Bargaining with an Endogenous Deadline

We study a sequential bargaining game with a deadline from which the size of the cake decays. Two bargaining procedures are considered: a model with alternating-offers and a model with iterated simultaneous demands. We show that the bargaining game with alternating-offers has a unique SPE outcome, while the game with iterated demands possesses a unique Pareto robust-SPE outcome. Then, we endogenize the choice of the deadline: the bargaining game with alternating-offers is characterized by a deadline effect, whereas the other game is not. That is, once we endogenize the deadline, the occurrence of a deadline effect depends on the bargaining procedure used. But as the bargaining period goes to zero, the unique SPE outcome of the game with alternating-offers approaches the unique Pareto robust-SPE outcome of the game with iterated demands.