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.

A. Bargaining Without Offer-of-Settlement Rules

Consider bargaining in the absence of any offer-of-settlement rules. Let В represent the expected outcome of such an ordinary bargaining game. That is, let В denote the amount that the defendant can expect to pay the plaintiff in a settlement, which we can express as a function of D. We can derive the expected settlement amount B(D) as the solution to this bargaining game.
Proposition 1: The parties will settle in the first round of bargaining, and the expected settlement amount would be:
Proof: See Appendix.
Remark: Note that the parties each receive their expected payoff from trial (net of litigation costs) plus a share of the surplus obtained through agreement. They divide this surplus — that is, the total litigation costs avoided by settlement, С = Cd + Cp – equally. This outcome is the same as under the Nash bargaining solution.
The settlement outcome will be more favorable to the plaintiff than one would expect the judgment itself to be if and only if Cd > Cp. Conversely, the settlement would be less favorable to the plaintiff if and only if the opposite inequality holds. Compared with the expected judgment D, the expected settlement amount B(D) will favor the party with lower litigation costs.
Example: To illustrate this effect, consider our numerical example, in which Cd < Cp. In that case, the expected settlement would be B(D) = 80, which is less than 100, the expected judgment. Thus, B(D) < D, and compared to the expected judgment, the expected settlement would favor the defendant.