<p>The Nash bargaining solution selects the unique solution to the maximization problem <span class="math-container">$\max_{s_1, s_2 } (s_1 - d_1) (s_2 - d_2)$</span> such that the solution satisfy the following axioms : </p>

<ol>
<li>Invariance </li>
<li>Symmetry </li>
<li>Pareto efficiency</li>
<li>Independence of irrelevant alternatives</li>
</ol>

<p>Does replacing the maximization problem by <span class="math-container">$\max_{s_1, s_2 } (s_1 - d_1)^{\alpha}  (s_2 - d_2)^{1-\alpha}$</span>  (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? </p>

CC BY-SA 4.0
2019-05-16T19:37:36.120Z
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
CC BY-SA 4.0
2019-05-17T12:15:56.230Z
Hello Alecos, the post has been edited. Thank you.
Kamel Ismaël
CC BY-SA 4.0
2019-05-17T18:43:03.677Z
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
CC BY-SA 4.0
2023-03-01T11:24:56.117Z
I believe, it depends on the choice of restrictions on $\alpha$. If $\alpha \ge 0$, then for some zero weights there may not be enough "pressure" on maximizing all components and Pareto efficiency may fail. If instead, $\alpha > 0$, the solution is stronger and does not include corner points where some players get exactly the disagreement payoff (this property is sometimes called Strong Individual Rationality).
kitsune
<microeconomics><game-theory><labor-economics><nash-equilibrium><bargaining>
Asymmetric Nash Bargaining
Kamel Ismaël
# Asymmetric Nash Bargaining

(Asked by: username_0 on 2019-05-16)

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?

**Tags:** microeconomics, game-theory, labor-economics, nash-equilibrium, bargaining

> **Comments:**
> **username_1**: 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)  
> **username_0**: Hello username_1, the post has been edited. Thank you.  
> **username_1**: I will probably provide an answer here, but you can find everything in the book,  Roth A. E. (1979). Axiomatic models of bargaining.  
> **username_2**: I believe, it depends on the choice of restrictions on $\alpha$. If $\alpha \ge 0$, then for some zero weights there may not be enough "pressure" on maximizing all components and Pareto efficiency may fail. If instead, $\alpha > 0$, the solution is stronger and does not include corner points where some players get exactly the disagreement payoff (this property is sometimes called Strong Individual Rationality).  

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## 0 answers

