Correlation-Robust Optimal Auctions

Abstract

We study the design of auction within the correlation-robust framework in which the auctioneer is assumed to have information only about marginal distributions, but does not know the correlation structure of the joint distribution. The performance of a mechanism is evaluated in the worst-case over the uncertainty of joint distributions that are consistent with the marginal distributions. For the two-bidder case, we characterize the Second Price Auction with Uniformly Distributed Reserves as a maxmin auction among dominant strategy incentive compatible (DSIC) and ex-post individually rational (EPIR) mechanisms under the robust-version regularity conditions. For the N -bidder (N ≥ 3) case, we characterize the Second Price Auction with Beta( 1 N −1 , 1) Distributed Reserves as a maxmin auction among exclusive (a bidder whose bid is not the highest will never be allocated) DSIC and EPIR mechanisms under the general robust-version regularity conditions (I).

Information-Robust Optimal Auctions

“…In this sense, this paper complements his work. This paper is closely related to Che (2019), Brooks and Du (2021a), He and Li (2022) and Zhang (2021a). Che ( 2019) considers a model of auction design in the private value environment and assumes that the seller only knows the mean of bidders' valuation distribution.…”

“…In addition, the solution concept in their paper is stronger than the one in mine, as there are no restrictions on the set of equilibria that the Nature can choose. He and Li (2022) and Zhang (2021a) both consider a model of auction design in the private value environment and assume that the seller knows the marginal distribution of a generic bidder's valuation but does not knows the correlation structure between bidders' valuations. Under different conditions on the marginal distributions, they characterize, among others, that second-price auctions with random reserves are maxmin mechanisms within (standard) dominant-strategy mechanisms.…”

“…Second, the minmax signal distribution is an equalrevenue distribution, defined by the property of a unit-elastic demand: in the monopoly pricing problem, the monopoly's revenue from charging any price in the support of this distribution is the same. Equal-revenue distributions are familiar in several literatures: they emerge endogenously in many robust mechanism design environments and information design environment, e.g., Bergemann and Schlag (2008), Carrasco et al (2018), Zhang (2021a), Roesler and Szentes (2017), Condorelli and Szentes (2020), Chen and Yang (2020), etc. Finally, the constituent equilibrium is the truth-telling equilibrium in which bidders always truthfully report their true signals.…”