Incremental cost sharing: Characterization by coalition strategy-proofness

Each one of n users consumes an idiosyncratic commodity produced in indivisible units. The n commodities are jointly produced by a central facility and total cost must be shared by the users. A "sequential stand alone mechanism" shares costs incrementally according to a fixed ordering of the users: the first user always pays stand alone cost, the second pays the stand alone cost of the first two users minus that of the first and so on. If the second derivatives of costs are of a constant sign, such a method yields a unique strong equilibrium at every profile of convex preferences in the game where each user chooses his own demand. This equilibrium, in turn, defines a coalition strategy-proof social choice function. Under decreasing marginal costs and submodular costs, the sequential stand alone mechanisms are almost characterized by these properties; the only exception is the binary demand case (each agent consumes zero or one unit) where a rich family of cost sharing methods (the Shapley value among them) yields a coalition strategy-proof equilibrium selection. Under increasing marginal costs and supermodular costs, coalition strategy-proofness characterizes a richer family of cost sharing methods: they give out one unit at a time while charging marginal costs, with the users taking turns according to a sequence fixed in advance. These methods contain serial cost sharing as a limit case.