Derandomization of auctions

Aggarwal, Gagan; Fiat, Amos; Goldberg, Andrew V.; Hartline, Jason D.; Immorlica, Nicole; Sudan, Madhu

doi:10.1145/1060590.1060682

Cited by 44 publications

(83 citation statements)

References 18 publications

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“…1 Moulin actually pursues a different objective (also based on worst-case analysis): whereas our objective is to maximize the percentage of VCG payments that are redistributed, Moulin tries to minimize the overall payments from agents as a percentage of efficiency. It turns out that the resulting mechanisms are the same.…”

Section: Introductionmentioning

confidence: 99%

Worst-case optimal redistribution of VCG payments

Guo

Conitzer

2007

Proceedings of the 8th ACM Conference on Electronic Commerce

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For allocation problems with one or more items, the wellknown Vickrey-Clarke-Groves (VCG) mechanism is efficient, strategy-proof, individually rational, and does not incur a deficit. However, the VCG mechanism is not (strongly) budget balanced: generally, the agents' payments will sum to more than 0. If there is an auctioneer who is selling the items, this may be desirable, because the surplus payment corresponds to revenue for the auctioneer. However, if the items do not have an owner and the agents are merely interested in allocating the items efficiently among themselves, any surplus payment is undesirable, because it will have to flow out of the system of agents. In 2006, Cavallo [3] proposed a mechanism that redistributes some of the VCG payment back to the agents, while maintaining efficiency, strategy-proofness, individual rationality, and the non-deficit property. In this paper, we extend this result in a restricted setting. We study allocation settings where there are multiple indistinguishable units of a single good, and agents have unit demand. (For this specific setting, Cavallo's mechanism coincides with a mechanism proposed by Bailey in 1997 [2].) Here we propose a family of mechanisms that redistribute some of the VCG payment back to the agents. All mechanisms in the family are efficient, strategyproof, individually rational, and never incur a deficit. The family includes the Bailey-Cavallo mechanism as a special case. We then provide an optimization model for finding the optimal mechanism-that is, the mechanism that maximizes redistribution in the worst case-inside the family, and show how to cast this model as a linear program. We give both numerical and analytical solutions of this linear program, and the (unique) resulting mechanism shows significant improvement over the Bailey-Cavallo mechanism (in the worst case). Finally, we prove that the obtained mechanism is optimal among all anonymous deterministic mechanisms that satisfy the above properties.

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Section: Introductionmentioning

confidence: 99%

Worst-case optimal redistribution of VCG payments

Guo

Conitzer

2007

Proceedings of the 8th ACM Conference on Electronic Commerce

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“…1 Following the OR/CS literature this m factor is called the approximation ratio of the mechanism. Clearly, an m approximation ratio is a very large ratio.…”

Section: Background and Motivation Nisan And Ronenmentioning

confidence: 99%

Optimal Lower Bounds for Anonymous Scheduling Mechanisms

Ashlagi¹,

Dobzinski

Lavi

2012

Mathematics of OR

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We consider the problem of designing truthful mechanisms on m unrelated machines, to minimize some optimization goal. Nisan and Ronen (1999) consider the specific goal of makespan minimization, and show a lower bound of 2, and an upper bound of m. This large gap inspired many attempts that yielded positive results for several special cases, but very partial success for the general case: the lower bound was slightly increased to 2.61 by Christodoulou et al. (2007) and Koutsoupias and Vidali (2007), while the best upper bound remains unchanged. In this paper we show the optimal lower bound on truthful anonymous mechanisms: no such mechanism can guarantee an approximation ratio better than m. Moreover, our proof yields similar optimal bounds for two other optimization goals: the sum of completion times and the lp norm of the schedule.

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“…We stress the fact that the result of Aggarwal et al [1] is more general in the sense that it deals with bid-vectors in [1, h] n , while Theorem 1 only deals with discrete bid-vectors. Still, discrete bid-vectors make more sense in real life auctions, where for example, bids are being made in Dollars and Cents.…”

Section: Introductionmentioning

confidence: 97%

“…Still, discrete bid-vectors make more sense in real life auctions, where for example, bids are being made in Dollars and Cents. We also note that the construction used in the proof of Theorem 1 is not polynomial time computable and that this is also the case in the construction of Aggarwal et al [1].…”

Section: Introductionmentioning

confidence: 97%

“…They also proved that randomization is essential assuming the auction is symmetric (that is, assuming the outcome of the auction does not depend on the order of the input bids). Aggarwal et al [1] later showed how to construct from any randomized auction a deterministic, asymmetric auction with approximately the same revenue. More accurately, given a randomized auction A which accepts bid-vectors in [1, h] n , they constructed a deterministic, asymmetric auction In this paper we show that in the case where the bid-vectors come from [h] n , one can improve the construction of A D above so as to guarantee a better lower bound for P A D (b), for the cases where…”

Section: Introductionmentioning

confidence: 99%

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A New Derandomization of Auctions

Ben-Zwi

Newman

Wolfovitz

2009

Algorithmic Game Theory

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Abstract. Let A be a randomized, unlimited supply, unit demand, single-item auction, which given a bid-vector b ∈ [h] n , has expected profit E[P (b)]. Aggarwal et al. showed that given A, there exists a deterministic auction which given a bid-vector b, guarantees a profit ofIn this paper we show that given A, there exists a deterministic auction which given a bid-vector b of length n, guarantees a profit ofAs is the case with the construction of Aggarwal et al., our construction is not polynomial time computable.

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Derandomization of auctions

Cited by 44 publications

References 18 publications

Worst-case optimal redistribution of VCG payments

Worst-case optimal redistribution of VCG payments

Optimal Lower Bounds for Anonymous Scheduling Mechanisms

A New Derandomization of Auctions

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