and settlement condition for the contingent client and the contingent lawyer are given by: (5cc) p! > p! + (!!)! (5cl) p! > p! + (!!/!!!! )! The contingent client does not bear the marginal costs of litigating, and it therefore more willing to choose to litigate rather than settle. Likewise, the contingent lawyer bears the marginal costs of litigation, yet only received a fraction (α) of the marginal benefits from litigating. This creates an agency cost with respect to the decision to settle (Miller (1986)). Because the model in this chapter treats lawyer effort and litigation expenditures as exogenous, the model does not address lawyer- client agency costs 10

12 involving the level of lawyer effort. For analyses of this aspect of the problem, see Smith and Cox (1985), Hay (1997), Polinsky & Rubinfeld (2003), Wickelgren (2004). III. Multistage Models A. Effect on the Decision to File Symmetric Costs and Credible NEV Suits In this section, changes to the structure of litigation and their effect on the predictions/implications of the one- stage model of litigation are considered. These models will show conditions under which a plaintiff will choose to rationally file a lawsuit that has negative expected value if litigated to judgment. The analysis focuses on the incentives of private litigants in multistage litigation and does not examine broader issues relating to the broader effects of litigation or the divergence between the private and social value of litigation (Kaplow (2014)). We begin by altering the simple one- stage model to include multiple stages. To begin the analysis, consider the case of a negative expected value suit, where E(J) = 100, and CP = CD = 210. Under the simple litigation structure set out in Figure 1, the threat to litigate such a case is not credible (Nalebuff). The plaintiff will not rationally choose to litigate the case, as such a decision will result in a loss of - 110k compared to the decision to drop and not file the case, which results in a net payoff of zero. The defendant, anticipating that the plaintiff will not file the case, will reject any offer of settlement S made at the outset. The payoffs for this example are illustrated in Figure 7. Plain&ff(Offers( (S(=100( P=0,(D=0( Defendant( Rejects(Offer( P=0,(D=0( Defendant( Accepts(Offer( P=100,(D=>100( Plain&ff(Files(&( Li&gates(Case( P(=>110,(D=>310( Plain&ff(Does(Not( File( P=0,(D=(0( Figure 7 One- Stage Negative Value Lawsuit However, the simple litigation structure illustrated in Figure 1 and Figure 7 is highly unrealistic. Litigation proceeds in a series of sequential stages, and the costs of litigation are incurred at each stage. Suppose that one alters the litigation 11

13 structure so that the litigation proceeds in three, equal cost stages, allowing the plaintiff to offer settlements before each stage (Bebchuk (1996)). Everything else is unchanged. Thus the expected judgment E(J) = 100K, and each of the three stages costs each side 70K, for a three stage total of 210K. If the case is litigated to judgment, the payoffs are identical to those in the one- stage game depicted in Figure 7. Figure 8 depicts this slightly more complex litigation structure. In contrast to the predictions of the one- stage model where the threat to litigate is not credible, the threat to litigate in the three- stage model is credible. To see this, consider first the plaintiff s choice at Stage 3. The plaintiff can litigate, and receive a payout of - 110K (and expected judgment of 100K minus 210K in total litigation costs. If he drops at stage 3, his total payoff is - 140K, the sunk litigation costs incurred during stages 1 and 2. Thus, his total payoff is higher if he chooses to litigate. Intuitively, the plaintiff should rationally ignore the - 140K in sunk costs, as proceeding to trial yields an expected net benefit of 30K (an expected judgment of 100K minus 70K in marginal litigation costs). Given that the plaintiff will choose to litigate at stage 3, the defendant s payoff if he rejects the plaintiffs offer of S=100 made after stage 2 is - 310K (100K in expected judgment and 210K in litigation costs). Thus, it is rational for the defendant to accept the plaintiff s settlement offer S=100 made after stage 2 to save the marginal litigation costs (70K) that would be incurred at stage 3. Given that the defendant will rationally accept the offer made after stage 2, it is rational for the plaintiff to continue rather than drop at stage 2. And knowing that the plaintiff will choose to continue at stage 2, the defendant will rationally accept the offer of S=100 made after stage 1. Working backwards, the three- stage model predicts that the plaintiff s assurance that he will litigate the case is credible. As a result, the plaintiff s initial offer will be accepted even though the case has negative expected value if litigated to judgment. 12

14 Offer%S%=100% Reject%Offer% P=30,%D=2170% Accept%Offer% P=100,%D=2100% Stage 1 File%(C=70)% Offer%S%=%100%% P%=30,%D=2170% Do%Not%File% P=0,%D=%0% Reject%Offer% P=240,%D=2240 %% Accept%offer% P=30,%D=2170% Stage 2 Pretrial%(C=70)% Offer%S=100% P=240,%D=2240% Drop% P=270,%D=270% Reject%Offer% P=2110,%D=2310% Accept%Offer% P=240,%D=2240% Stage 3 Li>gate%(C=70)% P=2110,%D=2310% Drop% P=2140,%D=2140% Figure 8 Three- Stage Model of Litigation B. Asymmetric and Sequential Costs In this section, we consider the effect of asymmetric and sequential costs (Rosenberg & Shavell (1985)). In their model, they show how asymmetric and sequentially incurred costs can allow a plaintiff to extract a settlement even when a case has zero judgment value. To see this, consider the litigation structure in Figure 9, where a plaintiff makes a discovery request at a cost CP. At the time of the request, the plaintiff also offers to settle the case for S. Note that the structure of litigation in Figure 9 alters the timing of when costs are incurred relative to the litigation structure contained in Figure 1. In particular, the structure depicted in Figure 9 does not permit the plaintiff to avoid the costs of litigation if the offer S is rejected. 12 The defendant can accept the offer S, or respond to the discovery request at a cost CD. The payoffs if the offer S is accepted are S CP for the plaintiff and S for the defendant. If the defendant chooses to reject the offer and respond to the request, the payoff of the plaintiff and defendant are (- CP, - CP). Under the assumption that the litigation has no judgment value, the case is dropped after discovery. 12 This assumption is critical. If the plaintiff could withdraw his discovery request and avoid C P, the defendant could reject the offer knowing that the plaintiff rationally will choose to withdraw to request. Altering the sequence of when costs are incurred makes the plaintiff s costs sunk and non-avoidable. 13

15 Con$nue'to' Discovery?' Plain$ff'Makes' Discovery'Request,' Offer'S' Plain$ff'Drops'Case' P'='0,'D'='0' Defendant'Responds' to'discovery'request' D' Defendant'Accepts' Offer' Figure 9 Asymmetric and Sequential Costs Examining the defendant s decision to accept the offer to settle or respond to the request, the defendant will choose to settle if S CD. Conditional upon an offer S being accepted, it will be rational for the plaintiff to make the offer S if S CP. If an acceptable offer S CP, or if S CD so that the offer will not be accepted by the defendant, the plaintiff will rationally choose to drop the case without making and incurring the cost of a discovery request. Thus, an offer S that will be accepted by the defendant and that is also profitable for the plaintiff requires that CP S CD. Thus, costs must be asymmetric and higher for the party responding to the discovery request, i.e., CD CP. 13 C. Multistage Models and Option Value a. Effect on Filing In this section, we further expand the sequential model to include the revelation of information. Figure 10 depicts a structure that has the same cost structure and expected value as the three- stage model used in part B. Each of the outcome boxes in stages 1 through 3 lists the probability of reaching the box, followed by the payoffs for the plaintiff and defendant when the box is reached. The expected judgment value of the case if unconditionally litigated to judgment is 100K. Each stage costs 70K, so the total cost of litigation for each side is 210K. The expected value of filing this suit if it is unconditionally litigated to judgment is - 110K for the plaintiff., and the expected exposure for the defendant is - 310K. As was shown above, given these payoffs, the threat to sue is not credible in the simple one- stage model depicted in Figures 1 and The existence of asymmetric costs and their ability to contribute to large settlements that reflect the cost of litigation rather than the merits of the case are at the center of the controversy over discovery cost in litigation and proposal for discovery reform. For a discussion of these issues, see Kobayashi (2014). 14

16 ["110,"310](.7( ["208.75K,"211.25K](.3( [120.42K,"540.42K]( Stage(1(.75( ["209K,"211K](.25( ["208K,"212K](.75( ["205K,"215K]](.25( [ K," K]( Stage(2(.9( ["210K,( "210K](.1( ["200K,( "220K](.8( ["210K,( "210K](.2( ["200K,( "220K](..75( ["210K,( "210K](.25( ["190K,( "230K](.333( ["210K,( "210K](.667( [1750K,( "2170K]( Stage(3( Figure 10 Three Stage Litigation with Information Revelation Total Payoffs The example in Figure 10 has two pre- trial motions (stage 1 and stage 2) and a trial stage (stage 3). In contrast to the multistage examples presented above, both the probability and the magnitude of the trial payoffs are conditional on the outcomes of earlier pretrial motions. In particular, there are four conditional trial outcomes, which are listed in Table 1. For simplicity, we assume that there are two defense motions, one a motion in limine to exclude the plaintiff s expert witness (stage 1 in Figure 10) and a motion to limit the scope of the plaintiff s supplemental discovery request (stage 2 in Figure 10). Table 1 Pre-Trial Motion Outcomes Motion in Limine Granted (p = 7/10) Motion in Limine Denied (p = 3/10) Motion to Limit Discovery Granted (p = 3/4) 1. Both motions Granted (p =.525) 2. Disc. Motion Granted, Evid. Motion Denied (p =.15) Motion to Limit Discovery Denied (p = 1/4). 3. Disc. Motion Denied, Evid. Motion Granted (p =.175) 4. Both motions Denied. (p =.075) Figure 10 depicts the total payoff if a stage is reached. Figure 11 shows the marginal payoffs of the litigation depicted in Figure 10 15

17 ["110,"310](.7( ["138.75K,"141.25K](.3( [190.42K,"470.42K]( Stage(1(.75( ["69,"71](.25( ["68K,"72K](.75( ["65K,"75K]](.25( [ K, K]( Stage(2(.9( [0,0](.1( [10K,"10K](.8( [0,0](.2( [10K,"10K](..75( [0,0](.25( [20K,"20K](.333( [0,0](.667( [1960K,( "1960K]( Stage(3( Figure 11 Three Stage Litigation with Information Revelation Marginal Payoffs Looking at Table 1, both of the defendant s motions are granted over half of the time (52.5%). This results in the far- left outcome during stage 3. Without their expert and with limited discovery, the plaintiff has a 1 in 10 chance of prevailing, with limited damages of 10K. Ignoring the 140K in sunk costs incurred during stage 1 and stage 2, the expected value of going to trial conditional upon both of the defendants motions being granted is 1K 70K = - 69K. In contrast, the best outcome for the plaintiff, when both of the defendant s motions are denied occurs 7.5% of the time. This results in the far- right outcome during stage 3. When the plaintiff goes to trial with his expert and after extensive discovery, he has a 2/3 chance of prevailing, with damages equal to 1.96 million. Conditional on both of the defendant s motions being denied, the expected value of going to trial, again ignoring sunk costs, is million. In addition, there are two mixed outcomes. The first is where the defendant s evidentiary motion is granted, but the discovery motion is denied. Thus the defendant successfully excludes the plaintiff s expert, but is unsuccessful in his attempt to limit discovery. This results in the expected stage 3 trial payoffs listed in the second to the left stage 2 outcome. The probability of recovery is 1 in 5, but damages are still limited to 10K. The plaintiffs expected payoff, net of litigation costs at trial, is - 68K. The other mixed outcome occurs when the defendant does not exclude the expert, but limits discovery. Here the probability of recovery is 1 in 4, and damages are 20K. The expected payoff, net of litigation costs at trial equals- 65K. At stage 1, the expected litigation payoff net of costs equals K if the plaintiff s expert is excluded. 25% of the time the plaintiff faces a net trial payoff of - 68K when he defeats the defendant s discovery motions, and 75% of the time he faces a net trial payoff of - 69 when the defendant s discovery motion is successful. The other three stage 1 payoffs are derived is a similar manner. Taking the expected 16

18 value of the stage 1 payoffs yields the expected value of this lawsuit when it is taken to judgment unconditionally, which is The defendant s exposure under the same circumstances is b. Option Value As noted by Cornell (1990), the expected value of the lawsuit depicted in Figures 10 and 11 is based on the assumption that the litigants will unconditionally take the case to judgment is not the value of the suit if the litigants can avoid negative payoff stages by ending the litigation. Given the parties option to end the litigation and avoid the cost of litigation, the option value of a lawsuit will be greater than the expected value of the lawsuit when the parties unconditionally proceed to litigate the case to judgment. Examining Figure 11, it is in the mutual interest of both parties to end the litigation at stage 3 unless the defendant loses both of his pre- trial motions. 14 Given that both parties would agree to end the litigation at this point, the marginal payoffs if any of the shaded in red stage 2 boxes would be zero for both parties. The parties would also agree to dismiss the case if they reached the left outcome in stage 1 (i.e., when the defendant successfully excludes the plaintiff s expert). Thus, the parties would agree to dismiss the case as soon as one of the defendant motions were granted. [1.75K,(194.25K]-.7- [0K,0K]-.3- [239.17K,(414.17K]-.75- [0K,0K]-.25- [ K,( K] [0K] [1960K]- Figure 12 Option Value 14 Federal Rule of Civil Procedure 41(a) governs dismissals of actions. Under FRCP 41(a)(1) an action can be dismissed by the plaintiff without order of court (i) by filing a notice of dismissal at any time before service by the adverse party of an answer or of a motion for summary judgment, whichever first occurs, or (ii) by filing a stipulation of dismissal signed by all parties who have appeared in the action. 17

19 Figure 12 shows the truncated decision tree that incorporates the parties decisions to dismiss the case. The plaintiff s option value of the lawsuit is higher than the expected value of the lawsuit when the parties unconditionally proceed to litigate the case to judgment. Moreover, the plaintiff s threat to file the lawsuit is credible, as the plaintiff s option value is positive. Note that early dismissal also benefits the defendant by reducing his expected litigation exposure. The source of the higher option value for both litigants is the ability of the litigants to avoid the costs of litigation when the payoffs are negative. When the defendant s stage 1 motion is granted and the plaintiff s expert is excluded, the parties will rationally agree to end the litigation and save both the costs of the discovery motion and the costs of the trial (saving 140K relative to the costs of unconditional litigation). When the defendant s stage 1 motion is denied, but his stage 2 motion to limit discovery is granted, the parties will also rationally agree to end the litigation. This saves the cost of the trial (70K relative to the costs of unconditional litigation). c. Settlement and Option Value Figure 12 assumes that the case will be litigated and does not consider settlement. In the one- stage model, the defendant will not rationally agree to a settlement because the plaintiff s threat to sue is not credible. But the threat to sue is credible when option value is considered. Because settlement allows the parties to avoid the costs of litigation in those stages where litigation proceeds, the effects of settlement complements the effects of the option to exit and can further increase the option value of the lawsuit for both parties. [S=98K](.7( [0K,0K](.3( [S=326.67](.75( [0K,0K](.25( [S= K](.333( [0K](.667( [1960K]( Figure 13 Option Value with Settlement 18

20 The effect of settlement is illustrated in Figure 13. The example assumes that the parties agree to a midpoint settlement prior to stage 3 that imposes the expected judgment at trial. Thus, the expected stage 3 payoffs are increased by 70K for each party (equal to the saved trial costs). A similar effect occurs at stage 2 when the defendant s motion to exclude the plaintiff s expert is denied. As a result of the anticipated cost savings, the settlement value of the case increases to 98K, which raises the plaintiff s recovery and reduces the defendant s litigation exposure relative to the option value litigation payoffs. 15 d. Separate versus Consolidated Motions The decision to consolidate or separate motions affects the option value of a lawsuit. 16 Figure 14 shows the marginal payoffs for the lawsuit depicted in Figures when the two pretrial motions are consolidated. That is, instead of first litigating the evidentiary motion in stage 1 and then separately litigating the discovery motion in stage 2, both motions are litigated (and the costs of litigating both motions are incurred) in a consolidated stage 1 and Figure 14 shows the expected value of the lawsuit when the parties unconditionally proceed to judgment is unaffected by the consolidation of stages 1 and 2. ["110,"310](.525( ["69K,"71K](.175( ["68K,"72K]( 0225( ["65K,"75K](.075( [ K," K]( Stage1(&(2(.9( [0,0](.1( [10K,"10K](.8( [0,0](.2( [10K,"10K](.75( [0,0](.25( [20K,"20K](.33( [0,0](.67( [1960K,( "1960K]( Stage(3( Figure 14 - Consolidated Pretrial Figure 15 depicts the option value of the lawsuit with consolidated pre- trial. Compared to the option value of the litigation illustrated in Figure 12, consolidation of stages 1 and 2 reduces the option value of the lawsuit. Intuitively, the option to mutually exit the lawsuit allows the parties to save the costs of trial (70K) 92.5% of the time. In contrast, taking the pretrial motions sequentially also allows saving the costs of trial 92.5% of the time, but also allows saving the costs of the second pre- trial stage (an additional 70K) 70% of the time. Indeed, consolidation results in 15 See generally Polinsky & Rubinfeld (1988) (examining the deterrent effects of settlements versus trials). 16 The consolidation or separation of issues is controlled by Federal Rule of Civil Procedure The example assumes that the cost of litigating the two motions together is the same as litigation the two motions sequentially. For an analysis of the effect of economies of scale in consolidating motions or trials, see Landes (1993, 1995). 19

21 negative option value for the plaintiff, again making the filing of the lawsuit non- credible. ["47.25K,"243.25K],.525, [0,0K],.175, [0,0], 0225, [0,0],.075, [ K," K],.33, [0,0],.67, [1960K,, "1960K], Figure 15 - Option Value with Consolidated Pretrial e. Order of Motions The option value of the lawsuit can also be affected by the order of motions. 18 It is easy to confirm that the expected value of the lawsuit when the parties unconditionally take the lawsuit to judgment is unaffected by switching the order of the motions. However, such a change can alter the option value of the litigation. Figure 16 shows the effect of switching the sequential order of the two pre- trial motions. That is, the discovery motion (formerly stage 2) is taken first, and the evidentiary motion (formerly stage 1) is taken second. Reversing the order of the pre- trial motions increases the option value for the plaintiff and lowers the litigation exposure for the defendant. Intuitively, taking the defendant s stronger motion first increases the probability that the lawsuit will be voluntarily dismissed after one motion by 5%, and thus increases option value by increasing the probability that the parties will save the cost of the second motion. Thus, even though the discovery motion is a stronger motion for the defendant, once litigation has commenced, the plaintiff will voluntarily agree to take that motion first. 18 For an analysis of the order of motions, including taking issues of damages before issues of liability, see Stevenson (2006). See also Beckner & Salop (1999). 20

22 Figure 16 Reversing Order and Option Value f. Effect of Fee Shifting Figure 17 illustrates the effect of two- way cost and fee shifting in the sequential multi- stage model when the parties unconditionally litigate the lawsuit to judgment. The figure assumes that cost and fee shifting is imposed at judgment to the prevailing party. Because the probability that the plaintiff is the prevailing party is less than ½, 19 a system of cost and fee- shifting lower the expected value to the plaintiff and reduces the defendant s litigation exposure. Thus, if the parties litigate the case to judgment, the effect of two- way cost and fee shifting is similar to its effect in the one- stage model. [5.25K,'190.75]-.75- [0K,0K]-.25- [301K,'483K]-.7- [0K,0K]-.3- [ K,' K] [0K] [1960K]- [" ," ]-.7- ["296.25K,+16.25K]-.3- [129.17K,"409.17K]- Stage ["237K,+97K]-.25- [194K,+54K]-.75- ["170K,+30K]]-.25- [ K, K]- Stage ["210K, +210K]-.1- [220K,- "220K]-.8- ["210K,- +210K]-.2- [220K,- "220K] ["210K,- +210K]-.25- [230K,- "230K] ["210K,- +210K] [2170K,- "2170K]- Stage-3- Figure 17 The Effect of Prevailing Litigant Two- Way Fee Shifting 19 The probability of judgment for the plaintiff is

23 Figure 18 illustrates the option value of the lawsuit with two- way cost and fee shifting. Note that the figure assumes that the plaintiff and unilaterally choose to dismiss the lawsuit. In contrast to its effect on the net present value of the case that is litigated unconditionally to judgment, the option value of the case is higher with two- way cost and fee- shifting. This is because prevailing party cost and fee shifting is not in the example imposed when the case is dismissed prior to judgment. Rather, in the example illustrated in Figure 18, it is imposed only when both of the defendant s motions are defeated. When the case is litigated to judgment, the probability of judgment for the plaintiff is 2/3, and two way cost and fee shifting increases the option value of the lawsuit. [7K,%199.5K]+.7+ [0K,0K]+.3+ [256.67K,%431.67K]+.75+ [0K,0K]+.25+ [ K,% K] [%210K] [2170K]+ Figure 18 Prevailing Litigant Two- Way Fee Shifting and Option Value The actual effect of two- way fee shifting thus can depend crucially on the plaintiff s ability to unilaterally dismiss the lawsuit. Note that in the examples of option value used in prior sections, it was in the interest of both parties to dismiss the action. However examining Figure 17, it is in the plaintiff s interest, but not in the defendant s interest, to dismiss the case when one of the defendant s motions is granted. Rather, as soon as one of the defendant s motions is granted, the defendant has an interest of continuing the litigation to judgment, where he has a high probability of prevailing, in order to trigger the shifting of costs and fees. Thus, if the plaintiff is unable to unilaterally dismiss the action, the option value model will not apply Indeed, the unilateral right to dismiss a case under FRCP 41(a) ends after the complaint is answered. In addition, the Court has ruled that voluntary dismissal of an action does not result in the dismissal of pending Rule 11 motions. See Cooter and Gell v. Hartmarx, 496 U.S. 384 (1990); Kobayashi & Parker (1993). 22

24 IV. External Effects and the Public versus Private Return to Litigation In this section, we return to the non- sequential model to set out a model of litigants incentives to litigate and settle cases takes into account external effects of judgment (Kobayashi (1996)) and the value of non- monetary or injunctive relief imposed via settlement, Kobayashi (2014b), Hylton and Cho (2010), Shavell (1993). To derive the settlement range in such a setting, we must examine again the litigant s trial payoffs. The minimum the plaintiff is willing to accept in settlement is determined by his trial payoff: (1E) TP = pp (J + GP) - (1 pp)lp CP The trial payoff in (1E) contains two new terms, GP, which are the plaintiff s external gains of a judgment not included in J, and LP, which are the external losses imposed on the plaintiff when there is a judgment for the defendant. For example, LP included the persuasive or preclusive effects of a judgment against a plaintiff that is a repeat litigant. One common example is an IP rights holder who is facing multiple infringers. If the defendant s intellectual property rights are invalidated the first time they are litigated, the defendant will be estopped from relitigating the issue of validity. 21 Thus, LP represents the loss of the patent due to preclusion (Kobayashi (2014)). Even in the absence of preclusion, an adverse judgment in one case may reduce the probability that the plaintiff will be successful in later cases. In this case LP represents the loss in litigation value of subsequent cases due to the persuasive effects of the earlier case. Note that LP generally does not include the value of precedent, as the effects of precedent that are separate from the preclusive or persuasive effects of litigation are generally spillover effects that are not internalized by the plaintiff (Shavell (1977, 1982), Kaplow (1986)). Gp would include, for example, the competitive benefits of deterred or blocked entry that would have occurred absent a judgment upholding the validity of the intellectual property right, or the persuasive effect of the judgment on later cases In the case of an repeat plaintiff, it does not generally include the effects of precedent for the reasons stated above, or the effects of preclusion. 22 The maximum defendant i is willing to pay is determined by his expected cost of going to trial: (2E) Ti = pi (J + Li) - (1 - pi)gi + Ci, The new terms Gi and Li are the net external gains and losses for litigant i imposed upon judgment that are not included in Ji. In intellectual property litigation, for 21 Blonder-Tongue Laboratories, Inc. v. University of Illinois Foundation, et al. 402 U.S. 313 (1971), Kobayashi (1996). 22 Id. 23

25 example, Gi can include the competitive benefits of early entry that would result from the invalidation of the plaintiff s intellectual property rights. Li can consist of the lost competitive benefits that results from entry that would have happened in the absence of litigation. An acceptable settlement would be any offer in which the monetary payment M plus the injunctive costs of a settlement, Ii, are less than the defendant s cost of going to trial: 23 (4Ei) S = M + Ii Ti so acceptable settlements for the plaintiff would include settlements where the monetary settlement M plus the non- monetary benefits of a settlement relative to the status quo, Ip, 24 are greater than the benefits of going to trial: (4Ep) S = M + IP TP. A sufficient, but not necessary, condition for litigation is the absence of a bargaining range. A bargaining range will be absent when TP IP > Ti Ii, or when: (5E) pp(dp + GP) - (1 pp)lp CP IP > pi (Di + Li) - (1 - pi)gi - Ii + Ci. or equivalently: pp(dp + GP) - pi (Di + Li) - (1 pp)lp + (1 - pi)gi + Ii IP > Ci +Cp. Equation (5E) shows that the sufficient condition for litigation is more likely to be satisfied, ceteris paribus, if the litigants are relatively optimistic (pp > pi), if the plaintiff has relatively large damages or high external benefits from a favorable judgment, if the defendant has relatively large external gains from a judgment favorable to him, or if the defendant s non- monetary costs from a settlement are larger than the patentee s non- monetary gains. Note that optimism is not required to generate litigation, as is the case in the standard model of litigation and settlement. Intuitively, judgments can have intrinsic value to the litigants, thus creating a demand for a judgment when these effects are positive, and litigation aversion when they are not. Examples of such judgment specific benefits would be the precedential or persuasive effects of a favorable judgment. Such effects produce external gains for the patentee by lowering the probability that the patent will be successfully challenged in the future. Another example of a judgment specific external effect is the negative effect of non- 23 Note that if the settlement generates benefits to the firm, I i < If the settlement does not alter the outcome relative to the case where the suit is terminated, this term will be zero. 24

26 party preclusion, which will prevent or estop the patentee from relitigating the validity of the patent held invalid in the first case. To see this, consider the case where there is no disagreement on the probability the plaintiff will prevail, so that pp = pi = p. This yields the following sufficient condition for litigation: (5E ) p(gp - Li) + (1 - p)(gi LP) + Ii IP > Ci +CP. Equation (5E ) shows that even in the absence of disagreement over p, litigation will be encouraged, ceteris paribus, if the patentee s expected external gain from a favorable judgment is greater than the infringer s expected external loss from such a judgment, when the infringer s expected external gain from a favorable judgment is greater than the patentee s loss from such a judgment, and when the infringer s non monetary costs of a settlement are greater than the patentee s non- monetary gains from a settlement. To illustrate the effects of the external effects model, suppose that a defendant in a patent case sued for infringement challenges the validity of a patent. If entry would not have occurred absent the invalidation of a patent, GP = Li = 0. If the patent is invalidated, the plaintiff/patentee suffers a reduction in profits during the time the patent would have been in force. These losses would be included in LP. In addition, the infringer can enter and earn profits during what would have been the time the patent would have been in force. These profits would be included in Gi. If the patent is invalidated, and the patentee is estopped from relitgating the validity of the patent, firms other than Firm i are free to enter. Under these conditions the benefits of early entry that inures to the benefit of other firms as well as the increased consumer surplus generated by a more competitive market are not part of Gi (Kobayashi (2014a, 2014b), Farrell & Shapiro (2008)). Similar to the effect of precedent, the invalidation of the patent provides a public good that for other entrants and consumers. As a result,, Gi < LP, and this setting provides heavy incentives to settle, especially in cases where the probability the patent will be invalidated (1 p) is high. Finally, looking at the last term in equation (5E ), the value of the injunctive part of the settlements can also provide heavy incentives to settle (Hylton & Cho (2010), Kobayashi (2014b)). For example, patentees with branded drugs facing generic entry have used reverse payments to induce potential generic entrants do delay the date of entry past the litigation adjusted expected life of the patent. Again, the benefit to the brand patentee IP (the preservation of monopoly) is greater than the forgone profits of the generic entrant Ii. Thus Ii < IP, further increasing the incentives for settlement. V. Conclusion The standard one- stage private litigation model has been a useful tool to analyze the economics of litigation and the effect of procedural rules and procedural reform. The basic model is extended to incorporate the sequential nature of 25