An Efficient <i>∊</i>-BIC to BIC Transformation and Its Application to Black-Box Reduction in Revenue Maximization

Cai, Yang; Grigoris, Velegkas,; Zhao, Mingfei

doi:10.1137/1.9781611976465.81

Cited by 12 publications

(11 citation statements)

References 32 publications

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“…This idea and the associated guarantees have been extended by Daskalakis and Weinberg (2012) and Rubinstein and Weinberg (2015) to multiple bidders settings using ideas developed in Hartline and Lucier (2010), Hartline et al (2011), Bei and Huang (2011). Cai et al (2021) have made these arguments computationally efficient. The rounding argument applied to our setting delivers an impossibility result, which, unfortunately, it is not tight for our problem.…”

Section: Literature Reviewmentioning

confidence: 99%

Mechanism Design under Approximate Incentive Compatibility

Balseiro¹,

Besbes²,

Castro³

2021

Preprint

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A fundamental assumption in classical mechanism design is that buyers are perfect optimizers. However, in practice, buyers may be limited by their computational capabilities or a lack of information, and may not be able to perfectly optimize their response to a mechanism. This has motivated the introduction of approximate incentive compatibility (IC) as an appealing solution concept for practical mechanism design. While most of the literature has focused on the analysis of particular approximate IC mechanisms, this paper is the first to study the design of optimal mechanisms in the space of approximate IC mechanisms and to explore how much revenue can be garnered by moving from exact to approximate incentive constraints. In particular, we study the problem of a seller facing one buyer with private values and analyze optimal selling mechanisms under ε-incentive compatibility. We establish that an optimal mechanism needs to randomize as soon as ε > 0 and that no mechanism can garner gains higher than order ε 2/3 . This improves upon state-of-the art results which imply maximum gains of ε 1/2 . Furthermore, we construct a mechanism that is guaranteed to achieve order ε 2/3 additional revenues, leading to a tight characterization of the revenue implications of approximate IC constraints. Our study sheds light on a novel class of optimization problems and the challenges that emerge when relaxing IC constraints. In particular, it brings forward the need to optimize not only over allocations and payments but also over best responses, and we develop a new framework to address this challenge.

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Section: Literature Reviewmentioning

confidence: 99%

Mechanism Design under Approximate Incentive Compatibility

Balseiro¹,

Besbes²,

Castro³

2021

Preprint

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“…It has also been useful to work with approximate-IC mechanisms, and these have been studied in various papers, e.g. (Daskalakis and Weinberg, 2012;Cai and Zhao, 2017;Rubinstein and Weinberg, 2018;Cai et al, 2019;Dütting et al, 2014;Duetting et al, 2019;Feng et al, 2018;Balcan et al, 2019;Lahaie et al, 2018;, and gained a lot of attention.…”

Section: Model and Notationmentioning

confidence: 99%

“…1.5 Further related work Dughmi et al (2017) propose a general transformation from any black-box algorithm A to a BIC mechanism that only incurs negligible loss of welfare, with only polynomial number queries to A, by using Bernoulli factory techniques. Concurrently and independently, Cai et al (2019) propose a polynomial time algorithm to transform any ε-BIC mechanism to an exactly BIC mechanism, with only sample access to the type distribution and query access to the original ε-BIC mechanism. Their technique builds on the replica-surrogate matching mechanism (Daskalakis and Weinberg, 2012), and (Dughmi et al, 2017), by extending replica-surrogate matching to handle negative weights in the graph.…”

Section: Our Techniquesmentioning

confidence: 99%

Welfare-Preserving $\varepsilon$-BIC to BIC Transformation with Negligible Revenue Loss

Conitzer¹,

Feng²,

Parkes³

et al. 2020

Preprint

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In this paper, we investigate the problem of transforming an ε-BIC mechanism into an exactly BIC mechanism without loss of social welfare, working in a general mechanism design setting. We can transform any ε-BIC mechanism to a BIC mechanism with no loss of social welfare and with additive and negligible revenue loss. We show that the revenue loss bound is tight given the requirement to maintain social welfare. This is the first ε-BIC to BIC transformation that preserves welfare and provides negligible revenue loss. Previous ε-BIC to BIC transformations preserve social welfare but have no revenue guarantee (Bei and Huang, 2011), or suffer welfare loss while incurring a revenue loss with both a multiplicative and an additive term, e.g., Daskalakis and Weinberg (2012); Cai and Zhao (2017); Rubinstein and Weinberg (2018). The revenue loss achieved by our transformation is incomparable to these earlier approaches and can sometimes be significantly less. We also analyze ε-expected ex-post IC (ε-EEIC) mechanisms (Dütting et al., 2014), and provide a welfare-preserving transformation with the same revenue loss guarantee for the special case of uniform type distributions. We give applications of our methods to both linear-programming based and machine-learning based methods of automated mechanism design. We also show the impossibility of welfare-preserving, ε-EEIC to BIC transformations with negligible loss of revenue for non-uniform distributions.

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“…On the conceptual front, this approach does not leverage state-of-the-art work in Auction Theory for the multi-bidder setting. Our work, on the other hand, leverages an exciting line of recent works (Hartline and Lucier, 2010;Hartline et al, 2011;Bei and Huang, 2011;Daskalakis and Weinberg, 2012;Rubinstein and Weinberg, 2018;Dughmi et al, 2017;Cai et al, 2019) on ε-truthful-to-truthful reductions. 1 On the technical front, we identify three areas for improvement.…”

Section: Introductionmentioning

confidence: 99%

“…To address this, Hartline et al (2015); Bei and Huang (2011); Dughmi et al (2017) develop a sophisticated reduction for turning algorithms into truthful mechanisms, which was later extended in Daskalakis and Weinberg (2012); Rubinstein and Weinberg (2018); Cai et al (2019) to reduce ε-truthful mechanisms into truthful mechanisms with small loss in revenue. For example, Lemma 2 follows immediately from Theorem 5.2 in Rubinstein and Weinberg (2018).…”

mentioning

confidence: 99%

Auction learning as a two-player game

Rahme¹,

Jelassi²,

Weinberg³

2020

Preprint

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Designing an incentive compatible auction that maximizes expected revenue is a central problem in Auction Design. While theoretical approaches to the problem have hit some limits, a recent research direction initiated by Duetting et al. (2019) consists in building neural network architectures to find optimal auctions. We propose two conceptual deviations from their approach which result in enhanced performance. First, we use recent results in theoretical auction design (Rubinstein and Weinberg, 2018) to introduce a time-independent Lagrangian. This not only circumvents the need for an expensive hyper-parameter search (as in prior work), but also provides a principled metric to compare the performance of two auctions (absent from prior work). Second,the optimization procedure in previous work uses an inner maximization loop to compute optimal misreports. We amortize this process through the introduction of an additional neural network. We demonstrate the effectiveness of our approach by learning competitive or strictly improved auctions compared to prior work. Both results together further imply a novel formulation of Auction Design as a two-player game with stationary utility functions.

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An Efficient ∊-BIC to BIC Transformation and Its Application to Black-Box Reduction in Revenue Maximization

Cited by 12 publications

References 32 publications

Mechanism Design under Approximate Incentive Compatibility

Mechanism Design under Approximate Incentive Compatibility

Welfare-Preserving $\varepsilon$-BIC to BIC Transformation with Negligible Revenue Loss

Auction learning as a two-player game

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