Multi-Item Screening with a Maximin-Ratio Objective

Abstract

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".