Simultaneous Auctions are Approximately Revenue-Optimal for Subadditive Bidders

We study revenue maximization in multi-item auctions, where bidders have subadditive valuations over independent items [48]. Providing a simple mechanism that is approximately revenue-optimal in this setting is a major open problem in mechanism design [20]. In this paper, we present the first simple mechanism whose revenue is at least a constant fraction of the optimal revenue in multi-item auctions with subadditive bidders. Our mechanism is a simultaneous auction that incorporates either a personalized entry fee or a personalized reserve price per item. We prove that for any simultaneous auction that satisfies c-efficiency– a new property we propose, its revenue is at least an $O(c)$-approximation to the optimal revenue. We further show that both the simultaneous first-price and the simultaneous all-pay auction are $\frac{1}{2}$-efficient. Providing revenue guarantees for non-truthful simple mechanisms, e.g., simultaneous auctions, in multi-dimensional environments has been recognized by Roughgarden et al. [47] as an important open question. Prior to our result, the only such revenue guarantees are due to Daskalakis et al. [30] for bidders who have additive valuations over independent items. Our result significantly extends the revenue guarantees of these non-truthful simple auctions to settings where bidders have combinatorial valuations.