Pretrial negotiations under optimism

• DOI: http://doi.org/10.1111/1756-2171.12273
• Date: 01 June 2019
• Author: Muhamet Yildiz,Shoshana Vasserman
• Published date: 01 June 2019

RAND Journal of Economics

Vol.50, No. 2, Summer 2019

pp. 359–390

Pretrial negotiations under optimism

Shoshana Vasserman∗

and

Muhamet Yildiz∗∗

Wedevelop a tractable and versatile model of pretrial negotiationin which the negotiating parties

are optimistic about the judge’s decision and anticipate the possible arrival of public information

about the case prior to the trial date. The parties will settle immediately upon the arrival of

information. However, they may also agree to settle prior to an arrival. We derive the settlement

dynamics prior to an arrival: negotiations result in either immediate agreement, a weak deadline

effect—settling at a particular date before the deadline, a strong deadline effect—settling at the

deadline, or impasse, depending on the level of optimism. Our findings match stylized facts.

1. Introduction

Costly settlement delays and impasse are common in pretrial negotiations. Whereas only

about 5% of the cases in the United States go to trial, the parties settle only after long, costly

delays.1Excessive optimism has been recognized as a major cause of delay and impasse in

pretrial negotiations, especially when the optimistic parties learn about the strength of their

cases over time. In this article, we develop a tractable model of pretrial negotiations in which

optimistic negotiators may receive public information relating to the outcomes of their cases as

negotiations progress. We determine the dates at which a settlement is possible and obtain sharp

characterizations of patterns of behavior as outputs of our model. Our analysis predicts some

well-known stylized facts and also makes a few novel predictions.

Optimism and self-serving biases are commonly observed, even among highly experienced

litigators. In an empirical study of lawyers’ aptitude in accurately predicting the outcomes of

∗Harvard University; svasserman@fas.harvard.edu.

∗∗Massachusetts Institute of Technology; myildiz@mit.edu.

Wethank Kathryn Spier and our anonymous referees for their detailed comments. We also thank Jim An for his assistance

in connecting our model to existing legal precedent and common legal practice. Finally, we thank the participants of the

Harvard Law and Economics Seminar and the ALEA 2016 annual meeting for their comments.

1Averagesettlement delay in malpractice insurance cases is reported to be 1.7 years (Watanabe, 2006). The legal

cost of settlement delays in high-stake cases are sometimes on the order of tens of millions of dollars. In the well-known

case of Pennzoil v.Texaco, the legal expenses were several hundreds of millions of dollars, and the case was settled for

$3 billion after a long litigation process (see Mnookin and Wilson, 1989; Lloyd,2004). In commercial litigation, ongoing

litigation also has indirect costs due to uncertainty, delayed decisions, missed business opportunities, and suppressed

market valuation, and these costs may dwarfthe legal expenses above.

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their cases, Goodman-Delahunty, Hartwig, and Loftus (2010) surveyeda cross section of lawyers

across the United States, asking for their assessments of the probability that they would meet a

self-identified minimum goal for a case set for trial.2Comparing the surveyed responses with

realized case outcomes, the authors found that even highly experienced lawyers (with 10+years

of experience) overestimated their probability of success by 9% on average.3

Moreover, although the probability of success reported to Goodman-Delahunty, Hartwig,

and Loftus (2010) varied between optimism and pessimism, there was not a strong relationship

between optimism and success. Whereas reported confidence levels (interpreted as subjective

probabilities of success) varied from around 20% to around 90%, the actualized success rates

were around 50% for most confidence levels. This suggests that the lawyers’ confidence was, at

least in large part, independent of superior knowledge or understanding. Note that this finding

is inconsistent with a model of asymmetric information with a common prior, as such a model

would predict that confidence rates are consistent estimators of the rate of success on average.

A number of experimental studies investigatingself-serving biases in negotiations have found

persistent evidence of overconfidence across contexts and treatments. In a classic experiment on

optimism in final offer arbitration, Neale and Bazerman (1983) found that subjects reported a

probability of 68%, on average, when asked the likelihood with which they believed that their

offer would be accepted. This finding suggests that the subjects did not have a common prior, as

a common prior would imply the subjects should report a probability of 50% on average—even

after counting for selection bias.4

In this article, we build on the canonical pretrial negotiation framework to construct a

tractable model of pretrial negotiations in the presence of optimism. A plaintiff has filed a case

against a defendant, and they negotiate over an out-of-court settlement. At each date, one party is

randomly selected as a proposer; the proposer proposes a settlement amount and the other party

accepts or rejects. If the parties cannot settle by a given deadline, a judge decides whether the

defendant is liable. If the judge determines that the defendant is liable, then the defendant pays

a fixed amount Jto the plaintiff; otherwise, he does not pay anything. Delays are costly, in that

each party pays a daily fee until the case is closed and pays an additional cost if the case goes to

trial. Unlike in the standard model, we assume that the plaintiff assigns a higher probability to

the defendant’s being found liable in court than the defendant does; the difference between the

two probabilities is the level of optimism, denoted by y. For example, in the Neale and Bazerman

experiment, we would have y=2×0.68 −1=0.36.

In our baseline model, we further assume that as time passes, the negotiating parties may

learn the strength of their respective cases by observing the arrival of new public information:

a single decisive piece of evidence that arrives with a fixed probability at each date, revealing

what the judge will decide. For example, in a securities fraud case, the negotiating parties might

anticipate evidence in the form of a contested internal memorandum that conclusively sheds

light on the corporate directives in question. Note that, for consistency, the probability that the

evidence would reveal a verdict in favor of the plaintiff (i.e., a verdict that finds the defendant

liable) upon arrival is equal to the probability that the court would find in favor of the plaintiff

at the trial date, and hence the level of optimism about the nature of the information is also y.It

is also worthwhile to emphasize that our baseline model assumes the American Rule: each party

incurs its own legal costs regardless of the outcome. Accordingly, the plaintiff can withdraw her

2See Loftus and Wagenaar (1988) and Malsch (1990) for earlier, similar analysesand Babcock and Loewenstein

(1997) for a review of the literature on the empirical evidence for excessiveoptimism among negotiators.

3Highly experienced lawyers reported a 63% probability of success on average, but only 55% achieved their

goals. Furthermore, there was almost no difference between lawyers who were highly experienced (with 10+years of

experience) and the rest of the sample, which predicted 64% probability of success on average, but had a 54% rate of

goal achievement.

4To put this in context,if both the plaintiff and defendant believe that they will win with 68% probability, then the

divergencebetween the parties’ expectations is 2 ×0.68 −1=0.36: the defendant believes that the plaintiff overestimates

her chances of success with 36%, and vice versa.

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case at any time, and she cannot commit to continue pursuing her case once it is revealed that the

court will find in favor of the defendant.

The basic dynamics and the logic of delay in our model are as follows. After the arrival

of information, our model is identical to the standard bilateral bargaining model as in Bebchuk

(1996), and the parties agree immediately. The settlement amount depends on the nature of the

information. If the information reveals a verdict in favor of the plaintiff, a settlement amount

Sis determined by splitting the savings from negotiation and litigation costs according to the

probability of making an offer for each party, which reflects that party’s bargaining power in the

standard model. If the information reveals a verdict in favor of the defendant, then the settlement

amount is zero. As Sis non-negative, the players are optimistic about the settlement amount after

an arrival of information in equilibrium, and so, the difference between the expected settlements

after an information arrival is yS. Such optimism turns out to be the main force toward a delay.

In equilibrium, the parties strategically settle at a given date without an information arrival if and

only if the expected benefit from waiting for yS through a future arrival of information is lower

than the total cost of waiting. Hence, we can determine the dynamics of strategic settlement by

simply analyzing the settlement amount Sin the standard model.

The resulting pattern of behavior relies heavily on which party has the stronger bargaining

position. When the plaintiff has more bargaining power, Sis an increasing function of the

remaining time until the court date, as the plaintiff gets some of the defendant’s cost savings

in the settlement. Hence, the incentive for delay increases as negotiations get farther from the

deadline. This results in a sharp prediction for the timing of the settlement. For high values of

optimism y, the players never settle strategically. They go to trial if information does not arrive,

no matter how far the trial date is. We call such an outcome impasse. For intermediate values of

optimism y, the players wait for an information arrival until the last possible day for settlement,

and strategically settle at the deadline. Such an agreement on the steps of the courthouse is

commonly observed in real-world negotiations and is referred to as the deadline effect in the

literature, as we discuss below. For low values of optimism, equilibrium is characterized by a

weaker version of the deadline effect: the parties wait until a fixed number of days before the

deadline to settle strategically. We define this as a weak deadline effect.

If the defendant has stronger bargaining power than the plaintiff, then Sis a decreasing

function of the time remaining until the deadline. In this case, the incentive to delay decreases

the farther away that the deadline is. In equilibrium, the parties strategically settle either at

the beginning or at the deadline, but never in between. Then, except for a settlement due to

information arrival, the only possible outcomes are: immediate agreement (for low values of yor

long deadlines), the deadline effect (for intermediate values of optimism), and impasse (for high

values of optimism).

Our model leads to sharp empirical predictions on the distribution of settlement times, which

is a combination of settlement due to an information arrival and strategic settlement. There are

point masses at the beginning and at the deadline—due to immediate agreement and the deadline

effect, respectively. In between, the overall frequency of settlements is decreasing, yielding a U-

shaped pattern. This is in line with empirical regularities. The frequency of settlements decreases

in the duration of negotiations (e.g., see Kessler, 1996), but a significant number of cases settle at

the deadline in studies that keep track of the trial date. For example, Williams(1983) repor ts that

70% of civil cases in Arizona were settled within 30 days of the trial date and 13% were settled

on the trial date itself. A U-shaped distribution of settlements also arises in some bargaining

models with incomplete information (Spier, 1992; Fanning, 2016). A more subtle parameter

that is considered in the empirical literature is the hazard rate of settlement, which measures the

frequency of settlements among cases that are ongoing. The hazard rate in our model is increasing

and convex—with a point mass at each end. The empirical studies that weare aware of are mixed:

Fournier and Zuehlke (1996) estimates a convexly increasing hazard rate as in here, whereas

Kessler (1996) reports a mildly decreasing hazard rate.

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