Can the defendant gain by making a special offer that does not equal 100? The defendant cannot gain by making any offer greater than 100, because the plaintiff would accept such an offer,15 and as a result the defendant would have to pay more than 100. If the defendant made a special offer less than 100, then the plaintiff would reject. The defendant would then be more likely than the plaintiff to bear any litigation costs, the expected judgment would be greater than 100, and the threat point would favor the plaintiff in the ordinary bargaining that would follow. Thus, the defendant would expect to pay more than 100 in the settlement that would follow rejection of a special offer of less than 100.
Finally, if the plaintiff rather than the defendant makes the special offer, the same logic applies. If the plaintiff mates a special offer of 100, then the plaintiff will obtain 100 in a settlement. If the plaintiff were to mate any other special offer, then the plaintiff would receive less than 100 in a settlement.

Optional Offers

If the use of the offer-of-settlement rule is optional, then a party’s decision on whether to invoke the rule will depend on whether a special offer would improve the terms of settlement for the offeror. If the effect on these terms favors the defendant, then the defendant will gain from invoking an offer-of-settlement rule, but the plaintiff will not. If this effect favors the plaintiff instead, then the plaintiff will prefer not to use such a rule, but the defendant will prefer to do so. Thus:
Proposition 5: If an offer-of-settlement rule with two-sided cost shifting permits but does not require the party in question to make a special offer, then the party will mate such an offer if and only if its litigation costs are higher. Specifically:

(a) The defendant would choose to mate a special offer if and only if Cd > Cp.

(b) The plaintiff would choose to mate a special offer if and only if Cp > Cd.

If the party that has the option elects to mate a special offer, then the settlement will be S* = D.
Proof: See Appendix.
Remark: If we wanted to ensure that the parties settled for an amount equal to the expected damages, we could do so using either one of two offer-of-settlement rules: (i) we could require either one of the parties to mate a special offer that would trigger two-sided cost-shifting, or (ii) we could give the party with higher litigation costs the option of making such an offer. We could implement the second rule only if we know how Cp and Cd compare. The first rule does not require such knowledge.