The remaining chapters of this study employ a large laboratory experiment to empir- ically investigate the properties of settlement delay when subjects are asymmetrically informed about the outcome of a potential trial verdict in mock tort disputes. Focus on the asymmetric information hypothesis is driven by its plausibility and popularity in theoretic models.24 Research addresses two broad empirical questions important
to understanding settlement delay and crafting efficient tort policy.
24The pervasive settlement delay observed in field data is almost certainly driven by a complicated
mix of factors. It remains for future studies to explore causes other than asymmetric information. The basic research design employed in the following chapters may be modified to test other hypothe- ses in subsequent studies.
Research Question 1. Can asymmetric information over trial verdicts plausibly contribute to the protracted delay observed in tort disputes?
This question is academically interesting as an empirical examination of theory. To my knowledge, this is the first experimental study of settlement delay in dispute resolution, and results may contribute to a range of other dispute resolution models. The practical relevance of the question is in identifying a potential contributor to the protracted settlement delay observed in tort disputes in the field.
Research Question 2. Can specific policies be identified which might mitigate the settlement delay caused by the presence of asymmetric information over trial verdicts? Assuming Research Question 1 is affirmed, the answer to this second question is of practical importance to policy-makers interested in changing United States tort policy. Study of how settlement bargaining behavior responds to changes in the bargaining environment also provides insights into the robustness of theoretic models which attribute settlement delay to asymmetric information.
The remainder of this study address these two broad research questions in detail. Though conceptually distinct, the questions share many common dependencies: in particular, the underlying theoretic model and experimental environment are effec- tively the same for both. This close relationship is exploited in construction of a complicated, but resource-efficient experimental design that addresses both research questions simultaneously. The following chapters are structured as follows.
Chapter II presents a theoretic model of settlement bargaining where delayed settlement results from asymmetric information over a potential trial verdict. The model is a minor variation on the popular model of settlement delay proposed by Spier (1989, 1992). Recognizing that theoretic predictions from bargaining models are often too stark to reliably describe behavior in the lab, this chapter also discusses
a number of observations from the behavioral economics of bargaining. Particular note is given to the inefficient disagreements and costly delays which pervade even simple bargaining models with complete information. Juxtaposed against theoretic predictions, behavioral caveats recommend a cautious interpretation of laboratory data and results.
Chapter III presents the experimental design employed in the present research. Payment-incentivized laboratory subjects interact in an experimental bargaining game closely based on the theoretic model described in Chapter II. A repeated measure- ment cross-over design exposes different subjects to different pairs of experimental treatments. This flexible design addresses a range of exploratory and confirmatory research questions while also providing strong experimental controls against various sources of potential design bias.
Chapter IV describes and summarizes the results of Sub-Experiment 1 (SE1), the objective of which is exploratory analysis of settlement bargaining behavior under a control treatment which closely adheres to the theoretic model of settlement bar- gaining with asymmetrically informed litigants. Data suggest mixed conformance between observed behavior and theoretic prediction. Settlement delay is pervasive in SE1, with resolution times distributed close to the theoretic prediction.
Chapter V describes and summarizes the results of Sub-Experiment 2 (SE2). The objective of SE2 is broadly confirmatory: experimental data are used to assess the causal influence of a controlled information asymmetry on average settlement delay. Under a variety of treatments designed to test the sensitivity of results, asymmetric information is affirmed to causally induce settlement delay.
Chapter VI describes and summarizes the results of Sub-Experiment 3 (SE3). The broad objectives of SE3 are both confirmatory and exploratory. Experimental data address the confirmatory question whether various “tort reform” policies might reduce
the settlement delay associated with asymmetric information. A subsequent inquiry looks to the wealth-distributive effects each policy. Investigated policies include a damages limit, damages cap, prejudgment interest rule, and Early Offers reform. No reforms are found to affect obvious reductions in settlement delay, but most reforms do cause clear changes in the relative earnings of tort dispute litigants.
Chapter VII provides concluding remarks about the findings of the present re- search. Implications of research findings are discussed (i) for future academic study of settlement delay in tort disputes, and (ii) for practical relevance in informing fu- ture tort policy. Limitations of the research design are also addressed, including concerns about the dynamic effects of imposing various reform measures, and the external validity of laboratory data to real-world tort disputes. Finally, extensions of the present research are suggested for the future study of settlement delay with laboratory experiments.
Chapter II
Model of Settlement Bargaining
A fully satisfactory model of settlement bargaining and the timing of dispute resolu- tion is difficult to imagine. Legal bargaining—with all its uncertainty, heterogeneity, intricacy, and emotional drama—is a far cry from the abstract bargaining environ- ments studied in non-cooperative game theory. But disengaging from the structure of negotiation to focus solely on axiomatic bargaining outcomes is also unsatisfying.25 In
abandoning the structure of bargaining, one concedes the ability to study settlement delay—effectively discarding the baby with the bathwater.
Understanding that no approach is perfect, the model of settlement bargaining adopted in the present study errs on the side of abstraction. For the broad research questions at hand, the capacity of a model to predict patterns of settlement delay is more important than generality in bargaining structure. Section 3 presents the model of non-cooperative settlement bargaining explored in this study. Equilibrium strate- gies predict rationally delayed settlement, with an uninformed defendant screening information from an informed plaintiff over multiple periods of bargaining.
Although theoretic bargaining models can provide strong predictions under rea- sonable assumptions, such predictions are often too stark to reliably describe bar- gaining behavior in the laboratory. To present a more rounded profile of predictions, Section 4 discusses important findings from the behavioral economics of bargaining. Several behavioral regularities oppose theoretic predictions in various classes of bar- gaining models. These regularities recommend a careful interpretation of theoretic predictions and their comparison to experimental results.
3
Theoretic Model
Theoretic predictions are derived from a slight modification of the asymmetric infor- mation “pre-trial” model of settlement bargaining presented by Spier (1989, 1992).26
The model provides an intuitive context for understanding how settlement delay may result from asymmetric information over a potential trial verdict. Attractive proper- ties of the model include (i) wide citation, meaning experimental results may pertain to many extant discussions, (ii) unique equilibrium play under reasonable refinements, (iii) robustness to an effectively continuous interpretation of bargaining, and (iv) con- crete predictions for the effects of various remedial tort policies.
Presentation of the model proceeds as follows. Details of the settlement bargaining game, rules of play, and associated notation are described in Section 3.1. Section 3.2 describes equilibrium strategies in the (standard) bargaining game with asymmetric information over a potential trial verdict. Section 3.3 describes equilibrium strategies in the special case of settlement bargaining with symmetric information over the potential verdict.
3.1
Model Description
The model characterizes settlement bargaining as follows. Litigants negotiate during at most T discrete periods of bargaining. In period t = 1, . . . , T , the defendant makes a proposal St for the size of a settlement wealth transfer, and the plaintiff decides
whether to accept or reject the proposal. Acceptance represents settlement, ending the game in period t with an immediate transfer of St from the defendant to the
26Relative to the Spier (1989, 1992) model, the present model reverses the bargaining roles of
plaintiff and defendant and introduces uncertainty over liability in the trial verdict (i.e. the chance of a plaintiff verdict). The Spier model is a multi-period concatenation of the Bebchuk (1984) model of settlement bargaining under asymmetric information, with the information asymmetry changed from liability to damages and with bargaining costs distinct from trial costs.
plaintiff; rejection means the game proceeds to period t + 1. If the parties fail to settle within T periods, the dispute is resolved by a trial verdict in period T + 1.
Trial verdicts are modeled as the product of two exogenous events: (i) the de- termination of liability, i.e. whether the defendant is legally liable for causing the plaintiff’s injury, and (ii) the determination of damages, i.e. the size of compensatory wealth transfer a liable defendant must make to the plaintiff. I model the liability decision as a simple probability π ∈ [0, 1]: the plaintiff wins positive damages with probability π and loses the case (zero damages) with probability 1 − π. The value of potential damages x is modeled as a random draw from the continuous distribu- tion F (x) with positive support on [x, x] ⊂ [0, ∞), and with (d/dx)F (x) = f (x). A victorious plaintiff is awarded a wealth transfer of x in period T + 1.
Other aspects of the model include delay costs, and risk and time preferences. To represent the costs of bargaining, the plaintiff and defendant (indexed p and d respectively) incur negotiation costs of cp and cd at the beginning of each bargaining
period t = 1, . . . , T . If the dispute goes to trial, one-time trial costs are kp and
kd in period t = T + 1. To avoid trivial special cases, I define cp, cd, kp, kd > 0.
Disputants are rational, risk neutral, and have time preferences represented by the common discount rate δ ∈ (0, 1) per period.
In the standard (asymmetric information) model, the value of potential damages x is the private information of the plaintiff. That is, the plaintiff starts a dispute knowing his or her type, in terms of what damages the court would award if the plaintiff were to win at trial. The defendant does not know the plaintiff’s type, but instead maintains beliefs over the type of plaintiff being faced. Conditional on rejec- tion of all prior proposals, the defendant’s period t beliefs are given by the probability density ρ(x|S1, . . . , St−1). All costs, π, F (x), δ, the structure of information, and the
Under this model of settlement bargaining, the plaintiff and defendant’s settlement preferences in each period, Up(St) and Ud(St), are the first-period net present value
of a period t settlement transfer of size St:
Up(St) = δt−1St− cp t X i=1 δi−1 Ud(St) = −δt−1St− cd t X i=1 δi−1 (1)
Note that because neither Up(St) nor Ud(St) depends on the plaintiff’s type, all plain-
tiffs and defendants have symmetric preferences over settlement options in every period. Note also that social utility, defined as Up(St) + Ud(St), is monotonically
decreasing in t. Delayed settlement is always socially inefficient.
The plaintiff and defendant’s preferences over a trial verdict, Wp(x) and Wd(x),
are defined by the size of potential damages x, net of bargaining and court costs and discounted to period t = 1: Wp(x) = δT(πx − kp) − cp T X i=1 δi−1 Wd(x) = −δT(πx + kd) − cd T X i=1 δi−1 (2)
In contrast to settlement preferences, trial preferences are explicitly a function of the plaintiff’s type. Informed about the value of potential damages, the plaintiff knows trial preferences with certainty. The defendant does not know the value of potential damages, and so operates off the expected value of trial preferences given beliefs:
E [Wd(x)] =
Z ∞
−∞
Wd(x)ρ(x|S1, . . . , St−1)dx t = 1, . . . , T + 1. (3)
A summary of game notation is consolidated in Table 2. Figure 2 illustrates the basic structure of the game. Because continuous choice spaces and multiple bargaining periods make the accounting intractable, information sets are omitted from Figure 2. It suffices to say that there are no proper subgames to the standard game.
Table 2: Summary of Notation
Notation Descriptiona
p, d index plaintiff and defendant respectively
x potential damages; private information of the plaintiff; x ≥ 0 F (x) distribution of potential damages in the population
f (x) density function of potential damages; f (x) = (d/dx)F (x) x, x upper/lower bounds on the support of potential damages;
x = sup{x : f (x) > 0}; x = inf{x : f (x) > 0}; [x, x] ⊂ [0, ∞) π probability that plaintiff wins damages at trial; π ∈ [0, 1] T final period of bargaining
T + 1 period of trial verdict
cp, cd negotiation costs paid at the start of every round of bargaining
(i.e. periods 1, . . . , T ); cp, cd> 0
kp, kd one-time court costs paid only if dispute is resolved by a trial
verdict (i.e. period T + 1); kp, kd> 0
δ common per-period discount factor; δ ∈ (0, 1)
St settlement proposal made by defendant in period t = 1, . . . , T
Up(St), Ud(St) plaintiff and defendant preferences over settlement at St in
period t = 1, . . . , T
Wp(x), Wd(x) plaintiff and defendant preferences over a trial verdict when
the plaintiff is of type x; period T + 1
ρ(x|S1, . . . , St−1) defendant’s period t beliefs about the plaintiff’s type (proba-
bility density over x), given observed play in prior periods
Figure 2: Illustration of the Settlement Bargaining Gamea x S1 accept reject S2 accept reject ST {S1− cp, −S1− cd} {δS2− δcp− cp, −δS2− δcd− cd} accept reject n δT −1ST− cpPT
i=1δi−1, −δT −1ST− cdPTi=1δi−1
o
plaintiff wins (π) plaintiff loses (1 − π)
n δT(x − kp) − cpPT i=1δi−1, −δT(x + kd) − cd PT i=1δi−1 o n −δTkp− c
pPTi=1δi−1, −δTkd− cdPTi=1δi−1
o nature (type assignment)
plaintiff (accept/reject S2) plaintiff (accept/reject S1)
plaintiff (accept/reject ST)
nature (trial outcome) defendant (propose S1)
defendant (propose S2)
defendant (propose ST) F (x) in population