# Monthly Archives: June 2014

## THE TERMS OF SETTLEMENT: BARGAINING WITH AND WITHOUT SPECIAL OFFERS 5

ONE SPECIAL OFFER WITH ONE-SIDED COST-SHIFTING
We will now apply the general principle set forth in Lemma 1 to derive the settlements that emerge under particular offer-of-settlement rules. Offer-of-settlement rules may provide for cost-shifting only in one direction, or they may provide for two-sided cost-shifting. In this section, we assume that the offer-of-settlement rule would only shift costs in favor of the party making the special offer. For example, suppose the defendant makes a special offer S. Under an offer-of-settlement rule shifting costs only in favor of the defendant, the plaintiff would be obliged to pay Cd to the defendant if the damages D are less than or equal to S.

## THE TERMS OF SETTLEMENT: BARGAINING WITH AND WITHOUT SPECIAL OFFERS 4

Suppose instead that the defendant makes the special offer. By similar reasoning, the defendant would have to pay max[S, B(S)] and could minimize the plaintiffs payoff by choosing S = B(S). Thus, (2) holds whether the plaintiff or the defendant mates the special offer.13 Finally, (3) follows from (2) and (4).
Remark: Figure 1 illustrates why S = B(S) is the optimal offer for either party to make.

## THE TERMS OF SETTLEMENT: BARGAINING WITH AND WITHOUT SPECIAL OFFERS 3

Consider the effect of an increase in S upon the judgment J(S). In those cases in which S changes from an amount less than D to an amount greater than or equal to D, liability for Cd will shift to the plaintiff, or liability for Cp will shift back to the plaintiff, or both, depending on which costs shift under the offer-of-settlement rule. In all other cases, the increase in S will not affect J(S). Therefore, the expected judgment, denoted E[J(S)], taking the expectation with respect to different possible values of D, is a nonincreasing function of S.
Thus, В is now a function of the settlement amount S proposed in the special offer, because В is a function of E[J(S)]. Let B(S) denote this function, and let S* denote the optimal special offer for the offeror. We can now show the following lemma:

## THE TERMS OF SETTLEMENT: BARGAINING WITH AND WITHOUT SPECIAL OFFERS 2

B. Bargaining with Offer-of-Settlement Rules

Let us now turn to bargaining under an offer-of-settlement rule. We will start by setting forth a general result that will enable us to predict the outcome under any given offer-of-settlement rule. The subsequent analysis will use this basic lemma to derive the settlement outcome under several specific offer-of-settlement rules.
Suppose that one party may make one special offer at time t — 0, immediately before the first round of ordinary bargaining and before the first stage of litigation. First, let us assume that only one party may make such an offer and that this party will indeed mate this offer. Let S denote the amount proposed in this special offer. Later, in Section VI, we will extend our analysis to two-party rules, under which both parties can mate special offers.

## THE TERMS OF SETTLEMENT: BARGAINING WITH AND WITHOUT SPECIAL OFFERS

In this section, we examine the outcome of bargaining under two different regimes. First, we analyze bargaining in the absence of offer-of-settlement rules. Second, we will introduce the possibility of invoking offer-of-settlement rules.

## THE TERMS OF SETTLEMENT: FRAMEWORK OF ANALYSIS 3

Given that the parties are risk-neutral, the defendant seeks to minimize its expected costs (its litigation costs plus any payment to the plaintiff), and the plaintiff seeks to maximize its expected payoff (any payment from the defendant minus its litigation costs). Assume that the parties have no mechanism (such as a repeat player might develop by cultivating a reputation for intransigence) that would enable them to bind themselves to a particular bargaining strategy. That is, neither party can commit credibly to a strategy of intransigence, which would enable it to obtain a larger fraction of the gains from settlement. Thus, each party would accept an offer if and only if it were unable to improve its expected payoff by rejecting the offer instead.
For simplicity, assume that an offeror under any applicable offer-of-settlement rule makes a special offer at time t = 0 before the first stage of the litigation process, before the parties incur any litigation costs, and before the first round of ordinary bargaining. We can extend the analysis to include the case in which special offers can be made at later points in time.10 Given the opportunity to mate a special offer, the offeror would choose to mate an offer if and only if it were unable to improve its expected payoff by doing otherwise.

## THE TERMS OF SETTLEMENT: FRAMEWORK OF ANALYSIS 2

Both parties share the same expectation regarding the outcome at trial. Let us assume at first that the defendant concedes liability and the parties dispute only the amount of damages that the defendant should pay the plaintiff. Let D represent the damages that the court would award to the plaintiff at trial. From the perspective of the parties, D will be a random variable. Let D denote the expected value of D, where D > 0. Assume that D is distributed according to a continuous probability density function f(D). Assume also that the probability that D exceeds its mean equals the probability that it does not: that is, assume that Pr(D < D) = Pr(D > D) = Vi. We will later extend our analysis to include skewed distributions, for which Pr(D < D) 9* Vi, as well as disputes over liability.

Let J repre...

## THE TERMS OF SETTLEMENT: FRAMEWORK OF ANALYSIS

The analysis in this paper is organized as follows. Section II presents our framework of analysis. Section П1 analyzes bargaining both with and without offer-of-settlement rules and puts forward the basic lemma that subsequent sections will use to identify the outcome under particular offer-of-settlement rules. Section IV analyzes the case of one special offer and one-sided cost-shifting, Section V analyzes the case of one special offer and two-sided cost-shifting, and Section VI analyzes the case in which each side makes a special offer. Section VII addresses an important extension of the model. Section VIII considers the implications of the model for the outcomes under the existing Rule 68. Section IX discusses some implications for the design of offer-of-settlement rules. Finally, Section X concludes.

## THE TERMS OF SETTLEMENT: INTRODUCTION 4

The identification of the settlement amount expected under any given offer-of-settlement rule will enable us to examine: (i) which party benefits from each rule, and (ii) how the settlement amount compares with the expected judgment (that is, the mean amount that the parties expect the plaintiff to win at trial). The analysis shows, surprisingly, that a large set of seemingly different rules produce identical settlements.
Our model has important implications for both positive and normative analysis. The model enables us to derive not only the settlement outcomes that emerge under existing offer-of-settlement rules but also those that would occur under proposed offer-of-settlement rules (should they be adopted). This analysis is essential for any positive account of the outcomes produced by legal rules as well as for any normative evaluation of performance of these rules in producing desired outcomes.

## THE TERMS OF SETTLEMENT: INTRODUCTION 3

The economic analysis of Rule 68 and of similar offer-of-settlement rules has focused on the effect of such rules on the likelihood of settlement. Scholars have examined the claim that rules like Rule 68 increase the likelihood of settlement. In contrast to this literature, our focus is on the effects of such rules on the terms of settlement.
Understanding the effects of procedural rules and institutional arrangements on the terms of settlement is very important. The vast majority of cases end in settlement rather than in judgment. The main impact of the law on outcomes (and in turn on ex ante behavior) is therefore not directly through judgments rendered by courts but rather indirectly by shaping the terms of settlements. Thus, identifying the effects of the legal system on settlement terms is important for any positive or normative analysis of the outcomes produced by the system.