# Asymmetric Nash Bargaining

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 :

1. Invariance
2. Symmetry
3. Pareto efficiency
4. 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?

• Please be more clear. What kind of axioms are you referring to, axioms related to what? (and I would suggest to edit your question rather than reply to this comment) – Alecos Papadopoulos May 16 '19 at 19:37
• Hello Alecos, the post has been edited. Thank you. – Kamel Ismaël May 17 '19 at 12:15
• I will probably provide an answer here, but you can find everything in the book, Roth A. E. (1979). Axiomatic models of bargaining. – Alecos Papadopoulos May 17 '19 at 18:43