Correlation-Robust Analysis of Single Item Auction.

We investigate the problem of revenue maximization in single-item auction within the new correlation-robust framework proposed by Carroll [2017] and further developed by Gravin and Lu [2018]. In this framework the auctioneer is assumed to have only partial information about marginal distributions, but does not know the dependency structure of the joint distribution. The auctioneer's revenue is evaluated in the worst-case over the uncertainty of possible joint distribution. For the problem of optimal auction design in the correlation robust-framework we observe that in most cases the optimal auction does not admit a simple form like the celebrated Myerson's auction for independent valuations. We analyze and compare performances of several DSIC mechanisms used in practice. Our main set of results concern the sequential posted-price mechanism (SPM). We show that SPM achieves a constant (4.78) approximation to the optimal correlation-robust mechanism. We also show that in the symmetric (anonymous) case when all bidders have the same marginal distribution, (i) SPM has almost matching worst-correlation revenue as any second price auction with common reserve price, and (ii) when the number of bidders is large, SPM converges to optimum. In addition, we extend some results on approximation and computational tractability for lookahead auctions to the correlation-robust framework.