Dynamics of multidimensional Simple Clock Auctions

Fuente: arXiv
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Autori principali: Zeroual, Jad, Akian, Marianne, Bechler, Aurélien, Chardy, Matthieu, Gaubert, Stéphane
Natura: Preprint
Pubblicazione: 2025
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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