A Multi-Dimensional Online Contention Resolution Scheme for Revenue Maximization
Shuchi Chawla, Dimitris Christou, Trung Dang, Zhiyi Huang, Gregory Kehne, Rojin Rezvan
TL;DR
This work develops a unified framework linking revenue maximization for many subadditive buyers to Online Contention Resolution Schemes (OCRS) via the ex ante relaxation $EARev$. It introduces Revenue Recovery Schemes (RRS) and a ConvexHullSampler to construct multi-dimensional OCRS that can be implemented online as sequential item pricings. The authors prove an $O( ext{log } m)$-OCRS for subadditive valuations, yielding an $O( ext{log } m)$-approximation to the ex ante revenue against item-pricing benchmarks, and extend the approach to BuyMany with an $O( ext{log }^2 m)$-approximation, along with tight lower bounds in several valuation classes. The results advance the understanding of when simple online mechanisms can closely approximate optimal revenue in complex multi-item, multi-buyer settings and suggest practical directions for algorithmic implementations.
Abstract
We study multi-buyer multi-item sequential item pricing mechanisms for revenue maximization with the goal of approximating a natural fractional relaxation -- the ex ante optimal revenue. We assume that buyers' values are subadditive but make no assumptions on the value distributions. While the optimal revenue, and therefore also the ex ante benchmark, is inapproximable by any simple mechanism in this context, previous work has shown that a weaker benchmark that optimizes over so-called ``buy-many" mechanisms can be approximable. Approximations are known, in particular, for settings with either a single buyer or many unit-demand buyers. We extend these results to the much broader setting of many subadditive buyers. We show that the ex ante buy-many revenue can be approximated via sequential item pricings to within an $O(\log^2 m)$ factor, where $m$ is the number of items. We also show that a logarithmic dependence on $m$ is necessary. Our approximation is achieved through the construction of a new multi-dimensional Online Contention Resolution Scheme (OCRS), that provides an online rounding of the optimal ex ante solution. Chawla et al. arXiv:2204.01962 previously constructed an OCRS for revenue for unit-demand buyers, but their construction relied heavily on the ``almost single dimensional" nature of unit-demand values. Prior to that work, OCRSes have only been studied in the context of social welfare maximization for single-parameter buyers. For the welfare objective, constant-factor approximations have been demonstrated for a wide range of combinatorial constraints on item allocations and classes of buyer valuation functions. Our work opens up the possibility of a similar success story for revenue maximization.