We initiate the study of contextual dynamic pricing with a heterogeneous population of buyers, where a seller repeatedly posts prices (over T rounds) that depend on the observable d-dimensional context and receives binary purchase feedback. Unlike prior work assuming homogeneous buyer types, in our setting the buyer's valuation type is drawn from an unknown distribution with finite support size K . We develop a contextual pricing algorithm based on optimistic posterior sampling with regret eO(K dT), which we prove to be tight in dand T up to logarithmic terms. Finally, we refine our analysis for the non-contextual pricing case, proposing a variance-aware zooming algorithm that achieves the optimal dependence on K .

We begin by characterizing the space of elements that test an agent's ability to optimally allocate1031 their limited resources to goods and services they desire. In economics and decision theory, the1032 most primitive approach to describing the preferences of decision-makers is to use a function that1033 maps a set of possible choices to the agent's optimal choice within that set. Under a set of intuitive1034 assumptions, such as transitivity (i.e., if bundle X is preferred to bundle Y, and Y is preferred to1035 bundle Z, then X must be preferred to Z), it becomes possible to "rationalize" preferences by instead1036 describing a utility function. This function assigns a real number to each bundle, and the agent selects1037 the bundle with the highest utility.1038 In this paper, we focus on these "rationalizable" preferences, where agent choice can be implemented1039 as utility maximization constrained by prices and income. The solution to these consumer choice1040 problems provides ...

Large language models (LLMs) are increasingly being asked to make economically rational decisions and indeed are already being applied to economic tasks like stock picking and financial analysis. Existing LLM benchmarks tend to focus on specific applications, making them insufficient for characterizing economic reasoning more broadly. In previous work, we offered a blueprint for comprehensively benchmarking strategic decision-making Raman et al. [2024]. However, this work did not engage with the even larger microeconomic literature on non-strategic settings. We address this gap here, taxonomizing microeconomic reasoning into 58distinct elements, each grounded in up to 10distinct domains, 5perspectives, and 3types. The generation of benchmark data across this combinatorial space is powered by a novel LLM-assisted data generation protocol that we dub auto-STEER, which generates a set of questions by adapting handwritten templates to target new domains and perspectives. By generating fresh questions for each element, auto-STEER induces diversity which could help to reduce the risk of data contamination. We use this benchmark to evaluate 27LLMs spanning a range of scales and adaptation strategies, comparing performance across multiple formats--multiple-choice and free-text question answering--and scoring schemes. Our results surface systematic limitations in current LLMs' ability to generalize economic reasoning across types, formats, and textual perturbations, and establish a foundation for evaluating and improving economic competence in foundation models.

We consider a novel dynamic pricing and learning setting where in addition to setting prices of products in sequential rounds, the seller also ex-ante commits to'advertising schemes'. That is, in the beginning of each round the seller can decide what kind of signal they will provide to the buyer about the product's quality upon realization. Using the popular Bayesian persuasion framework to model the effect of these signals on the buyers' valuation and purchase responses, we formulate the problem of finding an optimal design of the advertising scheme along with a pricing scheme that maximizes the seller's expected revenue. Without any apriori knowledge of the buyers' demand function, our goal is to design an online algorithm that can use past purchase responses to adaptively learn the optimal pricing and advertising strategy. We study the regret of the algorithm when compared to the optimal clairvoyant price and advertising scheme.

This paper develops a practical framework for using observational data to audit the consumer surplus effects of AI-driven decisions, specifically in targeted pricing and algorithmic lending. Traditional approaches first estimate demand functions and then integrate to compute consumer surplus, but these methods can be challenging to implement in practice due to model misspecification in parametric demand forms and the large data requirements and slow convergence of flexible nonparametric or machine learning approaches. Instead, we exploit the randomness inherent in modern algorithmic pricing, arising from the need to balance exploration and exploitation, and introduce an estimator that avoids explicit estimation and numerical integration of the demand function. Each observed purchase outcome at a randomized price is an unbiased estimate of demand and by carefully reweighting purchase outcomes using novel cumulative propensity weights (CPW), we are able to reconstruct the integral. Building on this idea, we introduce a doubly robust variant named the augmented cumulative propensity weighting (ACPW) estimator that only requires one of either the demand model or the historical pricing policy distribution to be correctly specified. Furthermore, this approach facilitates the use of flexible machine learning methods for estimating consumer surplus, since it achieves fast convergence rates by incorporating an estimate of demand, even when the machine learning estimate has slower convergence rates. Neither of these estimators is a standard application of off-policy evaluation techniques as the target estimand, consumer surplus, is unobserved. To address fairness, we extend this framework to an inequality-aware surplus measure, allowing regulators and firms to quantify the profit-equity trade-off. Finally, we validate our methods through comprehensive numerical studies.

We consider the Continuum Bandit problem where the goal is to find the optimal action under an unknown reward function, with an additional monotonicity constraint (or, markdown constraint) that requires that the action sequence be non-increasing. This problem faithfully models a natural single-product dynamic pricing problem, called markdown pricing, where the objective is to adaptively reduce the price over a finite sales horizon to maximize expected revenues. Jia et al '21 and Chen '21 independently showed a tight $T^{3/4}$ regret bound over $T$ rounds under *minimal* assumptions of unimodality and Lipschitzness in the reward (or, revenue) function. This bound shows that the demand learning in markdown pricing is harder than unconstrained (i.e., without the monotonicity constraint) pricing under unknown demand which suffers regret only of the order of $T^{2/3}$ under the same assumptions (Kleinberg '04). However, in practice the demand functions are usually assumed to have certain functional forms (e.g.

We initiate the study of contextual dynamic pricing with a heterogeneous population of buyers, where a seller repeatedly posts prices (over $T$ rounds) that depend on the observable $d$-dimensional context and receives binary purchase feedback. Unlike prior work assuming homogeneous buyer types, in our setting the buyer's valuation type is drawn from an unknown distribution with finite support size $K_{\star}$. We develop a contextual pricing algorithm based on optimistic posterior sampling with regret $\widetilde{O}(K_{\star}\sqrt{dT})$, which we prove to be tight in $d$ and $T$ up to logarithmic terms. Finally, we refine our analysis for the non-contextual pricing case, proposing a variance-aware zooming algorithm that achieves the optimal dependence on $K_{\star}$.

This problem faithfully models a natural revenue management problem, called "markdown pricing",