Research

E-commerce is shifting from search-based shopping to agentic purchasing, as AI shopping agents replace keyword search with multi-round conversations. We propose a solicit-then-suggest framework: an agent asks m targeted questions in a d-dimensional preference space to refine its belief about the customer’s ideal product, then recommends k products for the customer to choose from. Solicitation depth (m) and assortment breadth (k) are substitutes: total prior uncertainty is a fixed pie, split between what questioning eliminates and what the assortment can hedge. Yet the two work at sharply different rates. Expected loss falls as O(1/m) in the number of questions, whereas assortment breadth suffers a curse of dimensionality, with loss falling only as O(k^−2/d). A few well-targeted questions can thus achieve what would otherwise take exponentially many recommendations. The optimal assortment forms a Voronoi partition. For a single product, optimal questioning follows a water-filling rule that equalizes posterior uncertainty across preference dimensions. Larger assortments may call for selective focus, yet water-filling retains an approximation guarantee. These insights extend to non-Gaussian priors, for which the Gaussian model is a conservative benchmark that becomes asymptotically exact as the conversation lengthens.

We explore how platform mitigation can influence seller competitive behavior in an online marketplace. Specifically, by focusing on multiple newsvendor-type sellers with different cost structures competing to sell identical products on an e-commerce platform, we investigate the effects of different demand allocation rules on sellers’ inventory stocking decisions and the platform’s payoff. Somewhat surprisingly, we show that all inventory-agnostic priority rules, which follow a specific ranking to allocate sequentially arriving demand to sellers, yield a market outcome that exactly mirrors sole sourcing from the most efficient seller with the largest critical fractile. In contrast, incorporating randomness into demand allocation intensifies competition among sellers and increases the platform’s payoff. Moreover, inventory-aware random allocation rules further incentivize competitive behavior among sellers. We make two extensions. First, we examine how different platform allocation rules affect sellers and show that incorporating randomization and inventory information into these rules heightens sellers’ profit variability and ex-post unfairness while leaving ex-ante fairness unchanged, revealing an inherent efficiency-fairness trade-off in platform design. Second, we investigate a scenario in which sellers must learn the allocation rules through reinforcement learning algorithms, potentially leading to algorithmic collusion. We propose mitigation strategies and demonstrate how our studied allocation rules can be adapted to sustain a competitive marketplace in such a dynamic environment.

When competing sellers delegate pricing to a shared AI model, such as a large language model, the shared model can create correlated recommendations across firms. Combined with performance-driven updates that aggregate seller feedback, this raises the question: Can standard AI deployment practices inadvertently produce supracompetitive pricing? We develop a stylized duopoly model in which two sellers receive pricing recommendations from a shared AI model characterized by two parameters: a propensity parameter that captures the model’s tendency to set high prices, and an output-fidelity parameter that measures the alignment between this tendency and the model’s outputs. The model updates its propensity through periodic retraining on observed outcomes. We find that the seemingly prudent practice of configuring AI models for robustness and reproducibility can lead to supracompetitive pricing via a phase transition. We establish a critical output-fidelity threshold: below it, competitive pricing is the unique stable outcome. Above it, the model exhibits bistability, with both competitive and supracompetitive pricing being locally stable and the realized outcome determined by the model’s initial propensity. Supracompetitive pricing leads to higher average prices, but occasional low-price recommendations complicate detection. When output fidelity is perfect, full price coordination emerges from any interior initial propensity of the model. For finite training batches of size b, when the initial propensity lies in the supracompetitive basin, the probability of supracompetitive pricing approaches 1 as b increases. The region of indeterminate outcomes shrinks at a rate O(1/√b), so that larger batches convert more initial conditions into predictably supracompetitive trajectories. Our results identify a critical fidelity threshold below which competitive pricing is the unique long-run outcome. Any factor that reduces the effective alignment between the shared model’s propensity and sellers’ actual pricing, whether through diversifying AI providers, introducing recommendation noise, or reducing seller adherence, pushes the market toward competitive outcomes. Larger training batches amplify the risk of supracompetitive pricing by suppressing stochastic fluctuations that might otherwise restore competitive pricing.

We study integrated production planning and aggregate scheduling for large-scale make-to-order manufacturing. Each order carries bill-of-materials (BOM) requirements and routing operations, while orders compete for shared work-center capacity over time. Time-indexed mixed-integer linear programming (MILP) formulations model this setting directly, but become difficult to solve at industrial scale. We propose Lift-Sample-Repair (LSR), an LP-guided rounding method that converts a fractional LP solution into a reduced set of precedence-feasible whole-order timing patterns, samples one pattern per order, and repairs shared-capacity violations. We prove that this lift recovers a whole-order support whose size is linear in each order’s operation-period grid and that the expected loss relative to the LP benchmark is sublinear under capacity granularity, with an O(√N) bound when individual orders are small relative to capacity. These results provide theoretical support for LSR’s computational efficiency and solution quality. Empirically, base LSR reaches 94%–98% of the LP benchmark at the three largest tested scales, where the original time-indexed MILP certifies only 22 of 108 attempts within a two-hour budget. A loss decomposition shows that much of the residual gap remains after pattern construction, in pattern selection and repair. This motivates Agent-LSR, which automates policy search within the modular LSR interface. An LLM coding agent searches implementable rules for sampling, repair, refill, and multi-pass selection, while the recovered pattern set, model, LP relaxation, and feasibility guard remain fixed. On challenging structured instances, it reduces the average LP-relative gap from about 24% to about 6%. In an industrial PCB case study, LSR improves LP-relative performance relative to representative planning baselines, attaining mean LP-relative gaps below 1% on a fine-grained mass-production plant and 11.4% on a coarser custom plant under Agent-LSR. Beyond constructing feasible planning schedules, the same interface turns LP capacity shadow prices into managerial diagnostics for order triage, bottleneck-capacity planning, and decentralized work-center coordination.