Ultimatum Deadlines

A important characteristic of any offer is the deadline at which it expires. We consider an ultimatum deadline game in which the proposer’s decision variable is the offer deadline, while the responder faces a standard finite-horizon search problem. We show that the responder’s strategy is characterized by a shortest acceptable deadline: at the time of deadline, he accepts an offer if the deadline is longer than his shortest acceptable deadline, and rejects it otherwise. If the proposer has all information available to the responder, the optimal deadline is the responder’s shortest acceptable deadline. If the proposer is uncertain about the responder’s situation, the optimal deadline gets longer, unless this uncertainty is very large. After normative analysis of the deadline setting problem, we present results from a behavioral study of the game. The average shortest acceptable deadline set by the responders equals the one that would maximize the expected value, whereas the proposers tend to set deadlines that are too short. The prescriptive conclusion for a proposer, emerging from the model and the experiment, is that in case of uncertainty it is better to set a deadline longer than what would be optimal if uncertainty were ignored.