Dynamic Pricing

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Dynamic pricing studies how to choose prices over time when demand is uncertain or changing, and when decisions affect inventory, customer choices, or competitors. Common approaches include online bandits such as UCB, contextual and nonparametric demand learning, forecasting followed by constrained optimization, and reinforcement learning for competitive markets. Regret analysis provides guarantees for settings such as censored demand, limited inventory, and nonstationary markets, while deployed systems also combine pricing with assortment, advertising, or resource allocation. A central tension is how to learn prices that are profitable and feasible without causing unfair outcomes or encouraging supra-competitive behavior.

Latest papers

50 papers6 papers in the last four weeks, up 20% on the four weeks before. 0.0% of all new papers.

May 18, 2026

When Outcome Looks Right But Discipline Fails: Trace-Based Evaluation Under Hidden Competitor State

Outcome-only evaluation can certify economically unsafe agents: a policy can hit a business KPI while violating deployable behavioral discipline. In hotel pricing with hidden competitor state, a learner can achieve plausible revenue per available room while failing to preserve the rate discipline of a rule-based revenue-management competitor. We introduce discipline stability, a trace-based evaluation paradigm: define the benchmark behavior, restrict observations to the deployment regime, induce trace diagnostics from failure, separate mechanisms with ablations, and test transfer and deployment. Across a two-hotel benchmark and a compact hidden-budget bidding task, reward-only PPO variants miss trace alignment; revealing hidden state reduces label uncertainty; deterministic copy collapses uncertainty; and trace-prior or corrected history policies better preserve price or bid distributions. Pure behavior cloning is nearly enough for symmetric imitation, while Trace-Prior RL adds bounded adaptation under capacity asymmetry. The contribution is an evaluation and benchmark paradigm, not a new optimizer or a universal claim about MARL

Peiying Zhu, Sidi Chang

Blossom AI San Francisco, USA · Blossom AI Labs Tokyo, Japan

Partially Observable RL Dynamic Pricing Multi-Agent Reinforcement Learning

May 15, 2026

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

Predict-Then-Optimize Learning to Optimize Algorithmic Collusion Dynamic Pricing

May 14, 2026

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

Bandit Convex Optimization Dynamic Pricing

May 8, 2026

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 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

Corruption Robustness Dynamic Pricing

May 7, 2026

Constrained Triple-Head Price Optimization (C3PO) Network for Discrete-Choice Models

We propose a Constrained Triple-Head Price Optimization (C3PO) network for real-time bi-level decision making in discrete-choice environments. In these settings, a seller selects product or service offerings to achieve business objectives, while heterogeneous users make personalized acceptance or rejection decisions based on their preferences, ultimately determining seller outcomes. Existing approaches that fine-tune pre-trained tabular foundation models on synthetic data are limited by their imitation-learning paradigm and inability to enforce common pricing rules, including cross-product and global constraints. C3PO addresses these limitations through a novel transformer-based architecture that jointly integrates price imitation learning, multi-task revenue prediction, and in-context elasticity learning to generate robust pricing recommendations across domains without retraining. A lightweight differentiable constraint layer enables generated prices to satisfy business constraints while optimizing the revenue objective. We demonstrate strong out-of-distribution performance on simulated, synthetic, and real-world datasets. Across simulated benchmarks where the calibrated MNL model is misspecified relative to the ground-truth choice model, C3PO improves expected revenue by 1.4 to 7.9 percentage points over a calibrated MNL baseline. The constraint layer reduces average absolute constraint violations by more than 50%. We further deploy the model in real-world applications, including healthcare tender pricing and airline ancillary pricing, where C3PO improves directional pricing effectiveness, measured by price-increase and price-decrease recall, by 18--34 percentage points depending on the baselines considered, including calibrated MNL, classical optimization, and off-the-shelf tabular foundation-models.

Shivaram Subramanian, Zhengliang Xue, Markus Ettl +2

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

Large Language Model-Guided Optimization Discrete Choice Modeling Bilevel Optimization Dynamic Pricing

May 7, 2026

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

Reward Hacking Reinforcement Learning Partially Observable RL KL-Regularized RL Dynamic Pricing

May 7, 2026

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

Contextual Bandits UCB Algorithms Dynamic Pricing

Apr 22, 2026

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

Automated Negotiation Dynamic Pricing

Apr 19, 2026

A Model and Estimation of the Bitcoin Transaction Fee

Bitcoin transaction fees will become more important as the block subsidy declines, but fee formation is hard to study with blockchain data alone because the relevant queueing environment is unobserved. We develop and estimate a structural model of Bitcoin fee choice that treats the mempool as a market for scarce blockspace. We assemble a novel, high-frequency mempool panel, from a self-run Bitcoin node that records transaction arrivals, exits, block inclusion, fee-bumping events, and congestion snapshots. We characterize the fee market as a Vickery-Clarke-Groves mechanism and derive an equation to estimate fees. In the first-stage we estimate a monotone delay technology linking fee-rate priority and network state to expected confirmation delay. We then estimate how fees respond to that delay technology and to transaction characteristics. We find that congestion is the main determinant of delay; that the marginal value of priority is priced in fees, which is increasing in the gradient of confirmation time reduction per movement up in the fee queue; and that transactor choice of RBF, CPFP, and block conditions have economically important effects on fees.

Daniel Aronoff, Kristian Praizner, Armin Sabouri

MIT Department of Economics · MIT EECS · MIT Media Lab Digital Currency Initiative

Dynamic Pricing

Apr 15, 2026

A Comparative Study of Dynamic Programming and Reinforcement Learning in Finite Horizon Dynamic Pricing

This paper provides a systematic comparison between Fitted Dynamic Programming (DP), where demand is estimated from data, and Reinforcement Learning (RL) methods in finite-horizon dynamic pricing problems. We analyze their performance across environments of increasing structural complexity, ranging from a single typology benchmark to multi-typology settings with heterogeneous demand and inter-temporal revenue constraints. Unlike simplified comparisons that restrict DP to low-dimensional settings, we apply dynamic programming in richer, multi-dimensional environments with multiple product types and constraints. We evaluate revenue performance, stability, constraint satisfaction behavior, and computational scaling, highlighting the trade-offs between explicit expectation-based optimization and trajectory-based learning.

Lev Razumovskiy, Nikolay Karenin

Dynamic Pricing Reinforcement Learning Dynamic Programming

Apr 7, 2026

JD-BP: A Joint-Decision Generative Framework for Auto-Bidding and Pricing

Auto-bidding services optimize real-time bidding strategies for advertisers under key performance indicator (KPI) constraints such as target return on investment and budget. However, uncertainties such as model prediction errors and feedback latency can cause bidding strategies to deviate from ex-post optimality, leading to inefficient allocation. To address this issue, we propose JD-BP, a Joint generative Decision framework for Bidding and Pricing. Unlike prior methods, JD-BP jointly outputs a bid value and a pricing correction term that acts additively with the payment rule such as GSP. To mitigate adverse effects of historical constraint violations, we design a memory-less Return-to-Go that encourages future value maximizing of bidding actions while the cumulated bias is handled by the pricing correction. Moreover, a trajectory augmentation algorithm is proposed to generate joint bidding-pricing trajectories from a (possibly arbitrary) base bidding policy, enabling efficient plug-and-play deployment of our algorithm from existing RL/generative bidding models. Finally, we employ an Energy-Based Direct Preference Optimization method in conjunction with a cross-attention module to enhance the joint learning performance of bidding and pricing correction. Offline experiments on the AuctionNet dataset demonstrate that JD-BP achieves state-of-the-art performance. Online A/B tests at JD.com confirm its practical effectiveness, showing a 4.70% increase in ad revenue and a 6.48% improvement in target cost.

Linghui Meng, Chun Gan, Shengsheng Niu +8

JD.com China · The Chinese University of Hong Kong China

Automated Bidding Real-Time Bidding Online Advertising Dynamic Pricing

Mar 26, 2026

The Value of Information in Resource-Constrained Pricing

Firms that price perishable resources -- airline seats, hotel rooms, seasonal inventory -- now routinely use demand predictions, but these predictions vary widely in quality. Under hard capacity constraints, acting on an inaccurate prediction can irreversibly deplete inventory needed for future periods. We study how prediction uncertainty propagates into dynamic pricing decisions with linear demand, stochastic noise, and finite capacity. A certified demand forecast with known error bound~

ε^0

specifies where the system should operate: it shifts regret from

O(\sqrt{T})

to

O(\log T)

when

ε^0 \lesssim T^{-1/4}

, and we prove this threshold is tight. A misspecified surrogate model -- biased but correlated with true demand -- cannot set prices directly but reduces learning variance by a factor of

(1-ρ^2)

through control variates. The two mechanisms compose: the forecast determines the regret regime; the surrogate tightens estimation within it. All algorithms rest on a boundary attraction mechanism that stabilizes pricing near degenerate capacity boundaries without requiring non-degeneracy assumptions. Experiments confirm the phase transition threshold, the variance reduction from surrogates, and robustness across problem instances.

Ruicheng Ao, Jiashuo Jiang, David Simchi-Levi

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

Dynamic Pricing Decision-Making under Uncertainty Dynamic Regret Minimization

Mar 5, 2026

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

Mechanism Design Combinatorial Optimization Dynamic Pricing

Mar 5, 2026

Competitive Multi-Operator Reinforcement Learning for Joint Pricing and Fleet Rebalancing in AMoD Systems

Autonomous Mobility-on-Demand (AMoD) systems promise to revolutionize urban transportation by providing affordable on-demand services to meet growing travel demand. However, realistic AMoD markets will be competitive, with multiple operators competing for passengers through strategic pricing and fleet deployment. While reinforcement learning has shown promise in optimizing single-operator AMoD control, existing work fails to capture competitive market dynamics. We investigate the impact of competition on policy learning by introducing a multi-operator reinforcement learning framework where two operators simultaneously learn pricing and fleet rebalancing policies. By integrating discrete choice theory, we enable passenger allocation and demand competition to emerge endogenously from utility-maximizing decisions. Experiments using real-world data from multiple cities demonstrate that competition fundamentally alters learned behaviors, leading to lower prices and distinct fleet positioning patterns compared to monopolistic settings. Notably, we demonstrate that learning-based approaches are robust to the additional stochasticity of competition, with competitive agents successfully converging to effective policies while accounting for partially unobserved competitor strategies.

Emil Kragh Toft, Carolin Schmidt, Daniele Gammelli +1

Technical University of Denmark, Denmark · Technical University of Munich, Germany · Stanford University, USA

Dynamic Pricing Multi-Agent Reinforcement Learning Sequential MARL

Feb 28, 2026

Multi-Agent Reinforcement Learning for Dynamic Pricing: Balancing Profitability,Stability and Fairness

Dynamic pricing in competitive retail markets requires strategies that adapt to fluctuating demand and competitor behavior. In this work, we present a systematic empirical evaluation of multi-agent reinforcement learning (MARL) approaches-specifically MAPPO and MADDPG-for dynamic price optimization under competition. Using a simulated marketplace environment derived from real-world retail data, we benchmark these algorithms against an Independent DDPG (IDDPG) baseline, a widely used independent learner in MARL literature. We evaluate profit performance, stability across random seeds, fairness, and training efficiency. Our results show that MAPPO consistently achieves the highest average returns with low variance, offering a stable and reproducible approach for competitive price optimization, while MADDPG achieves slightly lower profit but the fairest profit distribution among agents. These findings demonstrate that MARL methods-particularly MAPPO-provide a scalable and stable alternative to independent learning approaches for dynamic retail pricing.

Krishna Kumar Neelakanta Pillai Santha Kumari Amma

Dynamic Pricing Reinforcement Learning Multi-Agent Reinforcement Learning

Feb 18, 2026

Poisson-MNL Bandit: Nearly Optimal Dynamic Joint Assortment and Pricing with Decision-Dependent Customer Arrivals

We study dynamic joint assortment and pricing where a seller updates decisions at regular accounting/operating intervals to maximize the cumulative per-period revenue over a horizon

T

. In many settings, assortment and prices affect not only what an arriving customer buys but also how many customers arrive within the period, whereas classical multinomial logit (MNL) models assume arrivals as fixed, potentially leading to suboptimal decisions. We propose a Poisson-MNL model that couples a contextual MNL choice model with a Poisson arrival model whose rate depends on the offered assortment and prices. Building on this model, we develop an efficient algorithm PMNL based on the idea of upper confidence bound (UCB). We establish its (near) optimality by proving a non-asymptotic regret bound of order

\sqrt{T\log{T}}

and a matching lower bound (up to

\log T

). Simulation studies underscore the importance of accounting for the dependency of arrival rates on assortment and pricing: PMNL effectively learns customer choice and arrival models and provides joint assortment-pricing decisions that outperform others that assume fixed arrival rates.

Junhui Cai, Ran Chen, Qitao Huang +2

Department of Information Technology, Analytics, and Operations, University of Notre Dame · Department of Statistics and Data Science, Washington University in St. Louis · Department of Mathematics, Tsinghua University +2

Assortment Optimization Dynamic Pricing Multi-Armed Bandits

Dec 28, 2025

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

Causal Effect Estimation Instrumental Variable Estimation Causal Inference Dynamic Pricing

Oct 10, 2025

LLP: LLM-Based Product Pricing in E-commerce

Unlike Business-to-Consumer e-commerce platforms (e.g., Amazon), inexperienced individual sellers on Consumer-to-Consumer platforms (e.g., eBay) often face significant challenges in setting prices for their second-hand products efficiently. Therefore, numerous studies have been proposed for automating price prediction. However, most of them are based on static regression models, which suffer from poor generalization performance and fail to capture market dynamics (e.g., the price of a used iPhone decreases over time). Inspired by recent breakthroughs in Large Language Models (LLMs), we introduce LLP, the first LLM-based generative framework for second-hand product pricing. LLP first retrieves similar products to better align with the dynamic market change. Afterwards, it leverages the LLMs' nuanced understanding of key pricing information in free-form text to generate accurate price suggestions. To strengthen the LLMs' domain reasoning over retrieved products, we apply a two-stage optimization, supervised fine-tuning (SFT) followed by group relative policy optimization (GRPO), on a dataset built via bidirectional reasoning. Moreover, LLP employs a confidence-based filtering mechanism to reject unreliable price suggestions. Extensive experiments demonstrate that LLP substantially surpasses existing methods while generalizing well to unseen categories. We have successfully deployed LLP on Xianyu\footnote{Xianyu is China's largest second-hand e-commerce platform.}, significantly outperforming the previous pricing method. Under the same 30% product coverage, it raises the static adoption rate (SAR) from 40% to 72%, and maintains a strong SAR of 47% even at 90% recall.

Hairu Wang, Sheng You, Qiheng Zhang +5

Xianyu of Alibaba, Hangzhou, China · University of Science and Technology of China, Suzhou, China

E-Commerce LLM Post-Training Dynamic Pricing

Aug 1, 2024

Online Linear Programming with Batching

We study Online Linear Programming (OLP) with batching. The planning horizon is cut into

K

batches, and decisions on orders can be delayed to the end of their associated batch. The ability to delay decisions improves operational performance, as measured by regret. We study two questions: (1) What is a lower bound on the regret as a function of

K

and the length of the planning horizon? (2) Which algorithms can achieve this regret lower bound? This paper analyzes these questions when the distribution of the reward has a continuous support. We provide an

Ω(\log K)

regret lower bound in the single-resource case, and we provide pricing algorithms having an

O(\log K)

regret in the setting with Poisson arrivals and multiple types of resources. All the algorithms update the prices at most

K

times and only delay orders of the first and the last batches. All the regret bounds are independent of the length of the planning horizon. Finally, we study a more realistic large support setting where the number of distinct order types is finite but scales with the total number of orders. We prove that our

Θ(\log K)

bounds still hold for the batching operation of a multisecretary problem with discretized uniform rewards in this large support setting, provided the support grows fast enough. This suggests that the continuous support setting that is the paper's focus serves as a useful theoretical surrogate for the more realistic large finite support setting.

Haoran Xu, Peter W. Glynn, Yinyu Ye

Department of Management Science and Engineering, Stanford University

Sequential Decision Making Regret Minimization Linear Programming Dynamic Pricing Online Resource Allocation Operations Research

Mar 31, 2024

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

Prompt Sensitivity Algorithmic Collusion Dynamic Pricing Multi-Agent LLMs