A complete characterization of group-strategyproof mechanisms of cost-sharing

TL;DR

This paper characterizes all group-strategyproof cost-sharing mechanisms through three key conditions, providing a complete theoretical framework and revealing limitations in approximation ratios for certain cost functions.

Contribution

It introduces Fence Monotonicity, Stability, and Validity as necessary and sufficient conditions for group-strategyproofness, fully characterizing such mechanisms.

Findings

Fence Monotonicity characterizes group-strategyproof cost-sharing schemes.

Conditions are independent of the specific cost functions.

Existence of cost functions where mechanisms have unbounded approximation ratios.

Abstract

We study the problem of designing group-strategyproof cost-sharing mechanisms. The players report their bids for getting serviced and the mechanism decides which players are going to be serviced and how much each one of them is going to pay. We determine three conditions: \emph{Fence Monotonicity}, \emph{Stability} of the allocation and \emph{Validity} of the tie-breaking rule that are necessary and sufficient for group-strategyproofness, regardless of the cost function. Fence Monotonicity puts restrictions only on the payments of the mechanism and stability only on the allocation. Consequently Fence Monotonicity characterizes group-strategyproof cost-sharing schemes. Finally, we use our results to prove that there exist families of cost functions, where any group-strategyproof mechanism has unbounded approximation ratio.