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 wellknown 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.