In federal court—under Rule 68 of the Federal Rules of Civil Procedure—and in many states, there is an offer of judgment or offer of settlement procedure in which a party defending against a claim (defendant) may make an offer of judgment, or either party may make an offer of settlement.

If the party that receives the offer rejects it and does not win a better result at trial, the party who rejected the offer may be required to pay the offering party’s attorney fees and costs incurred after the offer was made.

An offer of judgment is an offer to allow a judgment to be taken against the party offering the judgment. An offer of judgment admits to liability and damages for a specific amount. An offer of settlement is similar but is in the form of an agreement or contract for settlement rather than a judgment from the court for the offered amount.

Laws vary from state to state and a state’s offer of judgment or offer of settlement procedure is usually located in its rules of civil procedure of code of civil procedure (statutes).

Under Rule 68 of the Federal Rules of Civil Procedure, a defendant in a federal court case can make an offer of judgment, and either party can make an offer of settlement. If the offeree rejects the offer and fails to obtain a more favorable judgment, they may be required to pay the offeror's post-offer attorney fees and costs. An offer of judgment is essentially an admission of liability for a certain amount, while an offer of settlement is a contractual agreement to settle. In Wyoming, the procedure for offers of judgment is governed by Wyoming Rules of Civil Procedure Rule 68, which mirrors the federal rule to some extent. However, state-specific nuances may exist, and it's important to consult with an attorney to understand the implications of making or responding to such offers in Wyoming state courts.