Bargaining with Independence of Higher or Irrelevant Claims

This paper studies independence of higher claims and independence of irrelevant
claims on the domain of bargaining problems with claims. Independence of higher
claims requires that the payoff of an agent does not depend on the higher claim of
another agent. Independence of irrelevant claims states that the payoffs should not
change when the claims decrease but remain higher than the payoffs. Interestingly, in conjunction with standard axioms from bargaining theory, these properties characterize a new constrained Nash solution, a constrained Kalai-Smorodinsky solution, and a constrained Kalai solution.