If you're interested in that topic, you may want to look at Don't Try this at Home: The Troubling Distortion Of Rule 68 by Bradley Girard. Here's the abstract:
Rule 68 of the Federal Rules of Civil Procedure was enacted to promote consensual settlement. Through a mandatory cost-shifting mechanism, the Rule incentivizes defendants to make offers to settle and plaintiffs to accept those offers. Over the last few decades, courts of appeals have begun to interpret the Rule in away that goes beyond simply shifting costs. Instead, these courts have held that if a plaintiff refuses a Rule 68 offer that contains all of the monetary or injunctive relief that a plaintiff is seeking, her claim becomes moot. The courts will moot a plaintiff ’s claim even if the defendant’s offer disclaims liability. Mooting a claim because of an unaccepted Rule 68 offer is supported neither by the Rule’s text nor by the Supreme Court’s interpretation of the Rule. Although settlement is a laudable goal, it does not justify the labored reading of Rule 68 that deprives plaintiffs of their day in court.