Monotonic Mechanisms for Selling Multiple Goods
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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.
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