The competition complexity of dynamic pricing

Brustle, Johannes, Correa, José, Duetting, Paul and Verdugo, Victor (2024) The competition complexity of dynamic pricing. Mathematics of Operations Research, 49 (3). 1986 - 2008. ISSN 0364-765X

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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:	25 Nov 2024 21:39
URI:	http://eprints.lse.ac.uk/id/eprint/124364

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