  Maximizing the revenue from selling _more than one_ good (or item) to a
single buyer is a notoriously difficult problem, in stark contrast to the
one-good case. For two goods, we show that simple "one-dimensional" mechanisms,
such as selling the goods separately, _guarantee_ at least 73% of the optimal
revenue when the valuations of the two goods are independent and identically
distributed, and at least $50\%$ when they are independent. For the case of
$k>2$ independent goods, we show that selling them separately guarantees at
least a $c/\log^2 k$ fraction of the optimal revenue; and, for independent and
identically distributed goods, we show that selling them as one bundle
guarantees at least a $c/\log k$ fraction of the optimal revenue. Additional
results compare the revenues from the two simple mechanisms of selling the
goods separately and bundled, identify situations where bundling is optimal,
and extend the analysis to multiple buyers.
