N.Y. CVP Law § 3220

Rule 3220. Offer to liquidate damages conditionally. At any time not\nlater than ten days before trial, any party against whom a cause of\naction based upon contract, express or implied, is asserted may serve\nupon the claimant a written offer to allow judgment to be taken against\nhim for a sum therein specified, with costs then accrued, if the party\nagainst whom the claim is asserted fails in his defense. If within ten\ndays thereafter the claimant serves a written notice that he accepts the\noffer, and damages are awarded to him on the trial, they shall be\nassessed in the sum specified in the offer. If the offer is not so\naccepted and the claimant fails to obtain a more favorable judgment, he\nshall pay the expenses necessarily incurred by the party against whom\nthe claim is asserted, for trying the issue of damages from the time of\nthe offer. The expenses shall be ascertained by the judge or referee\nbefore whom the case is tried. An offer under this rule shall not be\nmade known to the jury.\n