On Nash Bargaining with Non-Transferable Utilities

We discuss the failure of the non-levelness of the bargaining set in bargaining problems appearing in a series of papers that study bargaining over quantity produced between a firm and a labor union. The associated bargaining does not feature transferable utilities and the disagreement point is chosen such that the bargaining set no longer satisfies non-levelness. The appeal of the Nash bargaining solution becomes questionable as this solution may not be sustained via a noncooperative game in subgame perfect equilibrium when non-levelness fails. We restore this condition in such bargaining problems and reinforce the justifiability of using the Nash bargaining solution in these environments