The ultimatum game with externalities

Abstract

This paper examines the equilibrium properties of an ultimatum game model with externalities. Unlike the equilibrium of the traditional version of this game and even recent extensions of it in a similar direction as ours, three novel results may emerge: (i) a negotiation breakdown, (ii) a perfectly equitable sharing solution, and (iii) a solution in which the responder gets a higher fraction of the pie under division than the proposer. It is shown that whereas the first result depends on the externality level suffered by both players, the two last, conditional on that an agreement exists, only depend on the responder's externality level. It is further argued that these results can be especially relevant in negotiations involving interpersonal interactions and resolution of highly polarized conflicts.