After an action for the recovery of money is brought, the defendant may offer in court to confess judgment for part of the amount claimed, or part of the causes involved in the action. Whereupon, if the plaintiff, being present, refuses to accept such confession of judgment in full of his demands against the defendant in the action, or, having had such notice that the offer would be made, of its amount and of the time of making it, as the court shall deem reasonable, fail to attend, and on the trial do not recover more than was so offered to be confessed, such plaintiff shall pay all the costs of the defendant incurred after the offer. The offer shall not be deemed to be an admission of the cause of action or amount to which the plaintiff is entitled, nor be given in evidence upon the trial.