Tight Welfare Guarantees for Pure Nash Equilibria of the Uniform Price Auction

Birmpas, Georgios; Markakis, Evangelos; Telelis, Orestis; Tsikiridis, Artem

doi:10.1007/s00224-018-9889-7

Cited by 3 publications

(8 citation statements)

References 15 publications

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“…The authors prove a clear separation for the POA in single-item first-price auctions: While the CE-POA is 1 (even with overbidding), the CCE-POA increases to 1.229 (without overbidding) and e/(e − 1) (with overbidding). A similar separation holds for the multi-unit auction setting and the uniform price auction, where the PNE-POA is (e − 1)/e (without overbidding) [12] and 2.1885 (with overbidding) [1]. Our results contribute to this line of research also because we show that the POA might improve significantly under the no-overbidding assumption.…”

Section: Introductionsupporting

confidence: 74%

“…We show that the pure POA (PNE-POA) of γ-Hybrid in the multi-unit auction setting is 1 for γ ∈ (0, 1). This result is complemented by PNE-POA = 2.1885 for γ = 0 [1] and PNE-POA = 1 for γ = 1 [4]. Note that this reveals an interesting transition at γ = 0.…”

Section: Introductionmentioning

confidence: 70%

“…Pure Price of Anarchy. The pure price of anarchy of γ-Hybrid without overbidding has been analyzed before for γ = 0 and γ = 1: Birmpas et al [1] show that the PNE-POA is 2.1885 for the second-price multi-unit auction (γ = 0), while de Keijzer et al [4] show that the PNE-POA is 1 for the first-price multi-unit auction (γ = 1). Interestingly, we do not find a smooth interpolation between these two boundary points when analyzing the PNE-POA for the range γ ∈ [0, 1].…”

Section: Multi-unit Auctionmentioning

confidence: 99%

“…Note that implicitly we make the following assumptions (see also [10]): (1) The auction is "semi-open" in the sense that at some stage a sealed bid part as described above takes place. In fact, in practice many auctions have this characteristic.…”

Section: Introductionmentioning

confidence: 99%

“…For the more general class of subadditive valuations, the POA of Bayes-Nash equilibria for the first-price multi-unit auction is 2, which follows from [3] and [2]. Birmpas et al [1] recently settled the PNE-POA of the second-price multi-unit auction and show that it is 2.1885.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Corruption in Auctions: Social Welfare Loss in Hybrid Multi-Unit Auctions

Beek¹,

Brokkelkamp²,

Schäfer³

2021

Preprint

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Corruption in auctions is a phenomenon that is theoretically still poorly understood, despite the fact that it occurs rather frequently in practice. In this paper, we initiate the study of the social welfare loss caused by a corrupt auctioneer, both in the single-item and the multi-unit auction setting. In our model, the auctioneer may collude with the winners of the auction by letting them lower their bids in exchange for a fixed fraction γ of the surplus. As it turns out, this setting is equivalent to a γ-hybrid auction in which the payments are a convex combination (parameterized by γ) of the first-price and the second-price payments. Our goal is thus to obtain a precise understanding of the (robust) price of anarchy of γ-hybrid auctions. If no further restrictions are imposed on the bids, we prove a bound on the robust POA which is tight (over the entire range of γ) for the singleitem and the multi-unit auction setting. On the other hand, if the bids satisfy the no-overbidding assumption a more fine-grained landscape of the price of anarchy emerges, depending on the auction setting and the equilibrium notion. We derive tight bounds for single-item auctions up to the correlated price of anarchy and for the pure price of anarchy in multi-unit auctions. These results are complemented by nearly tight bounds on the coarse correlated price of anarchy in both settings.

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Section: Introductionsupporting

confidence: 74%

Section: Introductionmentioning

confidence: 70%