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

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

doi:10.1007/978-3-319-66700-3_2

Cited by 2 publications

(1 citation statement)

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“…This methodology was initiated by Chen et al (2014) and Alaei et al (2019). Employing a similar approach, Birmpas et al (2017) recently obtained a tight price of anarchy for multi-unit auction. Our work further supports the power of this framework in proving tight bounds.…”

Section: Our Resultsmentioning

confidence: 99%

Tight Revenue Gaps among Simple Mechanisms

Jin

Tang

et al. 2019

Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms

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We consider a fundamental problem in microeconomics: selling a single item to a number of potential buyers, whose values are drawn from known independent and regular (not necessarily identical) distributions. There are four widely-used and widely-studied mechanisms in the literature: Myerson Auction (OPT), Sequential Posted-Pricing (SPM), Second-Price Auction with Anonymous Reserve (AR), and Anonymous Pricing (AP).OPT is revenue-optimal but complicated, which also experiences several issues in practice such as fairness; AP is the simplest mechanism, but also generates the lowest revenue among these four mechanisms; SPM and AR are of intermediate complexity and revenue. We explore revenue gaps among these mechanisms, each of which is defined as the largest ratio between revenues from a pair of mechanisms. We establish two tight bounds and one improved bound:1. SPM vs. AP: this ratio studies the power of discrimination in pricing schemes. We obtain the tight ratio of C * ≈ 2.62, closing the gap between e e−1 , e left before.2. AR vs. AP: this ratio measures the relative power of auction scheme vs. pricing scheme, when no discrimination is allowed. We attain the tight ratio of π 2 6 ≈ 1.64, closing the previously known bounds e e−1 , e .3. OPT vs. AR: this ratio quantifies the power of discrimination in auction schemes, and is previously known to be somewhere between 2, e . The lower-bound of 2 was conjectured to be tight by Hartline andRoughgarden (2009) and Alaei et al. (2015). We acquire a better lower-bound of 2.15, and thus disprove this conjecture.

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Section: Our Resultsmentioning

confidence: 99%