Beyond VCG: frugality of truthful mechanisms

We study truthful mechanisms for auctions in which the auctioneer is trying to hire a team of agents to perform a complex task, and paying them for their work. As common in the field of mechanism design, we assume that the agents are selfish and will act in such a way as to maximize their profit, which in particular may include misrepresenting their true incurred cost. Our first contribution is a new and natural definition of the frugality ratio of a mechanism, measuring the amount by which a mechanism "overpays ", and extending previous definitions to all monopoly-free set systems. After reexamining several known results in light of this new definition, we proceed to study in detail shortest path auctions and 'r-out-of-k sets" auctions. We show that when individual set systems (e.g., graphs) are considered instead of worst cases over all instances, these problems exhibit a rich structure, and the performance of mechanisms may be vastly different. In particular, we show that the well-known VCG mechanism may be far from optimal in these settings, and we propose and analyze a mechanism that is always within a constant factor of optimal.