A Complete Characterization of Group‐Strategyproof Mechanisms of Cost‐Sharing

We study the problem of designing group‐strategyproof cost‐sharing mechanisms. The players report their bids for getting serviced and the mechanism decides a set of players that are going to be serviced and how much each one of them is going to pay. We determine three conditions: Fence Monotonicity, Stability of the allocation and Validity of the tie‐breaking rule that are necessary and sufficient for group‐strategyproofness, regardless of the cost function. Consequently, Fence Monotonicity characterizes group‐strategyproof cost‐sharing schemes closing an important open problem. Finally, we use our results to prove that there exist families of cost functions, where any group‐strategyproof mechanism has arbitrarily poor budget balance.