Alternative Characterizations of the Proportional Solution for Nonconvex Bargaining Problems with Claims

We provide three alternative characterizations of the proportional solution defined on <i>compact</i> and <i>comprehensive</i> bargaining problems with claims that are not necessarily convex. One characterization result is obtained by using, together with other standard axioms, two solidarity axioms. Another characterization theorem shows that the single-valuedness axiom is dispensable even within the class of nonconvex problems if the standard symmetry axiom is imposed.