Approximately Optimal Auctions With a Strong Bidder
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917777775788032 |
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| author | Anderlini, Luca Kim, GaOn |
| author_facet | Anderlini, Luca Kim, GaOn |
| contents | We consider auctions with N+1 bidders. Of these, N are symmetric and N+1 is "sufficiently strong" relative to the others. The auction is a "tournament" in which the first N players bid to win the right to compete with N+1. The bids of the first N players are binding and the highest bidder proceeds to a second-price competition with N+1.
When N+1's values converge in distribution to an atom above the upper end of the distribution of the N bidders and the rest of the distribution is drained away from low values sufficiently slowly, the auction's expected revenue is arbitrarily close to the one obtained in a Myerson (1981) optimal auction.
The tournament design is "detail free" in the sense that no specific knowledge of the distributions is needed in addition to the fact that bidder N+1 is stronger than the others as required. In particular, no additional information about the value of the atom is needed. This is important since mis-calibrating by a small amount an attempt to implement the optimal auction can lead to large losses in revenue.
We provide an interpretation of these results as possibly providing guidelines to a seller on how to strategically "populate" auctions with a single bidder even when only weaker bidders are available. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_11048 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Approximately Optimal Auctions With a Strong Bidder Anderlini, Luca Kim, GaOn Theoretical Economics We consider auctions with N+1 bidders. Of these, N are symmetric and N+1 is "sufficiently strong" relative to the others. The auction is a "tournament" in which the first N players bid to win the right to compete with N+1. The bids of the first N players are binding and the highest bidder proceeds to a second-price competition with N+1. When N+1's values converge in distribution to an atom above the upper end of the distribution of the N bidders and the rest of the distribution is drained away from low values sufficiently slowly, the auction's expected revenue is arbitrarily close to the one obtained in a Myerson (1981) optimal auction. The tournament design is "detail free" in the sense that no specific knowledge of the distributions is needed in addition to the fact that bidder N+1 is stronger than the others as required. In particular, no additional information about the value of the atom is needed. This is important since mis-calibrating by a small amount an attempt to implement the optimal auction can lead to large losses in revenue. We provide an interpretation of these results as possibly providing guidelines to a seller on how to strategically "populate" auctions with a single bidder even when only weaker bidders are available. |
| title | Approximately Optimal Auctions With a Strong Bidder |
| topic | Theoretical Economics |
| url | https://arxiv.org/abs/2409.11048 |