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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?

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    $\begingroup$ 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) $\endgroup$
    – Alecos Papadopoulos
    May 16, 2019 at 19:37
  • $\begingroup$ Hello Alecos, the post has been edited. Thank you. $\endgroup$
    – Kamel Ismaël
    May 17, 2019 at 12:15
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    $\begingroup$ I will probably provide an answer here, but you can find everything in the book, Roth A. E. (1979). Axiomatic models of bargaining. $\endgroup$
    – Alecos Papadopoulos
    May 17, 2019 at 18:43

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