The decision tree for Plaintiff is given below, with the relevant payoffs. In the tree, Cp is the cost of filing a suit, C, is the cost of out-of-court settling, C, is the cost of trial, C, is the cost of appeal, Pw is the probability of winning the trial by Plaintiff, P, is the probability of winning the appeal by Plaintiff. The parties are perfectly aware of each other's costs and evaluations of probabilities. do not file to cel file complaint Itrial Settle Cs S win lose $1,000 Pu do not appeal to appeal CA lose win PA $0 44000 2. Assume the following (excessive relative optimism): Each party, Plaintiff and Defendant, pay their own costs. Both parties encounter the costs at every stage; the only difference is Plaintiff pays CF if she files the complaint, Defendant does not pay anything at the filing stage. Parties do not perceive same probability P. C-$200. C. $80. . C C. $400. . C, $800. Plaintiff thinks that Pw -0.95 while Defendant thinks that Pw -0.05. Both parties perceive same probability P = 0.5 (because they are totally ignorant of how the appeals work). The parties are unable to correct the excessive relative optimism at the settlement stage (i.e., possible bargaining during the settlement stage does not change their evaluations of probabilities P, and P). a. Calculate expected value of appeal EVA to Plaintiff. (2) b. Calculate expected value of trial EVT to Plaintiff. (2) c. Calculate expected value of trial EVT, to Defendant. (2) D d. Find the reasonable settlement S to Plaintiff. (2) e. Calculate expected value of filing the complaint EVC to Plaintiff. (2) f. What will happen in this case (will the complaint be filed, will it be settled or proceed to trial, will the appeal be filed if Plaintiff loses the trial)? (2) You will have to properly trim the decision tree in order to evaluate the expected values. Hint: Figure 10.4a (p. 388) and Figure 10.4b (p. 391) may be quite helpful when you work on the homework questions. EVA-S10 FIGURE 10.40 Expected value of a legal claim to the plaintiff. SO appeal 9/ 320 lose EVT $30 O trial 5 -$20 lose EVB=543 ) .1 win EVC = $46.30 hugain don't $100 exchange information 3 settle Swin or settle discover 7 7 settle-51 S10) $3.30 sue file - $10 SSO . 7 settle-$1 $50 don't file SO We are grateful to Raoul Meier of Switzerland for pointing out an error in how we stated this rule in previ- Dus editions II. Why Sue? 389 In order to compute expected values in a sequence of events, one begins with the last possible event, which is "appeal" in Figure 10.4a, and works toward the first event, which is the decision to file a complaint. We will take this approach to computing the expected value of the legal claim at each step in the legal process. Assume that each side pays his own legal costs. According to Figure 10.4a, the plaintiff who has lost al trial must pay $20 to appeal the case. On appeal, the plaintiff stands to win $100 with probability. I and to lose with probability 9. Thus, the expected value of the appeal (EVA) equals -$10: EVA = 1(S100) + 9($0) - $20 = - $10. Because the expected value of appeal is negative, the rational plaintiff who loses at trial will not appeal the case. (Notice that if the rule were changed from each pays his own" to "loser pays all," the expected value of trial would fall even further; so, the decision not to appeal is the same under the American rule and the European rule.) Having computed the expected value of appeal (second trial), we can now compute the expected value of the first trial. According to Figure 10.4a, the plaintiff who failed to settle out of court by bargaining must pay $20 to go to trial . At trial, the plaintiff stands to win $100 with probability and to lose with probability.5. If the plaintiff loses, he will not appeal the case and so will receive a payoff equal to So. We combine these numbers to obtain the expected value of the first trial (EVT): EVT = 5($100) + 5($0) - $20 = $30. ($) (Confirm for yourself that, assuming defendant's litigation costs are the same as plain- tiff's litigation costs, EVT is the same under the European rule and the American rule.-) Having computed the expected value of the trial, we can now compute the ex- pected value of bargaining to a settlement before beginning the trial. According to Figure 10.4a, the plaintiff who completed the process of exchanging information with the defendant can bargain to a settlement out of court with probability of success equal to.7. If bargaining succeeds, the plaintiff settles for $50 and pays settlement costs of SI. Bargaining fails to reach a settlement with probability.3, in which case the plaintiff proceeds to trial, whose expected value equals $30. We combine these numbers to obtain the expected value of the settlement bargain (EVB): EVB = 7(550-$1) + 3($30) = $43.30. Because the expected value of the settlement bargain is positive, the plaintiff who reaches this stage will bargain. the parties may settle. According to Figure 10.4a, the plaintiff who files a suit settles immediately with probability 7, in which case he or she receives $50 and pays in settlement costs. Alternatively, the plaintiff fails to settle immediately with probability .3 and proceeds to exchange information with the defendant, which costs $3.30. After exchanging information, the parties continue to bargain. We already computed the ex- pected value of the bargain, which equals $43.30. We combine these numbers to obtain the expected value of the legal claim when the plaintiff initiates the suit by filing the complaint (EVC): EVC = 7$50 - $1) + 3($43.30 - $3.30) = $46,30. (+ $= In Germany and other European countries, discovery does not occur before the beginning of a trial. Rather, the first phase of a trial concerns the "giving of proofs" (beweisverfahren), in which the parties present evidence supporting the basic facts of the case. For purposes of computing the value of a claim from the decision tree, dis- covery and the giving of proofs are the same. (Some important differences between them must be taken into account in a more specific analysis.) The filing costs (FC) include the costs of hiring a lawyer, drafting the complaint, and paying the filing fee assessed by the court. According to Figure 10.41, the filing costs equal S10. After filing, the plaintiff expects to receive the value of the claim at the time of filing (EVC), which equals $46.30. Therefore, the expected net payoff from filing equals $46.30 - S10 = $36.30. The rational plaintiff files a complaint if its ex- pected net payoff is positive: EVC 2 FC - lile legal complaint; EVC