Multi-Item Nontruthful Auctions Achieve Good Revenue

We present a general framework for designing approximately revenue-optimal mechanisms multi-item additive auctions, which applies to both truthful and nontruthful auctions. Given (not necessarily truthful) single-item auction format satisfying certain technical conditions, we run simultaneous item auctions augmented with personalized entry fee each bidder that must be paid before the can accessed. These fees depend only on prior distribution of types in particular are independent realized bids. bound revenue resulting two-part tariff mechanism using novel geometric technique enables guarantees many common previously had none. Our approach adapts extends duality Cai, Devanur, Weinberg [SIAM J. Comput., 50 (2021), pp. STOC16-160–STOC16-200] beyond used formats, such as first-price, second-price, all-pay results first-price first multidimensional environments, addressing an open question literature [T. Roughgarden, V. Syrgkanis, E. Tardos, Artificial Intelligence Res., 59 (2017), 59–101]. If used, prove is also credible sense auctioneer cannot benefit by deviating from stated after observing agent This static achieves constant factor optimal revenue. second-price obtain -approximate fixed amenable tuning via online learning techniques.