  The Adjusted Winner procedure is an important fair division mechanism
proposed by Brams and Taylor for allocating goods between two parties. 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 $\epsilon$-Nash equilibria for
each $\epsilon$ > 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.
