We introduce an arbitrator into a well-known bilateral bargaining game (see Nash Econometrica 21:128–140, 1953). This arbitrator (i) (optimally) splits a unit-size pie into two pieces, k and \(1-k\) , (ii) lets players divide k in a simultaneous-move bargaining game, and then (iii) assigns an ultimatum power to the less greedy player in that game in the division of the remaining portion. Our modeling choices are motivated by gradualism (step-by-step approach), reasonableness (no severe punishment), and promotion of agreeableness (assigning favorable roles to more agreeable parties). We assume that the arbitrator aims to induce a particular division of the pie. We characterize his optimal split of the pie that eventually induces the desired division as the unique equilibrium outcome. Our results highlight a road map to resolve bargaining conflicts while respecting various procedural justice and efficiency concerns.
