Kalai–Smorodinsky bargaining solution

The Kalai–Smorodinsky (KS) bargaining solution is a solution to the Bargaining problem. It was suggested by Ehud Kalai and Meir Smorodinsky, as an alternative to Nash's bargaining solution suggested 25 years earlier. The main difference between the two solutions is that the Nash solution satisfies independence of irrelevant alternatives while the KS solution satisfies monotonicity.

A two-person bargain problem consists of a pair ${\displaystyle (F,d)}$:

It is assumed that the problem is nontrivial, i.e, the agreements in ${\displaystyle F}$ are better for both parties than the disagreement.

A bargaining solution is a function ${\displaystyle f}$ that takes a bargaining problem ${\displaystyle (F,d)}$ and returns a point in its feasible agreements set, ${\displaystyle f(F,d)\in F}$.

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