Author
Listed:
- Jerry Anunrojwong
(Graduate School of Business, Columbia University, New York, New York 10027)
- Santiago R. Balseiro
(Graduate School of Business, Columbia University, New York, New York 10027)
- Omar Besbes
(Graduate School of Business, Columbia University, New York, New York 10027)
Abstract
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, whereas 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.
Suggested Citation
Jerry Anunrojwong & Santiago R. Balseiro & Omar Besbes, 2025.
"On the Robustness of Second-Price Auctions in Prior-Independent Mechanism Design,"
Operations Research, INFORMS, vol. 73(3), pages 1659-1674, May.
Handle:
RePEc:inm:oropre:v:73:y:2025:i:3:p:1659-1674
DOI: 10.1287/opre.2022.0428
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