Truthful and Near-Optimal Mechanism Design via Linear Programming

Ron Lavi · Chaitanya Swamy

218 citations0/0 files storedAnnual Symposium on Foundations of Computer Science

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Auction Theory and Applications Complexity and Algorithms in Graphs Game Theory and Voting Systems

Abstract

We give a general technique to obtain approximation mechanisms that are truthful in expectation. We show that for packing domains, any /spl alpha/-approximation algorithm that also bounds the integrality gap of the IF relaxation of the problem by a can be used to construct an /spl alpha/-approximation mechanism that is truthful in expectation. This immediately yields a variety of new and significantly improved results for various problem domains and furthermore, yields truthful (in expectation) mechanisms with guarantees that match the best known approximation guarantees when truthfulness is not required. In particular, we obtain the first truthful mechanisms with approximation guarantees for a variety of multi-parameter domains. We obtain truthful (in expectation) mechanisms achieving approximation guarantees of O(/spl radic/m) for combinatorial auctions (CAs), (1 + /spl epsi/ ) for multiunit CAs with B = /spl Omega/(log m) copies of each item, and 2 for multiparameter knapsack problems (multiunit auctions). Our construction is based on considering an LP relaxation of the problem and using the classic VCG mechanism by W. Vickrey (1961), E. Clarke (1971) and T. Groves (1973) to obtain a truthful mechanism in this fractional domain. We argue that the (fractional) optimal solution scaled down by a, where a is the integrality gap of the problem, can be represented as a convex combination of integer solutions, and by viewing this convex combination as specifying a probability distribution over integer solutions, we get a randomized, truthful in expectation mechanism. Our construction can be seen as a way of exploiting VCG in a computational tractable way even when the underlying social-welfare maximization problem is NP-hard.

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References

1961COUNTERSPECULATION, AUCTIONS, AND COMPETITIVE SEALED TENDERS 1973Incentives in Teams 1971Multipart pricing of public goods 2001Algorithmic Mechanism Design 2002Truth revelation in approximately efficient combinatorial auctions 2001Truthful mechanisms for one-parameter agents 2005Combinatorial auctions with decreasing marginal utilities 2004Towards a characterization of truthful combinatorial auctions

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2009Approximate mechanism design without money 2006Truthful randomized mechanisms for combinatorial auctions 2010Asymptotically optimal strategy-proof mechanisms for two-facility games 2013Approximate Mechanism Design without Money 2006On maximizing welfare when utility functions are subadditive 2008Item pricing for revenue maximization 2009On Maximizing Welfare When Utility Functions Are Subadditive

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