Monotonic Mechanisms for Selling Multiple Goods
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866910482428854272 |
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| author | Ben-Moshe, Ran Hart, Sergiu Nisan, Noam |
| author_facet | Ben-Moshe, Ran Hart, Sergiu Nisan, Noam |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2210_17150 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Monotonic Mechanisms for Selling Multiple Goods Ben-Moshe, Ran Hart, Sergiu Nisan, Noam Computer Science and Game Theory Theoretical Economics 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. |
| title | Monotonic Mechanisms for Selling Multiple Goods |
| topic | Computer Science and Game Theory Theoretical Economics |
| url | https://arxiv.org/abs/2210.17150 |