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Implementing the Lexicographic Maxmin Bargaining Solution

Research paper by Ashish Goel, Anilesh K. Krishnaswamy

Indexed on: 01 Oct '18Published on: 01 Oct '18Published in: arXiv - Computer Science - Computer Science and Game Theory



Abstract

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.