2016 New York Laws
CVP - Civil Practice Law & Rules
Article 32 - (Civil Practice Law & Rules) ACCELERATED JUDGMENT
R3220 - Offer to liquidate damages conditionally.

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