A 'divide and choose' approach to compromising

We study dispute resolution in the compromise model of Borgers and Postl (2009), which provides an alternative framework for analyzing the real-world procedure of tri-offer arbitration studied in Ashenfelter et al (1992). Two parties involved in a dispute have to choose between their conflicting positions and a compromise settlement proposed by a neutral mediator. We ask how an adaptation of the familiar `divide and choose' mechanism (DCM) performs as a protocol for dispute resolution in the absence of an arbitrator. We show that there is a unique equilibrium of the DCM if the parties' von Neumann Morgenstern utilities from the compromise settlement are drawn independently from a concave distribution, or from any Beta-distribution (which need not be concave). Furthermore, for Beta-distributions that concentrate increasing probability mass on high von Neumann Morgenstern utilities of the compromise, the social choice rule implied by the DCM is asymptotically ex post Pareto efficient.