  There has been much work on exhibiting mechanisms that implement various
bargaining solutions, in particular, the Kalai-Smorodinsky solution
\cite{moulin1984implementing} and the Nash Bargaining solution. Another
well-known and axiomatically well-studied solution is the lexicographic maxmin
solution. However, there is no mechanism known for its implementation. To fill
this gap, we construct a mechanism that implements the lexicographic maxmin
solution as the unique subgame perfect equilibrium outcome in the n-player
setting. As is standard in the literature on implementation of bargaining
solutions, we use the assumption that any player can grab the entire surplus.
Our mechanism consists of a binary game tree, with each node corresponding to a
subgame where the players are allowed to choose between two outcomes. We
characterize novel combinatorial properties of the lexicographic maxmin
solution which are crucial to the design of our mechanism.
