Yuhang Wu

On a platform with many sellers, should a pricing algorithm explicitly model competitors' prices when learning demand? Classical arguments suggest that ignoring competitors induces model misspecification and inefficiency, yet findings from algorithmic collusion suggest that ignoring competitor prices may, surprisingly, facilitate collusive outcomes and improve profits. We study this problem in a competitive market with unknown noisy demand, in which sellers repeatedly set prices, either incorporating competitor prices in learning their demand models (informed), or ignoring them (oblivious). We show that, relative to a monopolist, an oblivious seller in a competitive market must conduct more aggressive price exploration to compensate for the loss of dynamic competitor information. When all sellers are oblivious, prices converge to the competitive outcome under persistent exploration, while a continuum of pseudo-equilibria arises when exploration is "insufficient." In markets with a mix of oblivious and informed sellers, the informed strictly out-earn the oblivious. In game-theoretic terms, the unique Nash equilibrium is the all-informed market, in which prices converge to the competitive outcome efficiently, and oblivious modeling does not robustly lead to collusive patterns.

With the rise of large language models (LLMs), generative engines have become powerful alternatives to traditional search, creating 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 understudied. In e-commerce, for instance, conversational shopping agents now guide consumers to relevant products, yet it is unclear if GEO can affect how products surface to users. We address this gap by introducing E-GEO, which contains 13,746 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 a large-scale empirical study of e-commerce GEO across five representative generative engines, seven LLM rewriters, and fifteen rewriting heuristics. We further formulate GEO as an optimization problem and develop a prompt meta-optimization algorithm that significantly improves over heuristic baselines. Notably, prompts independently optimized from different heuristics converge to a stable pattern, suggesting a shared, transferable GEO strategy. Finally, we red-team the GEO system through both static and optimization-based attacks and show that, under a simple in-prompt defense in our setting, gains from GEO reflect genuine content improvement, anchoring GEO as a substantive optimization problem.

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.

Persona simulation based on large language models---often referred to as digital twin simulation---is increasingly used for market research, recommender systems, and social science research. However, these simulations often exhibit systematic bias and miscalibration relative to real human behavior. We propose SYN-DIGITS, a model-agnostic, post-hoc calibration framework that learns relationships among questions from digital twins and transfers them to predict human responses. We focus on a cold-start setting in which no human response to the target question is observed, so calibration must rely on digital twins and human data on reference questions. Our analysis shows that, though digital twins may not reproduce individual human responses accurately, they can capture nontrivial relationships among questions that can be effectively transferred to the human side. When individual-level data is unavailable and we only have access to marginal information on reference questions, our framework also supports distribution-level calibration for predicting the distribution of human responses on the target question. Across three datasets and thirteen persona constructions, experiments show that SYN-DIGITS achieves 11% to 417% relative improvements in individual-level correlation and 46%--57% relative reductions in distributional discrepancy compared to uncalibrated baselines.

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.