Monotonic Mechanisms for Selling Multiple Goods
Ran Ben Moshe, Sergiu Hart, and Noam Nisan
Abstract
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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First version: December 2021
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Revised: June 2022
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Revised: October 2022
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arXiv: https://doi.org/10.48550/arXiv.2210.17150,
October 2022
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The Hebrew University of Jerusalem,
Center for Rationality DP-747, October 2022
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Revised: December 2023
Last modified:
© Sergiu Hart