  We investigate the objective of utility maximization from the perspective of
Bayesian mechanism design, initiating this direction, and focus on the
unit-demand setting where values are i.i.d. across both items and buyers. We
take the approach of developing simple, approximately optimal mechanisms,
targeting the simplest benchmark of optimal welfare. We give a
$(1-1/e)$-approximation when there are more items than buyers, and an
$O(\log(n/m))$-approximation when there are more buyers than items, which is
tight up to constant factors. We also characterize complexities in this setting
that defy our intuition from the welfare and revenue literature, and motivate
why coming up with a better benchmark than welfare is a hard problem itself.
