ecommerce platform designers

Abstract: We study simple auctions for one additive buyer whose values for $m$ items are independent. Write $\mathrm{REV}$ for optimal revenue, $\mathrm{SREV}$ and $\mathrm{BREV}$ for the revenues from separate selling and grand bundling, and $\mathrm{BSPA}_2$ for grand-bundle second-price revenue with two independent bidders. For independent regular items, we prove $\mathrm{REV}\le\mathrm{BSPA}_2\le2\mathrm{BREV}$. This establishes tight approximation and competition guarantees for bundling under regularity and answers an open question from Beyhaghi et al. (EC 2025). For general independent items, we prove $\mathrm{REV} \le \mathrm{SREV} + \frac{π^2}{6}\mathrm{BREV} \le 2.645 \max\{\mathrm{SREV}, \mathrm{BREV}\}$. This improves the previous approximation factors of $6$ from Babaioff, Immorlica, Lucier, and Weinberg (FOCS 2014, JACM 2020) and $5.2$ from Ma and Simchi-Levi (AISTATS 2021). On the lower bound side, we construct an instance in which prices for three disjoint bundles earn more than $2.11\max\{\mathrm{SREV},\mathrm{BREV}\}$, improving the previous lower bound of $2$ from Rubinstein (ITCS 2016). We also show that exact recovery of one buyer's optimal revenue by the better of separate selling and bundling requires $Θ(\log m)$ bidders in the worst case.

Abstract: A commercial incentive need not enter the final ranking algorithm to affect a shopping assistant's recommendation: it may instead influence which preference question the assistant asks. We make this distinction experimentally observable in a deliberately small, synthetic setting. Each task has two products, three verified numerical attributes, a price limit, and a private fixed preference vector. An honest simulated user answers one pairwise question. A separate recommender receives the products and this answer but not the sponsorship assignment. We contrast a neutral question, a soft commercial instruction, and an explicitly adversarial instruction to ask about the sponsor's advantage while omitting the rival's advantage. Across 40 held-out sponsorship-assignment cases (20 distinct catalog-preference contexts), the soft instruction changes no selections. The targeted instruction raises sponsored selection by 0.30 and reduces mean synthetic utility by 0.0547 relative to neutral questioning (95% context-bootstrap interval [-0.0828, -0.0291]) for one language-model recommender. A fixed Bayesian recommender shows a similar effect; a second model makes the same choices on all 120 frozen question-answer inputs. A terminal-answer consistency judge rates all 20 sampled targeted answers consistent, although five have synthetic regret above 0.05; a separate question-coverage dimension flags their one-sided elicitation. A robust partial-preference certificate remains valid under the stipulated synthetic utility but certifies only 16 of 40 targeted cases and is not better than asking a neutral question directly. These results establish neither typical behavior under advertising incentives nor effects on actual consumers.

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 $2$.

Abstract: Consumers increasingly delegate purchasing decisions to Large Language Models (LLMs) acting as surrogate consumers. Using "Tool-Lab," an adaptation of information-board process tracing that places product attributes behind costly tool calls, we examine how marketing pricing cues (i.e., just-below pricing and promotional framing) influence AI shopping agents. Across eight commercially deployed LLMs from three providers, we trace pre-choice information acquisition. Under zero cost, pricing cues rarely mislead. Imposing acquisition costs under a vague goal prompt leads LLMs to omit diagnostic attributes required to compute unit price and choose suboptimal choices resembling human heuristics. Relative to a specific goal prompt that mainly preserves diagnostic search and choice optimality, a vague goal prompt under constraints creates a search-mediated vulnerability. This research demonstrates that marketing heuristics in delegated AI shopping are governed by storefront information architecture, not necessarily immutable LLM flaws.