The Nash Bargaining Solution is Nash Implementable

Abstract

Some authors present models in which they show that the Nash bargaining solution fails to be Maskin monotonic and hence cannot be implemented in Nash equilibrium. We find this results misleading and discuss how implementability of the Nash bargaining solution can be discussed in utility space. Arguing that the status quo should be treated as initial endowments, we keep it fixed and show that with this assumption the Nash bargaining solution satisfies Maskin monotonicity. The key property used in the proof is independence of irrelevant alternatives which also turns out to be a necessary condition for implementability. We also show that the Nash bargaining solution satisfies a sufficient condition for implementability independent of the number of agents.