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.


Suppose that a risk-neutral plaintiff files a suit against a risk-neutral defendant at time t = 0. Assume that unless the parties settle out of court, the court will render judgment. If the parties proceed all the way to judgment, then in the intervening time, the plaintiff incurs positive litigation costs in the amount Cp, and the defendant, in the amount Cd. The parties may incur different litigation costs. For example, they may differ in terms of the costliness of the evidence they must produce in court or in terms of how disruptive they find litigation to be. Let С denote the total litigation costs: С = Cp + Cd.
Assume that there are n stages to the litigation process, from the filing of a suit to judgment at trial, and that the parties’ litigation costs are spread over these n stages. At each stage i = 1, …, n, each party incurs some portion of its total litigation costs. Let cp‘ and cd‘ denote the litigation expenditures in stage i by the plaintiff and the defendant respectively. Assume that the court can observe these litigation costs and can therefore allocate these costs between the parties according to any applicable cost-shifting rule. Assume that the parties have identical discount rates and that all money values are expressed in terms of their present discounted value at time t = 0.