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.

翻译：我们研究多买家多物品序贯定价机制以实现收益最大化，目标是对一个自然的分数松弛——事前最优收益进行近似。假设买家价值具有次可加性，但对价值分布不作任何假设。在此背景下，最优收益（从而事前基准）无法被任何简单机制近似，但先前研究表明，针对所谓的“多购买”机制进行优化的较弱基准是可近似的。具体而言，对于单一买家或多个单位需求买家的情况，已知存在近似结果。我们将这些结果推广到更广泛的多买家次可加性场景。我们证明，通过序贯物品定价，可将事前多购买收益近似到$O(\log^2 m)$因子内，其中$m$为物品数量。同时，我们证明对$m$的对数依赖是必要的。这一近似通过构建一种新的多维在线竞争解决策略（OCRS）实现，该策略提供了对最优事前解的在线舍入。Chawla等人（arXiv:2204.01962）此前曾为单位需求买家构建了用于收益的OCRS，但其构建高度依赖单位需求价值的“近似单维”特性。在此工作之前，OCRS仅被研究用于单参数买家的社会福利最大化。针对福利目标，在物品分配的多种组合约束及买家估值函数类别下，已实现了常数因子近似。我们的工作为收益最大化领域的类似成功故事开辟了可能性。