On demand responsiveness in additive cost sharing

Abstract

Under partial responsibility, the ranking of cost shares should never contradict that of demands.The Solidarity axiom says that if agent i demands more, j should not pay more if k pays less. It characterizes the quasi-proportional methods, sharing cost in proportion to `rescaled' demands. Full responsibility rules out cross-subsidization for additively separable costs. Restricting solidarity to submodular cost characterizes the fixed-flow methods, containing the Shapley–Shubik and serial methods. The quasi-proportional methods meet—but most fixed-flow methods fail— Group Monotonicity: if a group of agents increase their demands, not all of them pay less. Serial cost sharing is an exception.