Dynamic Pricing

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5 papers in the last four weeks, against 2 the four weeks before. 0.1% of all new papers.

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Latest papers 42

Sep 30, 2026stat.ML

Learning to Price Electricity for Optimal Demand Response

There is considerable interest in using time-varying electricity prices to shape consumer demand response, and better align energy demand with renewable production. However, optimal prices generally vary over time in response to complex signals such as weather forecasts, sunrise/sunset times, and day-of-week patterns; and existing methods are not able to make efficient use of such rich contextual information. Here, we propose a neural-network-based algorithm for contextual energy pricing, modeling pricing as a Stackelberg game and leveraging a mean-field solution representation from Mehrabi et al.~(2024). The approach learns constrained mappings from contextual features to feasible price signals. We validate our approach by simulating the energy grid in several US cities, and show that incorporating contextual information can considerably increase the value of the demand response programs.

Jing Shang, Mohammad Mehrabi, Xinyang Zhou +3

Stanford University · National Laboratory of the Rockies · Prime Coalition +1

Electricity Markets Demand Response Dynamic Pricing Mean-Field Limit Responses

Sep 28, 2026cs.LG

Persistent Partners Raise Prices Among Learning Agents

When pricing agents meet repeatedly on a platform, the platform decides who faces whom. We ask whether that choice moves the prices the agents learn, and whether a rise comes with learned punishment. In a pre-registered randomised experiment in the Bertrand duopoly of Calvano et al., each agent's price is set by a tabular Q-learning module, not by the small language model attached to it, and we randomise whether each agent keeps its partner, sees its rival's prices and can send messages. Keeping the same partner raises the level of profits, averaged over training, by 0.27 of the gap between competitive and monopoly profit (95% CI 0.20 to 0.35, all twenty paired runs positive), our registered primary result, and the resting price by 0.17 of the Nash-to-monopoly range (post hoc). A plain tabular learner reproduces the effect in all 25 further blocks, and there one permanent partner raises the level more than about three do (+0.23 against +0.05, exploratory). Where rival prices are hidden, the price-setting module cannot see a cut, so cannot punish it, yet the resting price rises as much and the rise lasts to the end of training, while with visible rivals it shrinks with longer training (post hoc). Where the rival is visible, a static best responder accounts for a third to a half of what a forced-deviation probe reads as punishment, on the starts where the rival can see the cut, and net of it the registered test of learned punishment is inconclusive. A test that looks only for punishment would thus miss the rise where the rival is hidden, while a check for profitable deviations flags most of those prices (post hoc). In an exploratory extension, untrained Qwen2.5 7B and 14B models under one prompt show the effect when the rival's price is left out of the prompt and inconsistently when it is shown, the 7B result replicating on fresh blocks, while two other model families show none.

Paul-Peter Arslan, Yubin Kim, Xiao Xiao

Institute For Future Technologies Devinci Higher Education · Massachusetts Institute of Technology

Dynamic Pricing Prices Strategic Agents Q-Learning Nash Equilibrium Agentic Framework

Sep 16, 2026cs.AI

Faithful yet Collusive: Why Chain-of-Thought Monitoring Cannot Detect Collusion in LLM Pricing Agents under Oligopolistic Competition

Large language models (LLM) deployed as autonomous pricing agents may sustain supracompetitive prices through tacit coordination. We develop a causal graph divergence framework that separately measures structural faithfulness and intent faithfulness of LLM pricing agents in Bertrand competition. Across nine LLMs under duopoly and triopoly conditions, collusive behavior and chain-of-thought (CoT) faithfulness dissociate along both dimensions: the most collusive model accurately reports cooperative intent yet reasons structurally unfaithfully, while the most structurally faithful model sustains supra-Nash pricing under both market structures. These findings establish that CoT monitoring alone cannot serve as a standalone safeguard against algorithmic collusion.

Dohun Lee, Hyunwoo Park

Graduate School of Data Science, Seoul National University

Collusion Dynamic Pricing Chain-of-Thought Reasoning

Sep 1, 2026cs.LG

Reinforcement Learning and Rule-Based Peer-to-Peer Pricing in Residential PV-BES Communities

This paper compares rule-based and learning-based pricing mechanisms for peer-to-peer (P2P) electricity trading in residential photovoltaic communities. The rule-based benchmarks comprise bill-sharing as an ex post allocation mechanism, the mid-market rate, and supply-demand-ratio pricing. The reinforcement-learning (RL) formulation is implemented through a Deep Q-Network and evaluated under multiplier-based and learnable SDR-shaped pricing, with a fixed-parameter SDR variant as a non-learning control. Performance is assessed through community savings together with complementary financial and operational indicators. In the base PV-only configuration, the rule-based benchmarks outperform the best RL policy. With battery energy storage, evaluated for the RL policies only, community savings under the best RL policy increase from EUR 734.23 to EUR 978.52. Across the learning-based modes and in both configurations, SDR-shaped pricing outperforms the multiplier-based parameterization considered. The results indicate that rule-based pricing remains highly competitive wherever the two families are compared directly, and that storage substantially improves the learning-based outcomes under this accounting, while the distribution of benefits remains heterogeneous across households.

Pablo Benalcazar, Maciej Kalka, Wilian Guamán +1

Division of Energy Economics, Mineral and Energy Economy Research Institute, Polish Academy of Sciences, Kraków, Poland · GITEA, Escuela Superior Politécnica de Chimborazo (ESPOCH), Riobamba, Ecuador

Electricity Markets Photovoltaic Dynamic Pricing Peer-To-Peer Prices

Sep 1, 2026cs.DS

Prediction-Assisted Pricing and Admission for LLM APIs with Stochastic Token Consumption

An LLM application often sells or internally allocates several service products: a small or premium model, a short or long token cap, and possibly multiple posted prices. The operational decision is not merely which model answers a prompt. A price changes purchase probability, a token cap changes both user value and the tail of resource consumption, and accepted requests compete for shared compute and premium-model capacity. Demand and output length are initially uncertain, while an offline model may provide useful but imperfect predictions. We formulate sequential pricing and admission with stochastic resource consumption. Each arriving request belongs to an observable segment. The platform chooses a product--price pair or makes no offer; purchase, revenue, and resource use are then random. An offline predictor supplies a uniform, validated error radius for every segment--product cell. We propose Prediction-Clipped UCB (PCUCB), which intersects the offline prediction interval with an online confidence interval, evaluates products using resource shadow prices, and reserves a sample-path envelope before commitment. The prior gives a fast start when accurate, while online learning protects the platform when predictions are coarse. The analysis is modular. On a simultaneous confidence event, regret against a buffered fluid benchmark is bounded by a pacing term plus the cumulative diameter of the intersected intervals. For

J

segment-product cells and prediction radius

\varepsilon

, this yields

\widetilde O\left( \sqrt{T}+(1+\barΛ) \min\{T\varepsilon,\sqrt{JT}\} \right),

where

\barΛ

bounds operational shadow prices. Thus the algorithm smoothly interpolates between an almost full-information regime and learning from scratch. Hard feasibility holds on every sample path through reservation envelopes.

Patrick Wong

Dynamic Pricing Prices Queue Control Admissibility

Aug 31, 2026cs.AI

The Irreversibility Budget: Fleet-Level Risk Accounting and Admission Control for Agent Operating Systems

Fleets of LLM agents now externalize effects that cannot be fully undone: they move money, deploy code, delete data, and disclose information. Current controls check one effect at a time, so a fleet of individually authorized agents can overdraw its principal's risk under a shared trigger while every local gate stays correct. We propose the irreversibility budget, a cumulative account of residual value-at-risk that a trusted runtime maintains for each principal across agents, workflows, and tenants. Treating irreversibility as a first-class resource, the runtime charges each effect its residual loss below the agent and denies the marginal effect once the aggregate would overdraw the budget. Getting the price right is hard, because effects are heterogeneous, adversarially declared, and correlated. We perform a controlled study in which per-effect gates admit fleet-level overdraws of up to 48 times the tenant's risk limit while the budget holds every correctly charged run within that limit. Conservative, dependency-aware pricing remains the central open problem for a deployable design.

Bardia Mohammadi, Laurent Bindschaedler

Max Planck Institute for Software Systems Saarbrücken, Germany

Runtime Safety Filtering Agentic Deployments Irreversibility Artificial Intelligence Risk Conditional-Value-At-Risk Admissibility+1

Aug 31, 2026cs.LG

Nonparametric Contextual Pricing and Inventory Learning under Censored Demand

In online retailing, when a product sells out, a retailer often sees only the units sold, not how many customers would have bought it had inventory been available. However, the inventory level determines how much demand is revealed, and this information can influence subsequent decisions and future profits. We study an online selling problem in which, in each round, the seller observes a market context and then makes pricing and stocking decisions based on censored sales data from previous rounds. The challenge is to learn a context-dependent pricing and stocking policy without assuming a particular formula for demand or observing realized profit. To overcome this difficulty, we propose a Mean-Calibrated Kernel UCB (MCK-UCB) algorithm that turns each incomplete sales record into a reliable guide for both inventory and price decisions, using data from past rounds with similar market conditions. This design allows us to learn while serving customers, without a separate exploration phase or the need to recover all demand hidden by stockouts. We prove the minimax optimality of the proposed algorithm, with strictly faster rates when expected profit varies more smoothly with price. Comprehensive numerical experiments have been conducted to confirm the effectiveness of the proposed algorithm.

Zean Han, Jing Liang, Ruihan Lin +2

Department of Industrial Engineering and Decision Analytics The Hong Kong University of Science and Technology

Inventory Control Dynamic Pricing Prices Incomplete

Aug 5, 2026cs.LG

Differentiating Through Dual Prices: End-to-End Policy Learning Under Capacity Constraints

Many social services assign scarce resources, such as housing assistance or hospital interventions, to people who arrive one at a time: each arrival must receive a decision immediately, and the long-run usage of every resource must stay within its capacity. We study how to learn such an assignment policy from logged observational data. The standard pipeline is decision-blind: fit one outcome model per arm by regression, price each capacitated resource from the fitted models, and assign each arrival the arm whose predicted outcome minus price is largest. We instead train the outcome models end-to-end, differentiating an off-policy estimate of the deployed policy's value through the dual prices themselves. We study two formulations: an exact nonconvex one, and a convex relaxation whose optimum always satisfies the capacity constraints in expectation and which is suboptimal by at most a term linear in the smoothing temperature and logarithmic in the number of arms. Every method is evaluated in a queueing simulation with resources replenished at their capacity rates. Across six datasets, the two end-to-end variants take the top slots on a deployment-adjusted value index at every delay cost, including zero; when capacities are binding, decision-blind baselines frequently violate them and incur much longer queueing delays. On the largest dataset, a hospital cohort of seventy thousand patients, end-to-end training also achieves significantly higher policy value, a margin that survives a capacity-matched neural baseline. Flexible decision-blind regression remains the stronger pure predictor where ground truth is measurable; end-to-end training is best suited to settings where resources are genuinely scarce and feasibility matters.

Mohammadsaeed Haghi, Mahdi Salmani, Nima Kelidari

University of Southern California

Queue Control Dynamic Pricing Optimal Policies Capacity

Aug 4, 2026stat.ML

Minimax-Optimal Semiparametric Contextual Dynamic Pricing with Multimodal Revenue

We study contextual dynamic pricing with arbitrary covariate sequences and bounded, possibly nonbinary purchase quantities. Demand follows a semiparametric surplus-index model with an unknown linear valuation parameter and an unknown Hölder-smooth response. We impose neither concavity nor strong unimodality on revenue and allow nonunique optimal prices. We develop a pilot-corrected layered decision-partitioning policy that combines directional pilot estimation, local polynomial learning, predictable data assignment, and global action elimination. Pilot correction removes the first-order effect of valuation-parameter error, while permanent labels enable concentration under adaptive sampling. The policy attains the minimax smoothness-dependent horizon rate up to logarithmic factors; a matching lower bound already holds for a constant-context binary-demand subclass.

Xueping Gong, Zhuoluo Zhang, Zhaowei Miao +1

School of Management, Xiamen University · Department of Industrial Engineering and Decision Analytics, The Hong Kong University of Science and Technology

Dynamic Pricing Prices Optimal Policies Discrete Choice Models Covariates Multi-Modal Data

Aug 2, 2026cs.AI

402Pilot: An x402 Decision Layer for Autonomous Agent Micropayments

Programmable-payment protocols such as x402 enable per-request micropayments, but they do not determine which payable service an autonomous agent should buy under a finite wallet. We formulate this buyer-side problem as agent-native payment decision-making: contextual provider selection under wallet pressure, chosen-only paid feedback, and changing market conditions. We propose 402Pilot, a protocol-agnostic buyer-side decision layer between autonomous agents and payment execution that implements purchasing policies for selecting among payable providers. We instantiate it with PA-DCT, a payment-aware discounted contextual Thompson-sampling policy that adapts purchasing decisions under wallet pressure while learning from post-payment feedback. To evaluate buyer-side payment policies, we introduce 402Pilot-Bench, a frozen-replay benchmark spanning 823 tasks, five heterogeneous provider pipelines, and three market regimes, each evaluated over 30 paired seeds. PA-DCT achieves the strongest fixed-wallet adaptive trade-off among non-oracle policies: it maintains competitive service quality while spending only 39 to 43 percent of the wallet and reallocates spending as market conditions change. It attains the best non-oracle PA-gap/T under the price shock and the best mean and worst-case ranks across the nine scenario-metric combinations of quality, ROI, and PA-gap/T. Comparisons with learning baselines and component ablations further support the effectiveness and design of the proposed decision policy. These results suggest that programmable payment must be complemented by buyer-side decision-making capable of learning service value and adapting purchasing decisions accordingly.

Yin Li, Yanbo He, Boo-Ho Yang +5

The Hong Kong University of Science and Technology (Guangzhou), Guangzhou, China · MOVENSYS Inc., Seongnam-si, Republic of Korea · Schneider Electric, Shanghai, China +2

Payment Networks Dynamic Pricing Autonomous Agents Incentives Pilot

Jul 28, 2026cs.AI

Distributed Constraint Optimization via Online Learning and Iterative Pricing with Application to Large-Scale Satellite Scheduling

Distributed constraint optimization problems (DCOPs) provide a popular framework for distributed decision making under limited communication, but many real-world instances are too large to solve monolithically. We address this challenge from two complementary directions. We revisit the connection between DCOPs and potential games, and adapt modern online learning algorithms for equilibrium finding to DCOPs. We show that these algorithms are competitive with representative incomplete DCOP algorithms. We then turn to decomposition frameworks for large-scale DCOPs, motivated by large-scale decentralized satellite scheduling. We propose a new framework that separates a DCOP into two interacting subproblems: a high-level meta-DCOP for task allocation, and independent local optimization problems for scheduling. To couple the two levels, we develop a novel iterative pricing method that updates the meta-level utilities using feedback from the local optimizers. Combining our online learning methods with our iterative pricing framework, we obtain near-optimal performance on real-world decentralized satellite scheduling problem instances, fulfilling over 99% of observation requests compared with 87% for state-of-the-art baselines.

Itai Zilberstein, Pranav Rajbhandari, Steve Chien +1

Department of Computer Science, Carnegie Mellon University · Jet Propulsion Laboratory, California Institute of Technology · Additional affiliations: Strategy Robot, Inc., Strategic Machine, Inc., Optimized Markets, Inc.

Decentralized Optimization Dynamic Pricing

Jul 27, 2026stat.ML

On Non-Stationary Dynamic Pricing: Adaptivity and Optimality

We study the contextual dynamic pricing problem under non-stationarity, where a firm sells products to

T

sequentially arriving consumers that behave according to an unknown demand model that can change over time. The demand model is assumed to be a generalized linear model (GLM), allowing for a feature vector in

\mathbb{R}^d

that encodes products and consumer information. To achieve optimal revenue (i.e., least regret), the firm needs to learn and exploit the unknown GLMs while monitoring for potential changes. We propose a multiscale change-point detection based algorithm that achieves a regret of order

\widetilde{O}(\sqrt{s_TdT}\wedge\{V_T^{1/3}d^{1/3}T^{2/3}+\sqrt{dT}\})

, where

s_T

is the number of piecewise stationary segments and

V_T

is a newly defined notion of design-adjusted variation budget of model parameters. Our algorithm is adaptive and does not require knowing

s_T

or

V_T

. Moreover, to our knowledge, this is the first dynamic pricing algorithm that is adaptive to the nature of changes and achieves the best-of-both-worlds rate, thus closing a long-standing gap in the literature. We remark that, due to the varying contexts, existing works in the adaptive non-stationary bandit literature cannot be applied to achieve optimality for contextual dynamic pricing. The regret is further accompanied with a newly constructed minimax lower bound, confirming the optimality of our algorithm (up to logarithmic factors). Extensive numerical experiments are conducted to illustrate the efficiency and robustness of the proposed algorithm in non-stationary dynamic pricing.

Feiyu Jiang, Zifeng Zhao

School of Management, Fudan University · Mendoza College of Business, University of Notre Dame

Dynamic Pricing Optimality Generalized Linear Model

Jul 18, 2026cs.LG

Certified-Gap Dual-Price Policies for Real-Time Truckload Bid Acceptance with Relocating, Clock-Constrained Resources

A truckload carrier must accept or reject each load tender within seconds. The decision depends on fleet state, hours-of-service (HOS) clocks, and appointment windows. We model this as a weakly coupled dynamic program in which the resources relocate and carry clocks: serving a request moves the truck to a new market and depletes its clocks, and whether a truck can serve a request depends on its state. Occupancy-based reusable-resource models do not cover this setting. We build a real-time dual-price policy from the same Lagrangian relaxation that gives the problem's upper bound. Policy and bound come from one object, so every run reports a certified optimality gap. We prove three things. First, the certificate is valid for any duals, any discretization, and any surrogate quality. Second, the policy's same-time spatial-gradient rule is exactly fluid complementary slackness, and the policy is asymptotically optimal in the subcritical fluid regime; the fitted prices are also portable across sample paths, by linear-programming basis stability. Third, certificates have limits: per-resource Lagrangian slack can stay bounded away from zero at every fleet size. We exhibit a three-truck kernel with an exact rational certificate and a replication lemma. On a public closed-loop benchmark with thirty paired seeds, the policy -- which needs no rollout labels, only one offline dual solve -- beats a rollout-trained surrogate on two of three scenarios (tight: +2.0 pp, 95% CI [+0.5, +3.6], Wilcoxon p = 0.023; mild: +3.5 pp, CI [+2.4, +4.5]) and ties the third. It decides in 0.04-0.09 ms, three orders of magnitude faster than the Monte Carlo rollout teacher. Its certificates are stable across ten bounded instances per scenario, at 57-64% of optimal, within 3-6 points of what the 1000x-slower teacher certifies.

Aswin Chandrasekaran

Bubba AI

Logistics Knapsack Constraint Dynamic Pricing Real-Time Systems Lagrangian Methods Human Relocalization

Jul 10, 2026cs.LG

Optimizing ARDL Models for Retail Sales Forecasting and Fair Pricing

Pricing food products to balance profitability with consumer welfare is a central challenge for retailers. Dynamic pricing is widely used to maximize revenue, yet most pricing models optimize business objectives while overlooking consumer fairness. This paper studies the risk of consumer exploitation under dynamic food pricing in Canada and proposes a methodology that embeds fairness constraints directly into retail sales forecasting. We model total retail trade sales with a log--log Autoregressive Distributed Lag (ARDL) specification, in which the coefficient on a product price is a sales elasticity, and pose the pricing problem as maximizing forecast sales subject to price bounds anchored to the Consumer Price Index (CPI). We solve this problem with both Linear Programming (LP) and Simulated Annealing (SA), under single-product and multi-product configurations. A key finding is that the fitted nominal elasticities are positive. As a result, an unconstrained sales-maximizer would push every price to its upper bound, and the CPI ceiling is the safeguard that prevents this. Simulated Annealing instead settles on conservative, interior prices that lower consumer cost while still meeting the sales target. We benchmark forecast accuracy against naive, seasonal-naive, ARIMA, and SARIMA baselines, and a CPI-deflated re-specification shows that the positive nominal elasticities are largely an inflation-driven artifact. The result is a transparent, fairness-aware pricing framework.

Sujay Uday Rittikar

Department of Applied Computer Science The University of Winnipeg Winnipeg, MB, Canada

Dynamic Pricing Maximization Algorithmic Fairness Autoregressive Model

Jul 9, 2026cs.LG

Quota Marketplace: Dynamic Pricing for Efficient Allocation of ML Training Resources

The escalating demand for Machine Learning (ML) training resources in recent years has resulted in a substantial gap between the high demand and the available supply. Efficient allocation of these scarce and expensive resources is crucial for organizations to maximize their return on investment. Existing resource allocation mechanisms, like Karma [OSDI'23], are designed to guarantee Pareto efficiency and max-min fairness in settings with dynamic (time-varying) user demands, but fail to preserve these key properties in the presence of demands with heterogeneous values. Given the ubiquity and inevitability of heterogeneity in organizational values of different workloads, effective resource allocation policies must accommodate these variations. In this paper, we describe the design, implementation, deployment, and theoretical analysis of Quota Marketplace, a market-based mechanism to efficiently allocate ML training chips (like GPUs), explicitly addressing scenarios with demands of heterogeneous value. We detail the implementation of this mechanism within Google and present metrics that demonstrate its impact. We also discuss many business-critical requirements that the Quota Marketplace handles quite effectively, and document the gains and opportunities it has unlocked. We establish theoretically how this market-based approach achieves the essential properties of Pareto efficiency and max-min fairness by allowing the users to express the value of their workloads and enabling dynamic resource pricing based on supply and demand fluctuations. Ultimately, the market facilitates resource allocation that aligns with organizational priorities.

Balasubramanian Sivan, Renato Paes Leme, Mihai Tiuca +6

Google · Drexel University

Schedulers Dynamic Pricing Inference Workloads Algorithmic Fairness

Jul 6, 2026cs.LG

Relational Multi-Agent Reinforcement Learning for Dynamic Pricing in High-Speed Railway Markets

In liberalised railway systems, operators must set prices dynamically in an environment with partial observability, as they retain private information about their objectives and performance, where regulatory constraints prohibit communication or direct information exchange between competitors to prevent explicit collusion. Consequently, agents must learn to infer strategic interactions only from observable market data which presents a significant challenge for multi-agent reinforcement learning, where standard approaches typically treat observations as unstructured vectors, ignoring the underlying market topology that governs strategic interactions. To address this, an entity graph modelling approach is proposed, which represents the environment as a graph of operational units, rather than decision-making agents or static infrastructure, encoding competition, coordination, and connectivity relations between entities. Then, an extension of the multi-agent twin delayed deep deterministic policy gradient algorithm with graph-based representation learning processes the features of the entities through a multi-layer relational graph convolutional network and aggregates them via a learnt attention mechanism. Experimental results in a rail pricing reinforcement learning environment show that this novel framework achieves higher revenue and stability in two different settings of increasing market complexity compared to a representative selection of relational and non-relational baselines. The code is publicly available at: https://github.com/Kinrre/RelationalRailPricing-RL

Enrique Adrian Villarrubia-Martin, David Muñoz-Valero, Luis Rodriguez-Benitez +2

Department of Technologies and Information Systems, Universidad de Castilla-La Mancha, Paseo de la Universidad 4, Ciudad Real, 13071, Spain · Department of Technologies and Information Systems, Universidad de Castilla-La Mancha, Avenida Carlos III, s/n, Toledo, 45071, Spain · Warwick Manufacturing Group, University of Warwick, Gibbet Hill Road, Coventry, CV4 7AL, UK

Multi-Agent Reinforcement Learning Dynamic Pricing Relighting Offline Reinforcement Learning Relational

Jul 6, 2026econ.TH

Strategic Buying Agents

Agentic AI is shifting online shopping from search toward delegated purchasing, where autonomous buying agents monitor markets and decide when to buy on a consumer's behalf. We study the design of such strategic buying agents, which must decide when to purchase within a finite shopping window, translating price observations, the remaining time horizon, and beliefs about future price changes into a purchase policy. We formulate this problem across three information regimes: stationary, Bayesian, and robust, and treat the resulting optimal policies as a policy menu for implementation. In the stationary regime, price adjustments follow a Poisson arrival process with a known post-adjustment price distribution; the optimal policy is a dynamic purchase-threshold rule, with the threshold governed by an ordinary differential equation. In the Bayesian regime, the adjustment intensity is known, but the price-adjustment distribution is uncertain; the optimal rule remains threshold-based, now depending on posterior beliefs, and we bound the value of knowing the true distribution. In the robust regime, the agent has only price bounds and seeks worst-case protection; randomized threshold policies achieve optimal competitive-ratio and minimax-regret guarantees. We evaluate the proposed policies on Amazon price histories from Keepa (367 items, 48,933 timestamped observations) and examine their integration into language-model buying agents. The stationary and Bayesian policies perform competitively on mean normalized consumer surplus despite their stylized assumptions, while the robust policy performs best at the distribution's 10th percentile. Results suggest language models are better suited to selecting among regimes and calibration samples than to making buy-or-wait decisions directly.

Mingyang Fu, Ming Hu

Rotman School of Management, University of Toronto

Agentic Commerce Dynamic Pricing Action Selection

Jun 25, 2026cs.LG

AIGP: An LLM-Based Framework for Long-Term Value Alignment in E-Commerce Pricing

Traditional dynamic pricing models in large-scale e-commerce suffer from limited interpretability, poor utilization of unstructured information, and misalignment with long-term business objectives such as cumulative Gross Merchandise Value (GMV), Return on Investment (ROI) and milestone achievement. We propose AIGP, a novel framework that leverages a Large Language Model (LLM) prompted with domain knowledge, structured data and textual context to make interpretable, knowledge-aware pricing decisions. For efficient deployment while maintaining high-quality outputs, we employ supervised fine-tuning for knowledge distillation. Central to AIGP is the Long-Term Value Estimator (LTVE), trained via offline reinforcement learning on historical data, which serves as a reward model to score candidate pricing actions and select preference pairs for Direct Preference Optimization (DPO), thereby aligning the pricing policy with long-term business objectives. Extensive offline evaluations and large-scale online A/B tests on Tao Factory demonstrate that AIGP achieves significant improvements: +13.21% in GMV, +7.59% in ROI, and +8.20% in milestone achievement rate over 14 days compared to the production baseline, while simultaneously providing interpretable and transparent pricing rationales.

Chennan Ma, Yanning Zhang, Siqi Hong +3

Taobao & Tmall Group of Alibaba Hangzhou, Zhejiang, China

Dynamic Pricing Prices Long-Term

Jun 22, 2026cs.LG

Dynamic multi-agent deep reinforcement learning-based pricing and incentivization approach in multimodal transportation networks

In multimodal transportation systems, shared mobility services (SMSs) are promoted for their potential to enhance flexibility and reduce congestion. However, SMS demand is often concentrated in high-density areas, which can limit the effectiveness and accessibility for various commuter groups. This uneven integration challenges transportation system efficiency, especially in terms of emissions and spatial equity. Addressing these issues requires coordination among multiple stakeholders whose objectives frequently conflict. Whereas authorities aim to ensure sustainable and equitable mobility, SMS providers focus on revenue maximization, and travelers seek to minimize personal travel costs. This paper proposes a multi-agent deep reinforcement learning framework that captures these interactions through dynamic pricing and incentivization strategies for SMSs and public transport. The framework integrates two reinforcement learning (RL) agents: (i) a public authority that allocates spatio-temporal public transport incentives to improve equity, emissions, and efficiency, and (ii) an SMS provider that dynamically adjusts fares to optimize revenue. The agents interact with the transportation system and adapt strategies in response to evolving demand, congestion, and network conditions. Numerical experiments conducted over a three-hour morning peak period show that dynamic incentivization effectively reduces congestion peaks, lowers commuters' costs by around 20% and emissions by approximately 10%, while nearly doubling public transport profit and supporting a more equitable distribution of benefits. When combined with dynamic SMS pricing, the two RL agents demonstrate the ability to balance conflicting objectives between private providers and public authorities. The proposed approach provides a decision-support tool for sustainable and equitable multimodal mobility planning.

Khadidja Kadem, Mostafa Ameli, Carlos Lima Azevedo +2

aCOSYS-GRETTIA, Univ Gustave Eiffel, Marne-la-Vallée, France · bDepartment of Electrical Engineering and Computer Sciences, University of California, Berkeley, Berkeley, USA · cDepartment of Technology, Management and Economics, Technical University of Denmark, Denmark

Multi-Agent Reinforcement Learning Dynamic Pricing Transport Incentives

Jun 15, 2026cs.LG

LLM-Powered Virtual Population for Demand Simulation and Pricing

We develop an LLM-powered virtual population model that simulates demand for pricing decisions, in settings where products are described by rich unstructured information, such as text descriptions and images, and where decision makers need not only mean-demand predictions but also uncertainty estimates for counterfactual prices. Our model represents exposed customers as draws from a finite mixture of customer personas. For each persona, product, and candidate price, an LLM elicits a persona-level purchase probability using both structured persona information and unstructured product information. These probabilities are aggregated through calibrated mixture weights to form a predictive distribution of aggregate demand. The resulting simulator can evaluate counterfactual prices under various pricing objectives, including expected revenue and risk-aware criteria such as conditional value at risk. We test the framework on an online H&M fashion dataset with product descriptions and images. The calibrated LLM-based simulator achieves the best overall predictive performance among the models considered, and supports sample-efficient pricing decisions. Our framework provides a practical way to use LLMs as demand simulators for products with limited historical demand data but rich product information. By producing a full predictive demand distribution rather than only a point forecast, it enables managers to compare candidate prices, quantify demand uncertainty, and choose prices that target either average-case revenue or risk-aware objectives.

Chengpiao Huang, Kaizheng Wang

Department of Industrial Engineering and Operations Research, Columbia University. · Department of Industrial Engineering and Operations Research and Data Science Institute, Columbia University.

User Simulation Consumption Dynamic Pricing Prices Population Dynamics Large-Scale Image Datasets

Jun 11, 2026cs.LG

High-Frequency Pricing at Scale for E-Commerce

This paper presents the design, development, and implementation of a specialized forecast-then-optimize algorithmic pricing tool for sales campaigns in fashion e-commerce. Sales events present unique challenges for pricing including volatile demand patterns, rapid pricing decisions, and the need to balance short-term revenue with long-term profitability. We describe our approach combining daily-resolution demand forecasting using gradient-boosted trees with a multi-objective optimization framework that maximizes both long-term profit and net merchandise value for more than 5 million articles. Our solution addresses key limitations of existing weekly-granularity systems by implementing a forecast-then-optimize architecture that reduces pricing decision time from hours to minutes. We validate our approach through 23 A/B tests across 12 markets during 2023-2024 sales campaigns at Zalando, one of Europe's leading online fashion retailers. Experimental results demonstrate that the new pricing system achieves approximately 6% higher profit while maintaining equivalent performance on sales and revenue compared to the previous manual-algorithmic hybrid approach. Based on these results, the algorithm was successfully deployed to production and now handles the majority of algorithmic pricing decisions for sales campaigns at the company.

Stefan Birr, Tobias Huelden, Mones Raslan +7

Zalando SE∗ · Zalando SE · Databricks†

Dynamic Pricing Prices Sales Lead High-Frequency Reconstruction Garments

Jun 5, 2026cs.CY

Learning Fair Demand Models

Data-driven pricing is increasingly prevalent in sectors such as airlines, lending, insurance, and retail. By learning demand models from customer features and setting prices accordingly, these systems may generate discriminatory outcomes that raise fairness concerns. This leads to fundamental questions - how and where should systems incorporate fairness considerations in the pricing pipeline, and how does it ultimately affect societal outcomes? To answer these, we study a stylized model where a seller has a two-stage decision pipeline comprising linear demand model estimation followed by price optimization. The seller considers fairness notions in training loss, price, and demand, under both parity-wise and Rawlsian perspectives. We show that equalizing training loss across consumer groups leads to multiple solutions, which in turn can result in undesirable outcomes despite being a standard approach in fair machine learning. Focusing instead on fairness applied directly to prices or demand, we compare two strategies that enforce fairness in either the demand estimation stage or the price optimization stage. For parity-wise fairness, we characterize when each strategy yields higher social welfare under small fairness levels. We show that when market sizes and prices in the dataset are similar, imposing price fairness in the estimation stage is more beneficial to consumers, whereas imposing demand fairness in the optimization stage yields better consumer outcomes. For Rawlsian fairness, the two strategies coincide exactly. Lastly, we extend our model to alternate demand functions and conduct a case study using real-world vaccine pricing data.

Adam N. Elmachtoub, Hyemi Kim, Jonathan Y. Tan

Department of Industrial Engineering and Operations Research and Data Science Institute, Columbia University, New York, NY 10027 · Department of Industrial Engineering and Operations Research, Columbia University, New York, NY 10027

Dynamic Pricing Algorithmic Fairness Discriminative

Jun 3, 2026cs.GT

Oblivious Learning and Collusive Pricing

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.

Yuhang Wu, Assaf Zeevi

Columbia Business School

Dynamic Pricing Matching Markets Collusion

Jun 3, 2026cs.MA

Failure Modes of Deep Multi-Agent RL in Asynchronous Pricing: Reproducible Triggers, Trace Diagnostics, and a Partial Fix

We study two reproducible failure modes of deep multi-agent reinforcement learning in continuous-time pricing markets: (i) tacit cartel formation between competing DDPG agents, and (ii) actor--critic instability at high event rates. We instantiate both inside a single CT-MARL benchmark (Poisson-clocked price updates, observation latency

δ

, interior-optimum logit demand), show that synchronous DDPG agents reliably trigger Failure Mode 1 with collusion index

Δ= 0.69 \pm 0.11

, and quantify a partial microstructure fix: asynchrony alone cuts collusion by 48% and adding latency drives it to a minimum of

Δ= 0.28

. The fix has clearly documented costs: it is partial (

Δ

remains supra-Bertrand), it is non-monotone in

δ

, and it does not survive Failure Mode 2, which emerges as DDPG critic divergence at

λ= 5

and corrupts the phase-diagram cell at

(λ{=}5, δ{=}1)

. We accompany the scalar collusion index with trajectory-level trace diagnostics that expose the within-episode signalling collapse and the post-shock non-recovery.

Shree Murthy, Rohan Pandey

DigitalOcean, USA

Multi-Agent Reinforcement Learning Dynamic Pricing Critic Learning Coalition Formation Mathematical Finance Reproducibility

Jun 2, 2026stat.ML

Resource-Constrained Adaptive Inference for Sequential Pricing

Resource-constrained pricing controllers can make fixed-price inference impossible: the controller's resource state may remove the target price neighborhood from the feasible set, even when every realized action has a known positive density. We formalize this support-exclusion failure through a local non-identification result and a realized information clock. We then design a target-aware pricing controller that certifies feasible target bands and logs continuous local densities. Localized debiasing gives studentized intervals whose width is governed by this clock. The resulting regret--information accounting, stated up to pilot re-solving error, shows that cheap exploration can be insufficient for inference: polynomial target mass gives polynomial rates, while a pure

1/t

target branch does not yield shrinking fixed-target intervals without additional local movement. Experiments show calibration in certified bands and diagnostic abstention when the resource state collapses target support.

Ruicheng Ao, Jiashuo Jiang, David Simchi-Levi

Institute for Data, Systems, and Society, Massachusetts Institute of Technology, Cambridge, MA 02139 · Department of Industrial Engineering and Decision Analytics, Hong Kong University of Science and Technology, Hong Kong · Department of Civil and Environmental Engineering and Operations Research Center, Massachusetts Institute of Technology, Cambridge, MA 02139

Dynamic Pricing Exploration Debiasing

May 27, 2026stat.ML

Insurance Pricing Optimization via Off-Policy Evaluation

Traditional insurance pricing relies on risk-based principles that ensure actuarial fairness and solvency but do not explicitly account for policyholders' price sensitivity. We formulate insurance pricing as a decision-making problem and study it using tools from off-policy evaluation and stochastic control. We propose a kernelized inverse propensity score estimator that exploits local structure in the action space and yields variance reduction compared to the classical inverse propensity score estimator. Building on these value estimates, we investigate policy optimization and present two practical approaches for computing optimal pricing rules: an interpretable data-shared Lasso formulation and a flexible policy parameterization based on neural networks. Using a controlled synthetic travel insurance environment, we empirically confirm the theoretical results and show that neural networks outperform existing techniques for policy optimization.

Sascha Günther, Dimitri Semenovich, Mario V. Wüthrich

Department of Mathematics, ETH Zurich

Dynamic Pricing

May 22, 2026cs.LG

Human-in-the-Loop Contextual Bandits for Short-Term Rental Dynamic Pricing: Structural Equivalence of Historical Warm-Up and Approval-Gated Live Learning

Dynamic pricing in short-term rental (STR) markets presents a distinctive challenge for online learning algorithms: pricing decisions carry significant financial risk, operators require explainability, and market feedback is sparse (one booking outcome per listed night). We introduce the Human-in-the-Loop Gated Bandit (HITL-GB) framework, in which a contextual bandit algorithm generates price recommendations but a human agent retains authority to accept, modify, or reject each recommendation before it is applied. We show that under this approval constraint, historical pricing data -- collected under a prior deterministic policy -- is structurally equivalent to on-policy warm-up data for initialising the bandit's posterior, bypassing the weeks-to-months cold-start period that renders pure online bandit learning impractical in sparse-feedback markets. We formalise the approval-gated reward signal, derive a regularised ridge-regression warm-up procedure from historical episodes, and validate the approach on real STR production data (anonymised urban market, 2 rooms, April 2022 -- April 2026, 1,461 nightly pricing episodes). Our warm-up procedure compresses effective cold-start from ~150 episodes to ~30 episodes when initialising agents from the Hierarchical Factored Thompson Sampling (HF-TS) family. We further argue that the structural equivalence result is domain-agnostic: any high-stakes domain where human approval is legally or operationally required -- including clinical drug dosing, credit origination, content moderation, and radiological diagnosis -- satisfies the same conditions and benefits from the same warm-up strategy. In regulated industries, mandatory human oversight is thus a statistical asset rather than a deployment constraint.

Oleg Miroshnichenko

Dynamic Pricing Contextual Bandit Framework Human-In-The-Loop Cold-Start Warm Starts On-Policy+1

May 21, 2026cs.LG

Integrable Elasticity via Neural Demand Potentials

We propose the Integrable Context-Dependent Demand Network (ICDN), a demand-first neural model for multiproduct retail demand. ICDN learns log-demand as a smooth, context-conditioned function of log-prices, allowing elasticities to be derived exactly from the learned demand surface. Across three retail datasets, the model achieves competitive out-of-sample prediction while producing analytically tractable, and economically regularized own- and cross-price responses.

Carlos Heredia, Daniel Roncel

IAMM Research, Department of Applied Artificial Intelligence DAMM, Carrer del Rossell´o 515, 08025 Barcelona, Catalonia, Spain

Dynamic Pricing Neural Fields

May 20, 2026cs.LG

Nonparametric Learning and Earning with One-Point Feedback under Nonstationarity

Firms increasingly rely on dynamic pricing to respond to evolving customer demand, yet in many applications they observe only the revenue generated by a single posted price in each period. At the same time, market conditions may shift gradually or abruptly due to changes in customer preferences, competition, or external shocks. These features create two intertwined challenges: learning the revenue--demand relationship from limited feedback and adapting pricing decisions to a changing environment. We study how a seller can learn and earn effectively under these constraints, without assuming a specific parametric form for demand. We develop a learning framework that updates prices using revenue-based gradient approximations constructed from one observation per period. To address environmental changes, we incorporate a restarting mechanism that periodically refreshes the learning process so that outdated information is discounted. When the degree of nonstationarity is unknown, we further introduce a meta-learning layer to adaptively hedge across multiple restarting schedules. We provide performance guarantees for our approach, showing how cumulative revenue loss relative to a fully informed benchmark depends on both the time horizon and the magnitude of market variation. Simulation experiments using synthetic and real-world data illustrate the effectiveness of the proposed procedures.

Xiangyu Yang, Feng Xu, Jian-Qiang Hu +1

School of Management, Shandong University · School of Management, Fudan University · Department of Applied Mathematics and Statistics, Stony Brook University

Dynamic Pricing Non-Stationarity Off-Policy Learning Exponential Family Meta-Learning Feedback

May 15, 2026cs.GT

Misspecified Estimate-then-Optimize Leads to Supra-Competitive Prices

We study whether simple algorithmic pricing systems can systematically produce collusive-like prices in multi-firm markets. We consider firms that price using a myopic estimate-then-optimize rule: each repeatedly fits a demand model to its own price and sales history and sets the price that maximizes estimated profit. This demand model is misspecified, omitting competitors' prices. We analyze the dynamics of this rule when it is initialized by an exploration phase of independent random prices. We characterize when this pipeline converges to supra-competitive prices above the Nash equilibrium, via a fluid-limit ordinary differential equation analysis. We show that supra-competitive prices arise when firms initially explore within similar price ranges on the same side of the Nash price. Moreover, prices can be substantially above the Nash price; we show that prices can reach monopoly levels under symmetric exploration. Simulations calibrated to a real multifamily rental market confirm that supra-competitive outcomes arise robustly beyond our theoretical assumptions, including under finite horizons, heterogeneous products, and nonlinear logit demand.

Jackie Baek, Vivek F. Farias, Farrell Wu

Stern School of Business, New York University · Massachusetts Institute of Technology

Dynamic Pricing Matching Markets Prices

May 14, 2026stat.ML

Harnessing Unimodality in Semiparametric Contextual Pricing via Oracle Price Map Learning

We study contextual dynamic pricing in a semiparametric scalar-index valuation model where the latent value is

v_t=μ_\ast(\mathsf c_t)+ξ_t

, with an unknown utility map

μ_\ast

and an unknown additive noise distribution. The key decision object is the one-dimensional oracle price map

u\mapsto p^\ast(u)

induced by the scalar index

u=μ_\ast(\mathsf c)

and the noise tail. Under the

β

-Hölder smoothness of the tail function for

β\geq 2

and a revenue-geometry condition that gives a unique, stable, interior maximizer, this oracle map is itself

(β-1)

-smooth. We exploit such structure through

\mathsf{ORBIT}

, a modular coarse-to-fine policy that takes a scalar pilot index as input, localizes a benchmark price in each active bin, and learns a local polynomial approximation of the oracle map inside a trust region via bandit convex optimization. For the baseline linear utility model

μ_\ast(\mathsf c)=\mathsf c^\topθ_\ast

, an adaptive elliptical exploration scheme constructs the required scalar pilot online without distributional assumptions on the contexts. The resulting policy achieves regret

\widetilde{O}\big(T^{\frac{2β-1}{4β-3}}+\sqrt{dT}\big)

. For fixed

d

, we establish a matching lower bound in the horizon dependence, unveiling that the nonparametric oracle-map learning term is minimax sharp. The same scalar-pilot interface also yields extensions to sparse high-dimensional linear utility and nonparametric Hölder utility.

Yingying Fan, Yuxuan Han, Jinchi Lv +2

Data Sciences and Operations Department, University of Southern California, Los Angeles, California 90089, USA · Stern School of Business, New York University, New York, NY 10003, USA

Dynamic Pricing Contextual Bandit Framework Independent-Pool Single-Draw Oracle Unimodal Metrics Pilot

May 8, 2026cs.LG

Toward Optimal Regret in Robust Pricing: Decoupling Corruption and Time

We design the first regret guarantees for robust dynamic pricing that decouple the dependence on the corruption

C

and the time horizon

T

. In dynamic pricing, a seller with unlimited supply of a good interacts with a stream of buyers over

T

rounds, with the goal of maximizing revenue. At each round

t

, the seller posts a price

p_t

, and the buyer purchases the good only if their unknown valuation

v^\star

exceeds this price. The seller observes only the binary feedback

\mathbb{I} \left\{ p_t \leq v^\star \right\}

, indicating whether a sale occurred. In the \emph{robust} pricing setting, a malicious adversary is allowed to corrupt this feedback in at most

C

rounds. Even if the learner knows the corruption

C

, the best known regret bound is

\mathcal{O}(C\log\log T)

by Gupta et al. [2025]. This leaves as an open problem to ``decouple'' the dependence on

C

and

T

. In this work, we resolve this open problem. In particular, we develop a robust variant of binary search that achieves regret

\mathcal{O}(C+\log T)

when the corruption

C

is known and

\mathcal{O}(C+\log^2 T)

when the corruption is unknown.

Kalana Kalupahana, Francesco Emanuele Stradi, Matteo Castiglioni +1

Politecnico di Milano

Dynamic Pricing Regret Adversarial Corruption Feedback

May 7, 2026cs.LG

Causal-Aware Foundation-Model for Bilevel Optimization in Discrete Choice Settings

We introduce a causal aware foundation-model framework for real time optimal decision making in discrete choice environments. We propose a constrained triple-head price optimization (C3PO) network to solve a bilevel decision problem in which a service provider selects an optimal assortment while heterogeneous users make personalized acceptance or rejection choices optimizing their own personalized preferences. C3PO integrates imitation learning of prices, multi-task learning of revenue responses, and in context learning of price elasticity to generate pricing recommendations while adhering to business constraints. During inference, frontier model prompting retrieves an enhanced elasticity prior for new products from behavioral economics literature, improving pricing effectiveness. We demonstrate strong in context learning performance using simulated, synthetic, and real-world datasets. C3PO is trained on simulated data generated from multiple classical discrete choice models in economics. The model is trained on data comprising simulated customer segments and counterfactual action and outcome pairs and evaluated on randomly generated choice environments with no access to the underlying preference structure. The trained model consistently improves the pricing KPIs, with gains increasing as customer price sensitivity increases. We also deploy the tuned foundation model for optimal pricing in real-world applications such as healthcare, tender pricing, airline ancillary pricing, and other domains, achieving substantial gains across multiple products, markets, and divisions.

Shivaram Subramanian, Zhengliang Xue, Markus Ettl +2

IBM T.J. Watson Research Center Yorktown Heights, New York, 10598, U.S.A.

Discrete Choice Models Dynamic Pricing Bilevel Optimization Imitation Learning

May 7, 2026cs.AI

Market-Alignment Risk in Pricing Agents: Trace Diagnostics and Trace-Prior RL under Hidden Competitor State

Outcome metrics can certify the wrong behavior. We study this failure in a two-hotel revenue-management simulator where Hotel A trains an agent against a fixed rule-based revenue-management competitor, Hotel B. A standard learning agent can obtain near-reference revenue per available room (RevPAR) while failing to learn market-like yield management: it sells too aggressively, undercuts, or collapses to modal price buckets. We diagnose this as a Goodhart-style failure under partial observability. Hotel A cannot observe the competitor's remaining inventory, booking curve, or pricing rule, so the same Hotel A-visible state maps to multiple plausible Hotel B prices. Deterministic value-based RL and deterministic copying collapse this unresolved uncertainty into shortcut behavior. We introduce a trace-level diagnostic protocol using RevPAR, occupancy, ADR, full price-bucket distributions, L1/JS distances, and seed-level confidence intervals. The verified repair is Trace-Prior RL: learn a distributional market prior from lagged market traces, then train a stochastic pricing policy with a RevPAR reward and a KL penalty to the learned prior. The final policy matches Hotel B's RevPAR, occupancy, ADR, and price distribution within seed-level uncertainty, while still optimizing Hotel A's own reward. We argue that the contribution is not a new optimizer and not a hotel-pricing leaderboard, but a reproducible failure-and-repair recipe for agentic systems where scalar rewards are easy to game and the intended behavior is only visible in traces. A key finding is that higher exact action accuracy can worsen aggregate trace alignment when the target is distributional.

Peiying Zhu, Sidi Chang

Blossom AI · Blossom AI Labs

Dynamic Pricing Traces Competition

May 7, 2026cs.LG

Optimal Contextual Pricing under Agnostic Non-Lipschitz Demand

We study contextual dynamic pricing with linear valuations and bounded-support agnostic noise, whose induced demand curve may be non-Lipschitz with arbitrary jumps and atoms. Such discontinuities break the cross-context interpolation arguments used by smooth-demand pricing algorithms, while the best previous method achieved only

\tilde O(T^{3/4})

regret. We propose Conservative-Markdown Redirect-UCB Pricing, a polynomial-time algorithm that combines randomized parameter estimation, conservative residual-grid probing, and confidence-based one-step redirection. Our algorithm achieves

\tilde O(T^{2/3})

optimal regret, matching the known lower bounds of Kleinberg and Leighton (2003) up to logarithmic factors and improving over the previous upper bound of Xu and Wang (2022). Under stochastic well-conditioned contexts, this closes the long-existing open regret gap in linear-valuation contextual pricing under agnostic non-Lipschitz noise distribution.

Jianyu Xu, Yu-Xiang Wang

Carnegie Mellon University Pittsburgh, PA 15213

Dynamic Pricing Interval Regret Lipschitz Continuity

May 3, 2026cs.AI

NH-CROP: Robust Pricing for Governed Language Data Assets under Cost Uncertainty

Language data are increasingly acquired and governed as assets, yet platforms often price candidate resources before knowing their true privacy or access costs. We study online pricing for governed language data assets under cost uncertainty. At each round, a platform observes an NLP task, a candidate asset, and a coarse cost estimate, may pay for a refined cost signal, posts a price, and receives safe net revenue. We introduce \textsc{NH-CROP}, a clipped robust pricing framework with a no-harm information-acquisition gate. The method compares direct pricing, risk-aware pricing, and verify-then-price, and acquires information only when its estimated decision value exceeds the best no-verification alternative. Across synthetic, real-proxy, and downstream-utility-grounded benchmarks, clipped \textsc{NH-CROP} variants improve or remain competitive with price-only and risk-aware baselines. Causal ablations show that paid verification is not the main source of gains in real-proxy and utility-grounded settings: the strongest learned policies often choose not to verify. Oracle and high-decision-value diagnostics show that refined cost information can still have substantial local value. Overall, governed language-data platforms should calibrate pricing under uncertain access costs first and verify only when information is cheap and decision-actionable.

Xu Zheng, Feiyu Wu, Zhuocheng Wang +2

School of Cyber Engineering, Xidian University

Dynamic Pricing Prices Cost-Aware

May 2, 2026cs.AI

Agentic AI Systems Should Be Designed as Marginal Token Allocators

This position paper argues that agentic AI systems should be designed and evaluated as \emph{marginal token allocation economies} rather than as text generators priced by the unit. We follow a single request -- a developer asking a coding agent to fix a failing test -- through four economic layers that today are designed in isolation: a router that decides which model answers, an agent that decides whether to plan, act, verify, or defer, a serving stack that decides how to produce each token, and a training pipeline that decides whether the trace is worth learning from. We show that all four layers are solving the \emph{same} first-order condition -- marginal benefit equals marginal cost plus latency cost plus risk cost -- with different index sets and different prices. The framing is deliberately minimal: we do not propose a complete theory of AI economics. But adopting marginal token allocation as the shared accounting object explains why systems that locally minimize tokens globally misallocate them, predicts a small set of recurring failure modes (over-routing, over-delegation, under-verification, serving congestion, stale rollouts, cache misuse), and points to a concrete research agenda in token-aware evaluation, autonomy pricing, congestion-priced serving, and risk-adjusted RL budgeting.

Siqi Zhu

University of Illinois Urbana-Champaign

Production Agentic Systems Economies Artificial Intelligence Systems Agentic Dynamic Pricing

Apr 22, 2026cs.MA

Anchor-and-Resume Concession Under Dynamic Pricing for LLM-Augmented Freight Negotiation

Freight brokerages negotiate thousands of carrier rates daily under dynamic pricing conditions where models frequently revise targets mid-conversation. Classical time-dependent concession frameworks use a fixed shape parameter

β

that cannot adapt to these updates. Deriving

β

from the live spread enables adaptation but introduces a new problem: a pricing shift can cause the formula to retract a previous offer, violating monotonicity. LLM-powered brokers offer flexibility but require expensive reasoning models, produce non-deterministic pricing, and remain vulnerable to prompt injection. We propose a two-index anchor-and-resume framework that addresses both limitations. A spread-derived

β

maps each load's margin structure to the correct concession posture, while the anchor-and-resume mechanism guarantees monotonically non-decreasing offers under arbitrary pricing shifts. All pricing decisions remain in a deterministic formula; the LLM, when used, serves only as a natural-language translation layer. Empirical evaluation across 115,125 negotiations shows that the adaptive

β

tailors behavior by regime: in narrow spreads, it concedes quickly to prioritize deal closure and load coverage; in medium and wide spreads, it matches or exceeds the best fixed-

β

baselines in broker savings. Against an unconstrained 20-billion-parameter LLM broker, it achieves similar agreement rates and savings. Against LLM-powered carriers as more realistic stochastic counterparties, it maintains comparable savings and higher agreement rates than against rule-based opponents. By decoupling the LLM from pricing logic, the framework scales horizontally to thousands of concurrent negotiations with negligible inference cost and transparent decision-making.

Hoang Nguyen, Lu Wang, Marta Gaia Bras

Georgia Institute of Technology · Atlanta, Georgia, USA · Transportation Insight / NTG

Dynamic Pricing Negotiation Contracts Congestion

Mar 5, 2026cs.AI

Agentic Service Markets Across the Computing Continuum: A Polymatroidal Architecture

Autonomous AI agents are becoming economic actors. They compose deadline-bound services across the device-edge-cloud continuum and contend for capacity no single operator owns. This article asks when decentralised pricing can coordinate them exactly and truthfully, and what their service dependencies must satisfy. We model the pipelines as service-dependency graphs under governance constraints and identify the decisive property: laminarity of the induced leaf-block family. Where it holds, the feasible allocation space is a polymatroid and efficient incentive-compatible clearing exists per epoch; where a crossing breaks it, exactness and truthfulness can fail, while clearing prices survive on every totally unimodular family. The formal results instantiate polymatroid, gross-substitutes and Vickrey-Clarke-Groves theory; the contribution is the bridge from dependency structure to that machinery and an integrator architecture that exposes a laminar interface. The node-level evaluation (32,020 runs), at testbed-calibrated congestion, locates the boundary. One crossing costs exactness in 14.7% of high-load rounds and none on laminar instances, and truthfulness fails where exactness does, across contention. An integrator's inner exposure restores exactness at a cost in admitted volume, and before translation overhead it cuts median latency by 16 to 17 percent. Against truth-free posted prices the tuned market leads at medium load and trails a demand-responsive one in four of six high-load cells. Recorded and composed agent workloads drive the allocation. For platform designers, laminar pipelines admit exact decentralised pricing, truthful under the VCG mechanism, and a crossing needs an integrator's inner exposure.

Lauri Lovén, Alaa Saleh, Reza Farahani +5

Future Computing Group, University of Oulu, Finland · Distributed Systems Group, TU Wien, Vienna, Austria · Department of Mechatronics, University of Prishtina, Kosova +4

Dynamic Pricing Decentralized Autonomous Organization Incentives Edge Platforms Continuum Time Discretization

Dec 28, 2025cs.LG

From Confounding to Learning: Dynamic Service Fee Pricing on Third-Party Platforms

We study the pricing behavior of third-party platforms facing strategic agents. Assuming the platform is a revenue maximizer, it observes market features that generally affect demand. Since only transacted quantities and prices can be observed, this presents a general demand learning problem under confounding. Mathematically, we develop an algorithm with optimal regret of

\Tilde{\mathcal{O}}(\sqrt{T}\wedgeσ_S^{-2})

. Our results reveal that supply-side noise fundamentally affects the learnability of demand, leading to a phase transition in regret. Technically, we show that non-i.i.d. actions can serve as instrumental variables for learning demand. We also propose a novel homeomorphic construction that allows us to establish estimation bounds without assuming star-shapedness, providing the first efficiency guarantee for learning demand with deep neural networks. Finally, we use simulations and offline counterfactuals from Talabat and Lyft data to illustrate the potential revenue implications of our approach.

Rui Ai, David Simchi-Levi, Feng Zhu

MIT

Dynamic Pricing Optimal Regret Strategic Agents

Sep 26, 2025cs.LG

Self-Improving Neural Pruning: A Graph Neural Network Framework for Scalable Mixed Bundle Pricing

Mixed bundle pricing is a classic revenue management problem arising in industries such as e-commerce, tourism, and video games. It refers to designing product combinations (i.e., bundles) and determining their prices to maximize expected profit. Exact mixed-bundling formulations capture this structure but are computationally intractable because the number of possible bundles grows exponentially with the number of products. We propose a graph neural network (GNN)-guided pruning framework for scalable (non-)additive bundle pricing. Instead of learning on the exponential bundle-level formulation, we encode each instance as a compact customer-product graph and train an edge-output GNN to learn the product-assignment probabilities from optimal mixed-bundling solutions. The predicted probabilities are then converted into restricted candidate bundle families through fixed cutoff pruning and progressive cutoff pruning; the final prices and assignments are obtained by solving the mixed bundling formulation over the retained bundles. We further introduce a GNN-guided local search and an iterative self-improvement procedure for larger instances. The local search refines the retained bundle family by prioritizing high-confidence add/drop moves, while the iterative self-improvement procedure generates high-quality solutions on larger instances for retraining. Theoretically, we show that under mild distinguishability conditions the proposed edge-output GNN class is expressive enough to recover the optimal product-assignment mapping. Experiments show that the proposed policies recover over 98% of the optimal profit on small instances and outperform bundle-size pricing on larger instances with substantial runtime savings.

Liangyu Ding, Chenghan Wu, Guokai Li +1

School of Data Science, The Chinese University of Hong Kong, Shenzhen, Guangdong, China

Dynamic Pricing Graph Neural Networks Gnn-Based Detectors Structured Pruning

Mar 31, 2024econ.GN

Algorithmic Collusion by Large Language Models

We conduct experiments with algorithmic pricing agents based on Large Language Models (LLMs). In oligopoly settings, LLM-based pricing agents quickly and autonomously reach supracompetitive prices and profits. Variation in seemingly innocuous phrases in LLM instructions ("prompts") substantially influence the degree of supracompetitive pricing. We develop novel techniques for behavioral analysis of LLMs and use them to uncover price-war concerns as a contributing factor. Our results extend to auction settings. Our findings uncover unique challenges to any future regulation of LLM-based pricing agents, and AI-based pricing agents more broadly.

Sara Fish, Yannai A. Gonczarowski, Ran I. Shorrer

†School of Engineering and Applied Sciences, Harvard University · ‡Department of Economics and Department of Computer Science, Harvard University · §Department of Economics, Penn State University

Dynamic Pricing Collusion Algorithmic Cores