Revenue-Optimal Pricing for Budget-Constrained Buyers in Data Markets

We study revenue-optimal pricing in data markets with rational, budget-constrained buyers. Such a market offers multiple datasets for sale, and buyers aim to improve the accuracy of their prediction tasks by acquiring data bundles. The market's objective is to price datasets to maximize total revenue, considering that buyers with quasi-linear utilities choose their bundles optimally under budget constraints. We allow the buyers to purchase fractions of datasets, and the amount they pay is proportional to the fraction they receive. Although competitive equilibrium gives revenue-optimal pricing in rivalrous markets with quasi-linear buyers, we show that revenue maximization in data markets is APX-hard. Despite the hardness, we design a 2-approximation algorithm when datasets arrive online, and a $(1-1/e)^{-1}$-approximation algorithm for the offline setting.