In multi-item screening, optimal selling mechanisms are challenging to characterize and implement, even with full knowledge of valuation distributions. In this paper, we aim to develop tractable, interpretable, and implementable mechanisms with strong performance guarantees in the absence of precise distributional knowledge. In particular, we study robust screening with a maximin ratio objective. We show that given the marginal support of valuations, the optimal mechanism is separable: each item's allocation probability and payment depend only on its own valuation and not on other items' valuations. However, we design the allocation and payment rules by leveraging the available joint support information. This enhanced separable mechanism can be efficiently implemented through randomized pricing for individual products, which is easy to interpret and implement. Moreover, our framework extends naturally to scenarios where the seller possesses marginal support information on aggregate valuations for any product bundle partition, for which we characterize a bundle-wise separable mechanism and its guarantee. Beyond rectangular-support ambiguity sets, we further establish the optimality of randomized grand bundling mechanisms within a broad class of ambiguity sets, which we term ``$\boldsymbol{\rho}-$scaled invariant ambiguity set".

翻译：在多物品甄别中，即使完全掌握估值分布，最优销售机制的表征与实施仍具挑战性。本文旨在缺乏精确分布知识的情况下，开发具有强性能保证、易于处理、可解释且可实施的机制。具体而言，我们研究以极大极小比率为目标的鲁棒甄别问题。我们证明，在给定估值边际支撑集的条件下，最优机制是可分离的：每件物品的分配概率与支付仅取决于其自身估值，而与其他物品估值无关。然而，我们通过利用已知的联合支撑集信息来设计分配与支付规则。这种增强的可分离机制可通过针对单个产品的随机定价高效实施，且易于解释与操作。此外，我们的框架可自然扩展到卖方掌握任意产品组合划分下聚合估值边际支撑信息的场景，为此我们刻画了组合式可分离机制及其性能保证。在矩形支撑模糊集之外，我们进一步在一类广泛的模糊集（称为“$\boldsymbol{\rho}-$缩放不变模糊集”）中确立了随机整体捆绑机制的最优性。