Robustly-Optimal Mechanism for Selling Multiple Goods

Che, Yeon‐Koo; Zhong, Weijie

doi:10.1145/3465456.3467570

Cited by 7 publications

(2 citation statements)

References 8 publications

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“…Lastly, there are also works on optimal robust mechanisms for selling multiple goods under various objectives and knowledge assumptions; see, e.g., Carroll [2017], Che and Zhong [2021].…”

Section: Related Workmentioning

confidence: 99%

On the Robustness of Second-Price Auctions in Prior-Independent Mechanism Design

Anunrojwong¹,

Balseiro²,

Besbes³

2022

Preprint

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Classical Bayesian mechanism design relies on the common prior assumption, but the common prior is often not available in practice. We study the design of prior-independent mechanisms that relax this assumption: the seller is selling an indivisible item to n buyers such that the buyers' valuations are drawn from a joint distribution that is unknown to both the buyers and the seller; buyers do not need to form beliefs about competitors, and the seller assumes the distribution is adversarially chosen from a specified class. We measure performance through the worst-case regret, or the difference between the expected revenue achievable with perfect knowledge of buyers' valuations and the actual mechanism revenue.We study a broad set of classes of valuation distributions that capture a wide spectrum of possible dependencies: independent and identically distributed (i.i.d.) distributions, mixtures of i.i.d. distributions, affiliated and exchangeable distributions, exchangeable distributions, and all joint distributions. We derive in quasi closed form the minimax values and the associated optimal mechanism. In particular, we show that the first three classes admit the same minimax regret value, which is decreasing with the number of competitors, while the last two have the same minimax regret equal to that of the case n = 1. Furthermore, we show that the minimax optimal mechanisms have a simple form across all settings: a second-price auction with random reserve prices, which shows its robustness in prior-independent mechanism design. En route to our results, we also develop a principled methodology to determine the form of the optimal mechanism and worst-case distribution via first-order conditions that should be of independent interest in other minimax problems.

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“…Lastly, there are also works on optimal robust mechanisms for selling multiple goods under various objectives and knowledge assumptions; see, e.g., Carroll [2017], Che and Zhong [2021].…”

Section: Related Workmentioning

confidence: 99%

On the Robustness of Second-Price Auctions in Prior-Independent Mechanism Design

Anunrojwong¹,

Balseiro²,

Besbes³

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…A recent line of work studies more than one item, applying robustness to the challenging domain of multi-parameter mechanism design. The robustness in this context is usually to correlation among the item values Carroll [2017], Gravin and Lu [2018], Babaioff et al [2020], and sometimes (in addition to correlation) to details of the marginal distributions Che and Zhong [2021], Brooks and Du [2021], Giannakopoulos et al [2020]. The basic setting has also been generalized to the complementary case of multiple bidders, where the robustness is to correlation among them (and possibly to distributional details as well) Suzdaltsev [2020b], Bei et al [2019], Che [2022], Koçyigit et al [2019], He and Li [2022].…”

Section: Additional Related Workmentioning

confidence: 99%

Distributional Robustness: From Pricing to Auctions

Nir¹,

Talgam-Cohen²

2022

Preprint

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Robust mechanism design is a rising alternative to Bayesian mechanism design, which yields designs that do not rely on assumptions like full distributional knowledge. We apply this approach to mechanisms for selling a single item, assuming that only the mean of the value distribution and an upper bound on the bidder values are known. We seek the mechanism that maximizes revenue over the worst-case distribution compatible with the known parameters. Such a mechanism arises as an equilibrium of a zero-sum game between the seller and an adversary who chooses the distribution, and so can be referred to as the max-min mechanism.Carrasco et al. [2018] derive the max-min pricing when the seller faces a single bidder for the item. We go from max-min pricing to max-min auctions by studying the canonical setting of two i.i.d. bidders, and show the max-min mechanism is the second-price auction with a randomized reserve. We derive a closed-form solution for the distribution over reserve prices, as well as the worst-case value distribution, for which there is simple economic intuition. In fact we derive a closed-form solution for the reserve price distribution for any number of bidders.Our technique for solving the zero-sum game is quite different than that of Carrasco et al.it involves analyzing a discretized version of the setting, then refining the discretization grid and deriving a closed-form solution for the non-discretized, original setting. Our results establish a difference between the case of two bidders and that of n ≥ 3 bidders.

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Separation in Distributionally Robust Monopolist Problem

Qiu,

Wang,

2023

Lecture Notes in Computer Science

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Robustly-Optimal Mechanism for Selling Multiple Goods

Cited by 7 publications

References 8 publications

On the Robustness of Second-Price Auctions in Prior-Independent Mechanism Design

On the Robustness of Second-Price Auctions in Prior-Independent Mechanism Design

Distributional Robustness: From Pricing to Auctions

Separation in Distributionally Robust Monopolist Problem

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