Price Doubling and Item Halving: Robust Revenue Guarantees for Item Pricing

We study approximation algorithms for revenue maximization based on static item pricing, where a seller chooses prices for various goods in the market, and then the buyers purchase utility-maximizing bundles at these given prices. We formulate two somewhat general techniques for designing good pricing algorithms for this setting: Price Doubling and Item Halving. Using these techniques, we unify many of the existing results in the item pricing literature under a common framework, as well as provide several new bicriteria algorithms for approximating both revenue and social welfare simultaneously. The main technical contribution of this paper is a O((log m + log k)2)-approximation algorithm for revenue maximization based on the item halving technique, for settings where buyers have XoS valuations, where m is the number of goods and k is the average supply. Surprisingly, ours is the first known item pricing algorithm with polylogarithmic approximation for such general classes of valuations, and partially resolves an important open question from the algorithmic pricing literature about the existence of item pricing algorithms with logarithmic factors for general valuations