  We study revenue maximization in multi-item auctions, where bidders have
subadditive valuations over independent items. Providing a simple mechanism
that is approximately revenue-optimal in this setting is a major open problem
in mechanism design. In this paper, we present the first \emph{simple
mechanism} whose revenue is at least a \emph{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 \emph{simultaneous first-price} and the \emph{simultaneous all-pay auction}
are $1\over 2$-efficient. Providing revenue guarantees for non-truthful simple
mechanisms, e.g., simultaneous auctions, in multi-dimensional environments has
been recognized by Roughgarden et al. as an important open question. Prior to
our result, the only such revenue guarantees are due to Daskalakis et al. 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.
