Improved bounds on losses from simple selling methods
Improved Revenue Guarantees for Selling Separately and Bundling
Computer Science and Game Theory
Summary
Many sellers want to make the most money when selling items to buyers, but the best methods can be very complicated. The paper looks at two simple ways to sell: selling items one by one or selling all items together as a bundle. The authors show that using the better of these two simple ways will get at least about one-third of the maximum possible money a seller could get. This improves previous estimates and helps us better understand how much money sellers lose by sticking to simpler methods.
What this means in practice
- •For ecommerce platform designers: Design pricing schemes that guarantee at least a third of maximum revenue using simple selling or bundling formats for digital or physical product listings.
- •For pricing strategy teams: Set revenue expectations and simplify pricing by relying on either separate sales or full bundling while knowing losses will be within a known range.
A theory result. No direct application yet.
Authors
Yang Cai, Vineet Gupta, Yanchen Jiang, Christopher Liaw, Aranyak Mehta, Grigoris Velegkas, Di Wang
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 $2$.