Abstract

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. 1

Citations

954	Counterspeculation, Auctions, and Competitive Sealed Tenders - Vickrey - 1961
914	Microeconomic Theory - Mas-Colell, Whinston, et al. - 1995
556	Multipart pricing of public goods - CLARKE - 1971
480	Algorithmic mechanism design - Nisan, Ronen
441	Incentives in Teams - GROVES - 1973
403	É.: How bad is selfish routing - Roughgarden, Tardos - 2002
348	Auction Theory - Krishna - 2010
302	Auction theory: a guide to the literature - Klemperer - 1999
190	A bgp-based mechanism for lowest-cost routing - Feigenbaum, Papadimitriou, et al. - 2002
150	T.: The price of stability for network design with fair cost allocation - Anshelevich, Dasgupta, et al. - 2008
150	E.: Truthful mechanisms for one-parameter agents - Archer, Tardos - 2001
138	Microeconomic Theory - Mas-Collel, Whinston, et al. - 1995
124	Algorithms, games and the Internet - Papadimitriou - 2001
122	Strategyproof sharing of submodular costs: budget balance versus efficiency - Moulin, Shenker - 2001
113	Competitive auctions and digital goods - Goldberg, Hartline, et al.
94	E.: Frugal path mechanisms - Archer, Tardos - 2002
73	Globally distributed computation over the internet-the popcorn project - Nisan, London, et al. - 1998
53	On certain connectivity properties of the internet topology - Mihail, Papadimitriou, et al. - 2003
53	QoS and fairness constrained convex optimization of resource allocation for wireless cellular and ad hoc networks - Julian, Chiang, et al.
46	K.: Frugality in path auctions - Elkind, Sahai, et al. - 2004
42	Linear programming and Vickrey auctions - Bikhchandani, Vohra, et al. - 2002
36	Virtual path bandwidth allocation in multiuser networks - Lazar, Orda, et al. - 1997
33	The price of truth: Frugality in truthful mechanisms - Talwar - 2003
32	Matroid Theory, (Oxford Science Publications - Oxley - 1992
31	Algorithms for selfish agents - mechanism design for distributed computation - Nisan - 1999
21	First-price path auctions - Immorlica, Karger, et al. - 2005
16	On the expected payment of mechanisms for task allocation - Czumaj, Ronen - 2004
13	Coalitional games on graphs: core structure, substitutes and frugality.” EC - Garg, Kumar, et al. - 2003
12	A contract and balancing mechanism for sharing capacity in a communication network - Anderson, Kelly, et al.