Some bargaining solutions may remain unchanged under any extension of
a bargaining set which does not affect the utopia point, despite the fact that there
is room to improve the utility of at least one agent. We call this phenomenon the
stagnation effect. A bargaining solution satisfies stagnation proofness if it does not
suffer from the stagnation effect. We show that stagnation proofness is compatible
with the restricted version of strong monotonicity (Thomson and Myerson in Int J
Game Theory 9(1):37–49, 1980), weak Pareto optimality, and scale invariance. The
four axioms together characterize the family of the bargaining solutions generated by
strictly-increasing paths ending at the utopia point (SI PU P-solutions).

• Stagnation proofness in n-agent bargaining problems