The power of two prices: Beyond cross-monotonicity

Abstract

Assuming strict consumer sovereignty (CS*), when can cost-sharing mechanisms simultaneously be group-strategyproof (GSP) and β-budget- balanced (β-BB)? Moulin mechanisms are GSP and 1-BB for submodular costs. We overcome the submodularity requirement and instead consider arbitrary-yet symmetric-costs: Already for 4 players, we show that symmetry of costs is not sufficient for the existence of a GSP and 1-BB mechanism. However, for only 3 players, we give a GSP and 1-BB mechanism. We introduce two-price cost-sharing forms (2P-CSFs) that define players' cost shares and present a novel mechanism that is GSP given any such 2P-CSF. For subadditive costs, we give an algorithm to compute 2P-CSFs that are √17+1/4-BB(≈ 1.28). This result is then shown to be tight for 2P-CSFs. Yet, this is a significant improvement over 2-BB, which is the best Moulin mechanisms can achieve. We give applications to the minimum makespan scheduling problem. A key feature of all our mechanisms is a preference order on the set of players. Higher cost shares are always payed by least preferred players. © Springer-Verlag Berlin Heidelberg 2007.