Brustle, Johannes, Correa, José, Duetting, Paul and Verdugo, Victor (2023) The competition complexity of dynamic pricing. Mathematics of Operations Research. ISSN 0364-765X
Full text not available from this repository.Abstract
We study the competition complexity of dynamic pricing relative to the optimal auction in the fundamental single-item setting. In prophet inequality terminology, we compare the expected reward () achievable by the optimal online policy on m independent and identically distributed (i.i.d.) random variables distributed according to F to the expected maximum () of n i.i.d. draws from F. We ask how big m has to be to ensure that (1+)()≥() for all F. We resolve this question and characterize the competition complexity as a function of ε. When =0, the competition complexity is unbounded. That is, for any n and m there is a distribution F such that ()<(). In contrast, for any >0, it is sufficient and necessary to have =(), where ()=Θ(log log 1/). Therefore, the competition complexity not only drops from unbounded to linear, it is actually linear with a very small constant. The technical core of our analysis is a lossless reduction to an infinite dimensional and nonlinear optimization problem that we solve optimally. A corollary of this reduction is a novel proof of the factor ≈0.745 i.i.d. prophet inequality, which simultaneously establishes matching upper and lower bounds.
| Item Type: | Article |
|---|---|
| Official URL: | https://pubsonline.informs.org/journal/moor |
| Additional Information: | © 2023 INFORMS |
| Divisions: | Mathematics |
| Subjects: | Q Science > QA Mathematics |
| Date Deposited: | 26 Jul 2024 09:03 |
| Last Modified: | 26 Jul 2024 09:03 |
| URI: | http://eprints.lse.ac.uk/id/eprint/124364 |
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