  We consider the problem of maximizing revenue for a monopolist offering
multiple items to multiple heterogeneous buyers. We develop a simple mechanism
that obtains a constant factor approximation under the assumption that the
buyers' values are additive subject to a feasibility constraint and independent
across items. Importantly, different buyers in our setting can have different
constraints on the sets of items they desire. Our mechanism is a sequential
variant of two-part tariffs. Prior to our work, simple approximation mechanisms
for such multi-buyer problems were known only for the special cases of all
unit-demand or all additive value buyers.
  Our work expands upon and unifies long lines of work on unit-demand settings
and additive settings. We employ the ex ante relaxation approach developed by
Alaei (2011) for reducing a multiple-buyer mechanism design problem with an ex
post supply constraint into single-buyer ones with ex ante supply constraints.
Solving the single-agent problems requires us to significantly extend
techniques developed in the context of additive values by Li and Yao (2013) and
their extension to subadditive values by Rubinstein and Weinberg (2015).
