Are Nash bargaining wage agreements unique? An investigation into bargaining sets for firm-union negotiations

The shapes of the bargaining sets for firm-union negotiations are rigorously analyzed in two cases, according to whether bargaining is over wages alone (with employment set according to the labour demand schedule) or over both wages and employment. When bargaining concerns wages only the bargaining set becomes a one-dimensional curve, and so the standard theory of the Nash bargaining solution does not apply. Therefore existence and uniqueness conditions are proved directly. The Kalai-Smorodinsky solution is also analysed, and results are illustrated using a constant elasticity example.