Inapproximability for VCG-Based Combinatorial Auctions

Buchfuhrer, Dave; Dughmi, Shaddin; Fu, Hengzhi; Kleinberg, Robert; Mossel, Elchanan; Papadimitriou, Christos; Schapira, Michael; Singer, Yoram; Umans, Christopher

doi:10.1137/1.9781611973075.45

Cited by 32 publications

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“…Unfortunately, several recent impossibility results have shed serious doubt on the possibility of this goal in general [15,47,7,8,12,25,20]. 3 This paper provides such positive results for welfare maximization in CAs and CPPs for a fundamental class of valuations, via a novel randomized mechanism design framework based on convex optimization.…”

Section: Combinatorial Auctions and Combinatorial Public Projectsmentioning

confidence: 97%

“…Since then, combinatorial auctions and combinatorial public projects have emerged as the paradigmatic "challenge problems" of the field, with much work in recent years establishing upper and lower bounds on truthful polynomial-time mechanisms for these problems (e.g. [36,16,18,17,15,11,19,47,7,8,12,24,21,25,20]). The most general approach known for designing (randomized) truthful mechanisms is via maximal-in-distributional range (MIDR) algorithms [13,22].…”

Section: The Challenge Of Algorithmic Mechanism Designmentioning

confidence: 99%

“…CGS valuations include most concrete examples of monotone submodular valuations that appear in the literature, including coverage functions. 7 Moreover, if P = N P and without regard to incentive-compatibility, 1 − 1/e is the best approximation possible in polynomial time for combinatorial auctions [35] when players have CGS valuations and for combinatorial public projects [48] even when players have GS valuations. 8 That said, we note that some interesting submodular functions -such as some budget additive functions 9 -are not in the CGS family (see Appendix B.3).…”

Section: Gross Substitutes and Cgs Valuationsmentioning

confidence: 99%

See 2 more Smart Citations

Optimal Mechanisms for Combinatorial Auctions and Combinatorial Public Projects via Convex Rounding

Dughmi

Roughgarden

Yan

2016

J. ACM

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We design the first truthful-in-expectation, constant-factor approximation mechanisms for N P -hard cases of the welfare maximization problem in combinatorial auctions with non-identical items and in combinatorial public projects. Our results apply to bidders with valuations that are nonnegative linear combinations of gross substitutes valuations, a class that encompasses many of the most well-studied subclasses of submodular functions, including coverage functions and weighted matroid rank functions. Our mechanisms have expected polynomial running time and achieve an approximation factor of 1 − 1/e. This approximation factor is the best possible for both problems, even for known and explicitly given coverage valuations, assuming P = N P . Recent impossibility results suggest that our results cannot be extended to a significantly larger valuation class.Both of our mechanisms are instantiations of a new framework for designing approximation mechanisms based on randomized rounding algorithms. The high-level idea of this framework is to optimize directly over the (random) output of the rounding algorithm, rather than the usual (and rarely truthful) approach of optimizing over the input to the rounding algorithm. This framework yields truthful-in-expectation mechanisms, and these mechanisms can be implemented efficiently when the corresponding objective function is concave. For bidders with valuations in the cone generated by gross substitutes valuations, we give novel randomized rounding algorithms that lead to both a concave objective function and a (1 − 1/e)-approximation of the optimal welfare. * Preliminary versions of this work appeared in

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Section: Combinatorial Auctions and Combinatorial Public Projectsmentioning

confidence: 97%

Section: The Challenge Of Algorithmic Mechanism Designmentioning

confidence: 99%

Section: Gross Substitutes and Cgs Valuationsmentioning

confidence: 99%

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Optimal Mechanisms for Combinatorial Auctions and Combinatorial Public Projects via Convex Rounding

Dughmi

Roughgarden

Yan

2016

J. ACM

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“…The latter property is crucial for truthfulness of our mechanisms, and we provide an example that our approach is not truthful if constraints are also private. Among other things, this implies that our mechanisms cannot be directly applied to combinatorial auctions with budgetadditive valuations [Buchfuhrer et al 2010;Chakrabarty and Goel 2010], which can be modeled via GAP with private constraints.…”

Section: Contribution and Overviewmentioning

confidence: 99%

Truthful mechanism design via correlated tree rounding

et al. 2016

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One of the most powerful algorithmic techniques for truthful mechanism design are maximal-indistributional-range (MIDR) mechanisms. Unfortunately, many algorithms using this paradigm rely on heavy algorithmic machinery and require the ellipsoid method or (approximate) solution of convex programs. In this paper, we present a simple and natural correlated rounding technique for designing mechanisms that are truthful in expectation. Our technique is elementary and can be implemented quickly. The main property we rely on is that the domain offers fractional optimum solutions with a tree structure.In auctions based on the generalized assignment problem, each bidder has a publicly known knapsack constraint that captures the subsets of items that are of value to him. He has a private valuation for each item and strives to maximize the value of assigned items minus payment. For this domain we design a mechanism for social welfare maximization. Our technique gives a truthful 2-approximate MIDR mechanism without using the ellipsoid method or convex programming. In contrast to some previous work, our mechanism achieves exact truthfulness.In restricted-related scheduling with selfish machines, each job comes with a public weight, and it must be assigned to a machine from a public job-specific subset. Each machine has a private speed and strives to maximize payments minus workload of jobs assigned to it. For this domain we design a mechanism for makespan minimization. Although this is a single-parameter domain, the approximation status of the underlying optimization problem is similar to unrelated scheduling: The best known algorithm gives a (nontruthful) 2-approximation for unrelated machines, and there is 1.5-hardness. Our mechanism matches this bound and provides a truthful 2-approximation.

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“…This fact was first established by Lavi, Mu'alem, and Nisan [19], and Papadimitriou, Schapira, and Singer [24] gave a quantitatively much stronger version of this lower bound. Additional evidence of the difficulty of multiparameter mechanism design was provided in [9] and [5] in the context of combinatorial auctions. These negative results do not apply to randomized mechanisms, however, and Dobzinski and Dughmi [7] showed that, for a variant of multi-unit auctions, truthful-in-expectation mechanisms are strictly more powerful than deter-ministic ones.…”

mentioning

confidence: 99%

Black-Box Randomized Reductions in Algorithmic Mechanism Design

Dughmi¹,

Roughgarden²

2014

SIAM J. Comput.

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Abstract. We give the first black-box reduction from approximation algorithms to truthful approximation mechanisms for a non-trivial class of multi-parameter problems. Specifically, we prove that every welfare-maximization problem that admits a fully polynomial-time approximation scheme (FPTAS) and can be encoded as a packing problem also admits a truthful-in-expectation randomized mechanism that is an FPTAS. Our reduction makes novel use of smoothed analysis by employing small perturbations as a tool in algorithmic mechanism design. We develop a "duality" between linear perturbations of the objective function of an optimization problem and of its feasible set, and we use the "primal" and "dual" viewpoints to prove the running time bound and the truthfulness guarantee, respectively, for our mechanism.

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Inapproximability for VCG-Based Combinatorial Auctions

Cited by 32 publications

References 0 publications

Optimal Mechanisms for Combinatorial Auctions and Combinatorial Public Projects via Convex Rounding

Optimal Mechanisms for Combinatorial Auctions and Combinatorial Public Projects via Convex Rounding

Truthful mechanism design via correlated tree rounding

Black-Box Randomized Reductions in Algorithmic Mechanism Design

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