Improved Revenue Guarantees for Selling Separately and Bundling

2026-09-23

AI Summary

This study investigates the upper bound on revenue loss when restricting mechanisms to separate sales or grand bundling in independent item auctions, relative to the optimal mechanism. Focusing on the single-buyer independent-values setting, the analysis rigorously integrates mechanism design theory, combinatorial auction analysis, and bounding techniques. The core contribution is establishing the novel upper bound OPT ≤ 3.52 max(SREV, BREV), which improves the best-known approximation ratio from 5.2 to 3.52 and substantially narrows the gap with the theoretical lower bound of 2. This result demonstrates that simple selling formats can effectively approximate optimal revenue, thereby refining the theoretical precision for evaluating the efficiency of simple mechanisms.

Abstract

We study how much revenue a seller can lose by restricting attention to selling separately or grand bundling, in the setting of a single additive buyer with independent item values. Although revenue-optimal mechanisms can require lotteries and infinite menus, Babaioff, Immorlica, Lucier, and Weinberg showed that the better of these two simple formats always achieves a constant fraction of optimal revenue. We prove that $\mathrm{OPT} \le 3.52 \max\{\mathrm{SREV}, \mathrm{BREV}\}$, where $\mathrm{SREV}$ and $\mathrm{BREV}$ are the optimal revenues from selling separately and grand bundling, respectively. This improves the previous best-known approximation factor of $5.2$ due to Ma and Simchi-Levi and narrows the gap to the known lower bound of $2$.

Problem

• Revenue guarantees
• Selling separately
• Grand bundling
• Mechanism design
• Approximation factor

Innovation

• Revenue approximation
• Separate selling
• Grand bundling
• Mechanism design
• Additive buyer