Patience and ultimatum in bargaining

This study investigates in a two-stage two-player model how the decision to make an ultimatum and how much to demand depends on the impatience of the agents and the pie uncertainty. First, players simultaneously decide on their ultimatums. If the ultimatum(s) are compatible then the player(s) receive his (their) demand(s) in the second period and the eventually remaining player becomes residual claimant. If no ultimatums are made then there is a Rubinstein-Ståhl bargaining. Relative impatience induces ultimatums but does not affect the demanded amount. In a discrete (continuous) setting there exist no equilibrium without an ultimatum (with mutual ultimatums).