The Adjusted Winner Procedure: Characterizations and Equilibria

Abstract

The Adjusted Winner procedure is an important mechanism proposed by Brams and Taylor for fairly allocating goods between two agents. It has been used in practice for divorce settlements and analyzing political disputes. Assuming truthful declaration of the valuations, it computes an allocation that is envy-free, equitable and Pareto optimal. We show that Adjusted Winner admits several elegant characterizations, which further shed light on the outcomes reached with strategic agents. We find that the procedure may not admit pure Nash equilibria in either the discrete or continuous variants, but is guaranteed to have ε-Nash equilibria for each ε > 0. Moreover, under informed tie-breaking, exact pure Nash equilibria always exist, are Pareto optimal, and their social welfare is at least 3/4 of the optimal.