Robust Reserve Pricing in Auctions Under Mean Constraints

Che, Ethan

doi:10.2139/ssrn.3488222

Cited by 7 publications

(7 citation statements)

References 20 publications

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“…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]. Distributional robustness has also been studied with asymptotically-many bidders [e.g.…”

Section: Additional Related Workmentioning

confidence: 99%

“…This parallel turns out to be a random pricing scheme where the price is distributed according to a log-uniform distribution -in line with the above intuition of hedging against uncertainty through randomization. Che [2022] tackles a generalization to more than one bidder, but allows the bidder values to be correlated in an unknown way (i.e., the adversary chooses the worst-case correlation among the values). Suzdaltsev [2020a] also tackles a generalization beyond a single bidder; in his model the bidders are i.i.d., but the seller's strategies in the zero-sum game are limited to deterministic auctions.…”

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confidence: 99%

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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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Section: Additional Related Workmentioning

confidence: 99%

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confidence: 99%

Distributional Robustness: From Pricing to Auctions

Nir¹,

Talgam-Cohen²

2022

Preprint

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“…With a single buyer, the optimal price is the solution to v(r) = 0, which indeed is arg max r r P(B > r). Hence, there are possibilities for deploying the robust Chebyshev bounds for other models in pricing and mechanism design, for instance distribution-free analysis of auctions with multiple independent bids (Suzdaltsev, 2018) or correlated bids (Che, 2019).…”

Section: Monopoly Pricingmentioning

confidence: 99%

Tight tail probability bounds for distribution-free decision making

Roos¹,

Brekelmans²,

Eekelen³

et al. 2020

Preprint

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Chebyshev's inequality provides an upper bound on the tail probability of a random variable based on its mean and variance. While tight, the inequality has been criticized for only being attained by pathological distributions that abuse the unboundedness of the underlying support and are not considered realistic in many applications. We provide alternative tight lower and upper bounds on the tail probability given a bounded support, mean and mean absolute deviation of the random variable. We obtain these bounds as exact solutions to semi-infinite linear programs. We leverage the bounds for distribution-free analysis of the newsvendor model, monopolistic pricing, and stop-loss reinsurance. We also exploit the bounds for safe approximations of sums of correlated random variables, and to find convex reformulations of single and joint ambiguous chance constraints that are ubiquitous in distributionally robust optimization.

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“…This paper contributes to the growing literature on robust mechanism design. The closest contributions to ours are Carrasco et al (2018a), He and Li (2020), Koçyigit et al (2020), Suzdaltsev (2020), Che (2019) and Neeman (2003). Carrasco et al (2018a) study the problem of selling the good to a single agent by a seller who maximizes worst-case expected revenue while knowing the first N moments of distribution.…”

Section: Related Literaturementioning

confidence: 99%

“…Some of the above papers find that with sufficiently many bidders, the robustly optimal reserve price is low. In He and Li (2020) and Che (2019), the optimal reserve price converges to seller's value as number of bidders goes to infinity; in Koçyigit et al (2020) and Suzdaltsev (2020), the optimal reserve is equal to seller's value starting from a certain number of bidders. In contrast, in the present paper it is equal to seller's value for all n ≥ 2.…”

Section: Related Literaturementioning

confidence: 99%

Distributionally Robust Pricing in Auctions

Suzdaltsev¹

2018

SSRN Journal

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Robust Reserve Pricing in Auctions Under Mean Constraints

Cited by 7 publications

References 20 publications

Distributional Robustness: From Pricing to Auctions

Distributional Robustness: From Pricing to Auctions

Tight tail probability bounds for distribution-free decision making

Distributionally Robust Pricing in Auctions

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