The first full characterization of social choice correspondences that are implementable in Nash equilibrium, given in Moore and Repullo (1990), together with the working principle behind an algorithm to check this condition, given in Sjöström (1991), can be used to give a simple necessary and...

Three alternative characterizations of the proportional solution defined on compact and comprehensive bargaining problems with claims are provided. Two new contraction-type and expansion-type axioms are used. Moreover, the single-valuedness axiom is dispensable if the classical symmetry axiom is...