Ordinal invariance in multicoalitional bargaining

A multicoalitional bargaining problem is a non-transferable utility game and for each coalition, a bargaining rule. We look for ordinally invariant solutions to such problems and discover a subrule of Bennett's (1997, Games Econ. Behav. 19, 151–179) that satisfies the property. On a subclass of problems that is closely related to standard bargaining problems and allocation problems with majority decision-making, the two rules coincide. Therefore, Bennett solutions to such problems are immune to misrepresentation of cardinal utility information. We also show that Shapley–Shubik solution to any bargaining problem is the limit of a sequence of unique Bennett solutions to associated multicoalitional problems