Non-cooperative implementation of the nucleolus: The 3-player case

The paper presents a non-cooperative bargaining game, in which responders may exit at any time and have endogenous outside options. When the order of proposers corresponds to the power that players have in the underlying coalitional function, the unique Markov perfect equilibrium outcome of the game is the prenucleolus. The result holds for 3-player superadditive games. An example shows that it cannot be extended to the same class of games for n players. The mechanism is inspired by the consistency property of the prenucleolus.