The Nash bargaining solution selects the unique solution to the maximization problem $\max_{s_1, s_2 } (s_1 - d_1) (s_2 - d_2)$ such that the solution satisfy the following axioms :
- Invariance
- Symmetry
- Pareto efficiency
- Independence of irrelevant alternatives
Does replacing the maximization problem by $\max_{s_1, s_2 } (s_1 - d_1)^{\alpha} (s_2 - d_2)^{1-\alpha}$ (i.e. give different bargaining power to the players) change the list of axioms satisfied by the former maximization problem ? From my understanding symmetry will be no longer be satisfied, but does that affect other axioms as well?