Dynamics of multidimensional Simple Clock Auctions
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914195132383232 |
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| author | Zeroual, Jad Akian, Marianne Bechler, Aurélien Chardy, Matthieu Gaubert, Stéphane |
| author_facet | Zeroual, Jad Akian, Marianne Bechler, Aurélien Chardy, Matthieu Gaubert, Stéphane |
| contents | Simple Clock Auctions (SCA) are a mechanism commonly used in spectrum auctions to sell lots of frequency bandwidths. We study such an auction with one player having access to perfect information against straightforward bidders. When the opponents' valuations satisfy the ordinary substitutes condition, we show that it is optimal to bid on a fixed lot overtime. In this setting, we consider a continuous-time version of the SCA auction in which the prices follow a differential inclusion with a piecewise-constant dynamics. We show that there exists a unique solution in the sense of Filippov. This guarantees that the continuous-time model coincides with the limit of the discrete-time auction when price increments tend to zero. Moreover, we show that the value function of this limit auction is piecewise linear (though possibly discontinuous). Finally, we illustrate these results by analyzing a simplified version of the multiband Australian spectrum auction of 2017. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_10614 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dynamics of multidimensional Simple Clock Auctions Zeroual, Jad Akian, Marianne Bechler, Aurélien Chardy, Matthieu Gaubert, Stéphane Computer Science and Game Theory Combinatorics Optimization and Control Simple Clock Auctions (SCA) are a mechanism commonly used in spectrum auctions to sell lots of frequency bandwidths. We study such an auction with one player having access to perfect information against straightforward bidders. When the opponents' valuations satisfy the ordinary substitutes condition, we show that it is optimal to bid on a fixed lot overtime. In this setting, we consider a continuous-time version of the SCA auction in which the prices follow a differential inclusion with a piecewise-constant dynamics. We show that there exists a unique solution in the sense of Filippov. This guarantees that the continuous-time model coincides with the limit of the discrete-time auction when price increments tend to zero. Moreover, we show that the value function of this limit auction is piecewise linear (though possibly discontinuous). Finally, we illustrate these results by analyzing a simplified version of the multiband Australian spectrum auction of 2017. |
| title | Dynamics of multidimensional Simple Clock Auctions |
| topic | Computer Science and Game Theory Combinatorics Optimization and Control |
| url | https://arxiv.org/abs/2512.10614 |