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.

This paper provides a framework for identifying the terms of settlement under offer-of-settlement rules. To this end, we develop a model of bargaining that can be used to identify the settlement terms expected under such rules. Indeed, the paper derives a general result that enables us to identify the expected settlement terms under any given offer-of-settlement rule. We then apply this result to derive the outcomes under the most important of these rules.
An essential element of the framework we will develop is the effect of a special offer on any subsequent bargaining between the parties. If an offeree rejects a special offer, this rejection does not imply that the parties will not settle. The parties may still subsequently make ordinary settlement offers, as they could in the absence of a special offer, and thereby reach a settlement. The parties will conduct these settlement negotiations, however, in the shadow of a different threat point than they would in the absence of a special offer. The presence of a special offer will affect the expected payoffs for the parties if the case goes all the way to judgment at trial. Therefore, the outcome of the bargaining game that the parties would play if an offeree rejects a special offer is a function of the settlement amount proposed in the special offer. Thus, an offeror would make a special offer in light of its anticipated effect on subsequent bargaining.