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

42 Pages Posted: 9 May 2022

See all articles by Jerry Anunrojwong

Jerry Anunrojwong

Columbia University - Columbia Business School, Decision Risk and Operations

Santiago Balseiro

Columbia University - Columbia Business School, Decision Risk and Operations

Omar Besbes

Columbia University - Columbia Business School, Decision Risk and Operations

Date Written: April 22, 2022

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, 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.

Keywords: prior-independent, robust mechanism design, minimax regret, second-price auction with random reserve

Suggested Citation

Anunrojwong, Jerry and Balseiro, Santiago and Besbes, Omar, On the Robustness of Second-Price Auctions in Prior-Independent Mechanism Design (April 22, 2022). Available at SSRN: https://ssrn.com/abstract=4090071 or http://dx.doi.org/10.2139/ssrn.4090071

Jerry Anunrojwong (Contact Author)

Columbia University - Columbia Business School, Decision Risk and Operations ( email )

New York, NY
United States

HOME PAGE: http://jerryanunroj.github.io/

Santiago Balseiro

Columbia University - Columbia Business School, Decision Risk and Operations ( email )

3022 Broadway
New York, NY 10027
United States

Omar Besbes

Columbia University - Columbia Business School, Decision Risk and Operations ( email )

New York, NY
United States

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