On the strategic role of outside options in bilateral bargaining

This paper studies a model of the situation in which two players are bargaining face-to-face over the partition of a unit size cake and, moreover, one of the players can choose to temporarily leave the negotiating table to search for an outside option. A main conclusion is that the equilibrium outcome does not depend on whether a bargainer is allowed (within the game form) to choose to return to the negotiating table to resume bargaining after having searched for some finite time. Moreover, it is shown that our strategic bargaining-search game approximately implements an appropriately defined Nash bargaining solution.