  Maximizing the revenue from selling two or more goods has been shown to
require the use of $nonmonotonic$ mechanisms, where a higher-valuation buyer
may pay less than a lower-valuation one. Here we show that the restriction to
$monotonic$ mechanisms may not just lower the revenue, but may in fact yield
only a $negligible$ $fraction$ of the maximal revenue; more precisely, the
revenue from monotonic mechanisms is no more than k times the simple revenue
obtainable by selling the goods separately, or bundled (where k is the number
of goods), whereas the maximal revenue may be arbitrarily larger. We then study
the class of monotonic mechanisms and its subclass of allocation-monotonic
mechanisms, and obtain useful characterizations and revenue bounds.
