A Multi Dimensional Online Contention Resolution Scheme

A Google TechTalk, presented by Shuchi Chawla, 2024-07-12 A Google Algorithms Seminar. 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. Prior to our 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. This talk is based on https://arxiv.org/abs/2404.14679. It has some overlap with a talk I'm giving at the INFORMS Market Design workshop at EC on Monday July 8. But this one will be more in-depth and technical, so interested folks are welcome to come to both. Both the talks will be self contained. About the Speaker: Shuchi Chawla holds an Endowed Professorship in Computer Science at UT-Austin. Shuchi is a theoretical computer scientist specializing in the areas of algorithm design and economics and computation. Prior to joining UT-Austin, she spent 15 years as a professor of CS at the University of Wisconsin-Madison. Shuchi is the recipient of an NSF Career award, a Sloan Foundation fellowship, and several awards for her research and teaching at UW-Madison.