Limitations of Deterministic Auction Design for Correlated Bidders.

The seminal work of Myerson (Mathematics of OR ’81) characterizes incentive-compatible single-item auctions among bidders with independent valuations. In this setting, relatively simple deterministic auction mechanisms achieve revenue optimality. When bidders have correlated valuations, designing the revenue-optimal deterministic auction is a computationally demanding problem; indeed, Papadimitriou and Pierrakos (STOC ’11) proved that it is APX-hard, obtaining an explicit inapproximability factor of 1999/2000 = 99.95%. In the current article, we strengthen this inapproximability factor to 63/64 ≈ 98.5%. Our proof is based on a gap-preserving reduction from the Max-NM 3SAT problem; a variant of the maximum satisfiability problem where each clause has exactly three literals and no clause contains both negated and unnegated literals. We furthermore show that the gap between the revenue of deterministic and randomized auctions can be as low as 13/14 ≈ 92.9%, improving an explicit gap of 947/948 ≈ 99.9% by Dobzinski, Fu, and Kleinberg (STOC ’11).