Stagnation proofness and individually monotonic bargaining solutions

The aim of this paper is to generalize the results of Peter and Tijs [10] and [9]. We propose a characterization that holds both for n-agent problems and for a larger class of problems. The axioms used in our characterization are weaker because they are implied by the characterization in the aforementioned references. We analyze a phenomenon known as stagnation effect, which takes place when a bargaining solution remains unchanged facing all possible expansions of the bargaining set not affecting the utopia point. Our main result relies on a very weak axiom, stagnation proofness. Whenever a bargaining solution satisfies this axiom, such solution does not suffer from the stagnation effect.