Posted Price Mechanisms for a Random Stream of Customers

Correa, José R.; Foncea, Patricio; Hoeksma, Ruben; Oosterwijk, Tim; Vredeveld, Tjark

doi:10.1145/3033274.3085137

Cited by 92 publications

(77 citation statements)

References 23 publications

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“…In general single-parameter environments with matroid feasibility constraints (this includes the single item setting we study as a special case), Chawla et al (2010) showed the the revenue of an ESP that uses the posted prices of an SPM as its personalized reserve prices is at least as high as the SPM's revenue. This, combined with the recent result of Correa et al (2017) showing that SPM can achieve a 0.745 fraction of MyeRev in the i.i.d. setting with possibly irregular distributions, shows that ESP can also achieve at least a 0.745 approximation factor in the i.i.d.…”

Section: Introductionsupporting

confidence: 72%

“…In this paper we establish the first separation results for ESP: we show that even in the case of distributions drawn i.i.d., but not necessarily satisfying the regularity condition, the ESP cannot achieve more than a 0.778 fraction of MyeRev in general. Combined with the result from Correa et al (2017) that ESP can achieve at least a 0.745 fraction of MyeRev, this nearly bridges the gap between upper and lower bounds on ESP's approximation factor. * Google Research.…”

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confidence: 62%

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Separation between second price auctions with personalized reserves and the revenue optimal auction

Sivan

2020

Operations Research Letters

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What fraction of the single item n buyers setting's expected optimal revenue (MyeRev) can the second price auction with reserves achieve? In the special case where the buyers' valuation distributions are all drawn i.i.d. and the distributions satisfy the regularity condition, the second price auction with an anonymous reserve (ASP) is the optimal auction itself. As the setting gets more complex, there are established upper bounds on the fraction of MyeRev that ASP can achieve. On the contrary, no such upper bounds are known for the fraction of MyeRev achievable by the second price auction with eager personalized reserves (ESP). In particular, no separation was earlier known between ESP's revenue and MyeRev even in the most general setting of non-identical product distributions that don't satisfy the regularity condition. In this paper we establish the first separation results for ESP: we show that even in the case of distributions drawn i.i.d., but not necessarily satisfying the regularity condition, the ESP cannot achieve more than a 0.778 fraction of MyeRev in general. Combined with the result from Correa et al. (2017) that ESP can achieve at least a 0.745 fraction of MyeRev, this nearly bridges the gap between upper and lower bounds on ESP's approximation factor. * Google Research. willma@google.com. † Google Research. balusivan@google.com.

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Section: Introductionsupporting

confidence: 72%

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confidence: 62%

Separation between second price auctions with personalized reserves and the revenue optimal auction

Sivan

2020

Operations Research Letters

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“…Going beyond 1 − 1/e has been challenging. Only recently, Abolhasani et al [1] and Correa et al [8] improve this factor for the single item i.i.d. setting.…”

Section: Related Workmentioning

confidence: 99%

Prophet Secretary for Combinatorial Auctions and Matroids

Ehsani¹,

Hajiaghayi²,

Keßelheim³

et al. 2018

Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms

108

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The secretary and the prophet inequality problems are central to the field of Stopping Theory. Recently, there has been a lot of work in generalizing these models to multiple items because of their applications in mechanism design. The most important of these generalizations are to matroids and to combinatorial auctions (extends bipartite matching). and Feldman et al. [17] show that for adversarial arrival order of random variables the optimal prophet inequalities give a 1/2-approximation. For many settings, however, it's conceivable that the arrival order is chosen uniformly at random, akin to the secretary problem. For such a random arrival model, we improve upon the 1/2-approximation and obtain (1 − 1/e)-approximation prophet inequalities for both matroids and combinatorial auctions. This also gives improvements to the results of Yan [45] and Esfandiari et al. [15] who worked in the special cases where we can fully control the arrival order or when there is only a single item.Our techniques are threshold based. We convert our discrete problem into a continuous setting and then give a generic template on how to dynamically adjust these thresholds to lower bound the expected total welfare.

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“…In terms of upper bounds it was unclear until very recently whether there was a separation between prophet secretary and the i.i.d prophet inequality, where the random variables are identically distributed. For this problem, Hill ad Kertz [18] provided the family of worst possible instances from which [20] proved the largest possible bound one could expect is 0.7451 and Correa et al [6] proved that this value is actually tight. Very recently, Correa et al show that no algorithm can achieve an approximation factor better than √ 3 − 1 ≈ 0.71 for the prophet secretary problem (see the full version of [9]).…”

Section: Introductionmentioning

confidence: 99%

The Two-Sided Game of Googol and Sample-Based Prophet Inequalities

Correa¹,

Cristi²,

Epstein³

et al. 2020

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

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The secretary problem or the game of Googol are classic models for online selection problems that have received significant attention in the last five decades. In this paper we consider a variant of the problem and explore its connections to data-driven online selection. Specifically, we are given n cards with arbitrary non-negative numbers written on both sides. The cards are randomly placed on n consecutive positions on a table, and for each card, the visible side is also selected at random. The player sees the visible side of all cards and wants to select the card with the maximum hidden value. To this end, the player flips the first card, sees its hidden value and decides whether to pick it or drop it and continue with the next card.We study algorithms for two natural objectives. In the first one, similar to the secretary problem, the player wants to maximize the probability of selecting the maximum hidden value. We show that this can be done with probability at least 0.45292. In the second objective, similar to the prophet inequality, the player wants to maximize the expectation of the selected hidden value. Here we show a guarantee of at least 0.63518 with respect to the expected maximum hidden value.Our algorithms result from combining three basic strategies. One is to stop whenever we see a value larger than the initial n visible numbers. The second one is to stop the first time the last flipped card's value is the largest of the currently n visible numbers in the table. And the third one is similar to the latter but to stop it additionally requires that the last flipped value is larger than the value on the other side of its card.We apply our results to the prophet secretary problem with unknown distributions, but with access to a single sample from each distribution. In particular, our guarantee improves upon 1 − 1/e for this problem, which is the currently best known guarantee and only works for the i.i.d. prophet inequality with samples.

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Posted Price Mechanisms for a Random Stream of Customers

Cited by 92 publications

References 23 publications

Separation between second price auctions with personalized reserves and the revenue optimal auction

Separation between second price auctions with personalized reserves and the revenue optimal auction

Prophet Secretary for Combinatorial Auctions and Matroids

The Two-Sided Game of Googol and Sample-Based Prophet Inequalities

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