Yuhang Wu

On a platform with many sellers, should a pricing algorithm explicitly model competitors' prices when learning demand? Classical learning arguments suggest an affirmative answer: ignoring competitors induces model misspecification and inefficiency. In contrast, recent work on algorithmic collusion suggests that strategic obliviousness -- deliberately ignoring competitor prices -- may facilitate collusive outcomes and improve profits. We study this modeling choice in a stylized competitive market with unknown noisy demand, in which multiple sellers repeatedly set prices and estimate demand via iterated least squares, and either incorporate competitors' prices into their demand models (informed) or ignore them (oblivious). We first show that, relative to a monopolist, an oblivious seller in a competitive market must explore more aggressively to compensate for the loss of dynamic competitor information. Building on this insight, we characterize market dynamics when all sellers are oblivious and show that prices converge to the competitive outcome under sufficient exploration, while a continuum of pseudo-equilibria arises when exploration decays. Analyzing the resulting price trajectories, we uncover an excursion phenomenon that gives rise to transient collusive patterns that dissipate as learning progresses. In markets with both oblivious and informed sellers, the informed strictly out-earn the oblivious. Read as a strategy game, the modeling choice has a unique Nash equilibrium: the all-informed market, in which prices converge to the competitive outcome efficiently. Overall, our results indicate that collusive patterns are not robust and are not sustained by oblivious modeling; therefore, incorporating competitor information, together with sufficient price exploration, remains a reliable strategy for sellers in competitive markets.

We study adaptive querying for learning user-dependent quantities of interest, such as responses to held-out items and psychometric indicators, within tight query budgets. Classical Bayesian design and computerized adaptive testing typically rely on restrictive parametric assumptions or expensive posterior approximations, limiting their use in heterogeneous, high-dimensional, and cold-start settings. We introduce a persona-induced latent variable model that represents a user's state through membership in a finite dictionary of AI personas, each offering response distributions produced by a large language model. This yields expressive priors with closed-form posterior updates and efficient finite-mixture predictions, enabling scalable Bayesian design for sequential item selection. Experiments on synthetic data and WorldValuesBench demonstrate that persona-based posteriors deliver accurate probabilistic predictions and an interpretable adaptive elicitation pipeline.

AI-based persona simulation -- often referred to as digital twin simulation -- is increasingly used for market research, recommender systems, and social sciences. Despite their flexibility, large language models (LLMs) often exhibit systematic bias and miscalibration relative to real human behavior, limiting their reliability. Inspired by synthetic control methods from causal inference, we propose SYN-DIGITS (SYNthetic Control Framework for Calibrated DIGItal Twin Simulation), a principled and lightweight calibration framework that learns latent structure from digital-twin responses and transfers it to align predictions with human ground truth. SYN-DIGITS operates as a post-processing layer on top of any LLM-based simulator and thus is model-agnostic. We develop a latent factor model that formalizes when and why calibration succeeds through latent space alignment conditions, and we systematically evaluate ten calibration methods across thirteen persona constructions, three LLMs, and two datasets. SYN-DIGITS supports both individual-level and distributional simulation for previously unseen questions and unobserved populations, with provable error guarantees. Experiments show that SYN-DIGITS achieves up to 50% relative improvements in individual-level correlation and 50--90% relative reductions in distributional discrepancy compared to uncalibrated baselines.

With the rise of large language models (LLMs), generative engines have become powerful alternatives to traditional search, reshaping retrieval tasks. In e-commerce, for instance, conversational shopping agents now guide consumers to relevant products. This shift has created the need for generative engine optimization (GEO)---improving content visibility and relevance for generative engines. Despite its growing importance, current GEO practices are largely ad hoc, and their impacts remain poorly understood, especially in the e-commerce setting. We address this gap by introducing E-GEO, the first dataset built specifically for e-commerce GEO. E-GEO contains 13,747 realistic, multi-sentence consumer product queries, each paired with 10 retrieved Amazon listings, capturing rich intent, constraints, preferences, and shopping contexts that existing datasets miss. Using this dataset, we conduct the first large-scale empirical study of e-commerce GEO across five representative generative engines, seven popular LLM rewriters, and fifteen hand-crafted rewriting heuristics. We further formulate GEO as an optimization problem and develop a lightweight prompt meta-optimization algorithm that significantly improves over heuristic baselines. Notably, the optimized prompts reveal a stable, domain-agnostic pattern, suggesting the existence of a "universally effective" GEO strategy. Finally, we red-team the GEO system through both heuristic and optimization-based attacks and show that, under a simple in-prompt defense, gains from GEO reflect genuine content improvement rather than manipulation, anchoring GEO as a substantive and well-defined optimization problem.

Large language models (LLMs) are increasingly used to simulate survey responses, but synthetic data can be misaligned with the human population, leading to unreliable inference. We develop a general framework that converts LLM-simulated responses into reliable confidence sets for population parameters of human responses, addressing the distribution shift between the simulated and real populations. The key design choice is the number of simulated responses: too many produce overly narrow sets with poor coverage, while too few yield excessively loose estimates. We propose a data-driven approach that adaptively selects the simulation sample size to achieve nominal average-case coverage, regardless of the LLM's simulation fidelity or the confidence set construction procedure. The selected sample size is further shown to reflect the effective human population size that the LLM can represent, providing a quantitative measure of its simulation fidelity. Experiments on real survey datasets reveal heterogeneous fidelity gaps across different LLMs and domains.