With two-sided cost-shifting, it is no longer unambiguously in a party’s interest to mate a special offer to settle, because such an offer will entail the risk that costs will shift against that party. Consider first a scheme in which such an offer is mandatory for the party in question. We will subsequently consider a scheme in which the party chooses whether to mate such an offer.

A. Mandatory Offers

Suppose that either the defendant or the plaintiff must make a special offer. Applying
Lemma 1, we can show the following:
Proposition 4: If an offer-of-settlement rule with two-sided cost-shifting requires either party to make a special offer, then the settlement amount will be S* = D.
Proof: See Appendix.
Remark: To see the intuition for this result, consider our numerical example. Suppose the defendant must make a special offer. If the defendant offers 100 and the plaintiff rejects this offer, then the parties will be equally likely to bear any litigation costs. Once the scheme incorporates two-sided cost-shifting, it no longer matters which party would have larger litigation costs. Instead, expectations regarding the final allocation of the total litigation costs C, which would turn upon the trial outcome, will determine the terms of settlement under any subsequent ordinary bargaining. If either party mates a special offer of 100, then each side would be equally likely to bear these litigation costs, and therefore the expected judgment is simply 100. Thus, the parties will settle for 100 whether the offeree accepts or rejects the special offer.