Dynamic Pricing

Dynamic Pricing is a strategy in which the price of a good or service is adjusted in real time based on demand, supply, competitor prices, inventory, and customer signals. It is typically driven by machine-learning models that forecast willingness to pay and optimise revenue or other objectives. Common in e-commerce, ride-hailing, travel, and logistics, it relies on continuous data feeds and automated decisioning.

Semantic Classification

Content

Compositional Relationships (Components)

SubClassOf(ai:DynamicPricing
  ObjectSomeValuesFrom(ai:hasPart ai:DemandForecastingModel))
SubClassOf(ai:DynamicPricing
  ObjectSomeValuesFrom(ai:hasPart ai:PriceElasticityModel))
SubClassOf(ai:DynamicPricing
  ObjectSomeValuesFrom(ai:hasPart ai:RevenueOptimisationEngine))
SubClassOf(ai:DynamicPricing
  ObjectSomeValuesFrom(ai:hasPart ai:WillingnessToPayEstimator))
SubClassOf(ai:DynamicPricing
  ObjectSomeValuesFrom(ai:hasPart ai:MarketSegmentationModule))
SubClassOf(ai:DynamicPricing
  ObjectSomeValuesFrom(ai:hasPart ai:RealTimeDataPipeline))
SubClassOf(ai:DynamicPricing
  ObjectSomeValuesFrom(ai:hasPart ai:ABTestingFramework))

Dependency Relationships

SubClassOf(ai:DynamicPricing
  ObjectSomeValuesFrom(ai:requires ai:DemandForecasting))
SubClassOf(ai:DynamicPricing
  ObjectSomeValuesFrom(ai:requires ai:DataAggregation))
SubClassOf(ai:DynamicPricing
  ObjectSomeValuesFrom(ai:requires ai:MachineLearning))
SubClassOf(ai:DynamicPricing
  ObjectSomeValuesFrom(ai:requires ai:PredictiveAnalytics))
SubClassOf(ai:DynamicPricing
  ObjectSomeValuesFrom(ai:requires ai:TimeSeriesAnalysis))
SubClassOf(ai:DynamicPricing
  ObjectSomeValuesFrom(ai:requires ai:RealTimeDataPipeline))

Capability Relationships

SubClassOf(ai:DynamicPricing
  ObjectSomeValuesFrom(ai:enables ai:RevenueManagement))
SubClassOf(ai:DynamicPricing
  ObjectSomeValuesFrom(ai:enables ai:LogisticsOptimisation))
SubClassOf(ai:DynamicPricing
  ObjectSomeValuesFrom(ai:enables ai:HyperPersonalisation))
SubClassOf(ai:DynamicPricing
  ObjectSomeValuesFrom(ai:enables ai:CapacityUtilisation))
SubClassOf(ai:DynamicPricing
  ObjectSomeValuesFrom(ai:enables ai:PersonalisedExperiences))
SubClassOf(ai:DynamicPricing
  ObjectSomeValuesFrom(ai:enables ai:SupplyChainPlanning))

Implementation Relationships

SubClassOf(ai:DynamicPricing
  ObjectSomeValuesFrom(ai:implements ai:ReinforcementLearning))
SubClassOf(ai:DynamicPricing
  ObjectSomeValuesFrom(ai:implements ai:GradientBoosting))
SubClassOf(ai:DynamicPricing
  ObjectSomeValuesFrom(ai:implements ai:BayesianOptimisation))
SubClassOf(ai:DynamicPricing
  ObjectSomeValuesFrom(ai:implements ai:MultiArmedBandit))
SubClassOf(ai:DynamicPricing
  ObjectSomeValuesFrom(ai:implements ai:QLearning))

Reduction Relationships

SubClassOf(ai:DynamicPricing
  ObjectSomeValuesFrom(ai:reducesTo ai:YieldManagement))
SubClassOf(ai:DynamicPricing
  ObjectSomeValuesFrom(ai:reducesTo ai:PriceDiscrimination))
SubClassOf(ai:AlgorithmicPricing
  ObjectSomeValuesFrom(ai:reducesTo ai:DynamicPricing))
SubClassOf(ai:DynamicPricing
  ObjectSomeValuesFrom(ai:reducesTo ai:TemporalPriceDiscrimination))
SubClassOf(ai:SurgePricing
  ObjectSomeValuesFrom(ai:reducesTo ai:DynamicPricing))
SubClassOf(ai:PersonalisedPricing
  ObjectSomeValuesFrom(ai:reducesTo ai:DynamicPricing))

Relationship-Axiom Extensions

SubClassOf(ai:DynamicPricing
  ObjectSomeValuesFrom(ai:supports ai:SupplyChainPlanning))
SubClassOf(ai:DynamicPricing
  ObjectSomeValuesFrom(ai:supports ai:DemandPlanning))
SubClassOf(ai:DynamicPricing
  ObjectSomeValuesFrom(ai:supports ai:InventoryManagement))
SubClassOf(ai:DynamicPricing
  ObjectSomeValuesFrom(ai:contrasts ai:FixedPricing))
SubClassOf(ai:DynamicPricing
  ObjectSomeValuesFrom(ai:contrasts ai:CostPlusPricing))
SubClassOf(ai:DynamicPricing
  ObjectSomeValuesFrom(ai:uses ai:DeepReinforcementLearning))
SubClassOf(ai:DynamicPricing
  ObjectSomeValuesFrom(ai:uses ai:GradientBoosting))
SubClassOf(ai:DynamicPricing
  ObjectSomeValuesFrom(ai:uses ai:NeuralNetwork))
SubClassOf(ai:DynamicPricing
  ObjectSomeValuesFrom(ai:isSubclassOf ai:Optimisation))
SubClassOf(ai:DynamicPricing
  ObjectSomeValuesFrom(ai:isSubclassOf ai:RevenueManagement))
SubClassOf(ai:DynamicPricing
  ObjectSomeValuesFrom(ai:standardizedBy ai:CompetitionAndMarketsAuthority))

About

Dynamic pricing is one of the oldest problems in commercial decision-making, but its algorithmic incarnation is a product of the data and compute abundance of the late twentieth and early twenty-first centuries. The challenge of setting prices that maximise revenue while clearing inventory and satisfying customers has occupied merchants, economists, and operations researchers for centuries. The economics of price discrimination were first formalised by Alfred Marshall (1890) and Arthur Pigou (1920), who classified pricing strategies by the granularity of consumer segmentation and analysed their welfare implications. However, the computational implementation of dynamic pricing at scale awaited the convergence of digital booking systems, large-scale transactional databases, and machine learning algorithms capable of modelling complex demand-price relationships in real time.

Historical Origins: Airline Yield Management

The practice originated in the airline industry, where American Airlines and other carriers introduced computer reservation systems—American’s SABRE (Semi-Automated Business Research Environment, 1964) being the most influential—that enabled systematic pricing of seat inventory by booking class, advance purchase window, and day of week. Robert Crandall, President of American Airlines, coined the term “yield management” in 1985 and formalised the practice of adjusting ticket prices continuously based on seat inventory, booking velocity, and demand forecasts, achieving reported annual revenue gains of hundreds of millions of dollars for American alone. The deregulation of the US airline industry (Airline Deregulation Act, 1978) eliminated regulated pricing and created the competitive pressure that made yield management a survival capability rather than an optional enhancement. UK carriers including British Caledonian and British Airways adopted similar systems through the 1980s and 1990s, with easyJet and Ryanair later demonstrating that low-cost carriers could achieve even more aggressive dynamic pricing by selling every seat at a unique price with no pre-specified booking classes.

The theoretical foundation for airline yield management was developed by Belobaba (1987) with the Expected Marginal Seat Revenue (EMSR) model, Williamson (1992) with bid-price control methods, and Talluri and van Ryzin’s comprehensive treatment (2004) that remains the standard reference. The core insight is that a perishable resource (an airline seat on a specific departure flight) has zero value after the departure date, so the optimal strategy is to sell at a price that maximises expected revenue given the remaining inventory and forecast demand, even if that means leaving some seats empty.

E-Commerce and Platform Economy Expansion

The transition from airline yield management to modern algorithmic dynamic pricing was enabled by two developments: the explosion of e-commerce producing continuous high-frequency price and purchase signals at internet scale, and the maturation of machine learning techniques capable of modelling complex, non-stationary demand-price relationships without hand-crafted parametric assumptions:

• Amazon: Launched its pricing engine around 2000 and by the mid-2010s was updating prices millions of times per day using gradient-boosted machine learning models trained on competitor price feeds, historical conversion data, search rank, and inventory signals. By 2026, Amazon changes approximately 2.5 million product prices per day. The system uses personalised pricing signals: if a consumer consistently purchases from Amazon, prices may be set higher based on inferred loyalty, while newcomers see lower prices to drive trial conversion.

• Uber: Launched surge pricing with the platform in 2010. The algorithm raises prices by a surge multiplier (1.2x, 1.5x, 2.0x, or higher) when available driver supply is insufficient to clear passenger demand in a geographic zone, incentivising additional drivers to activate while reducing demand from price-sensitive passengers. Uber’s pricing algorithm incorporates machine learning models using global news events, weather conditions, historical patterns, time of day, holidays, and real-time traffic data as inputs.

• Airbnb: Uses a binary classification model predicting booking probability for each listing-night, a regression model estimating optimal price, and personalisation logic to generate Smart Pricing recommendations. Hosts using the platform’s price recommendation are approximately four times more likely to receive a booking than those setting prices independently. Airbnb’s system updates nightly rates dynamically based on last-minute booking signals, local event announcements, and competitive market intelligence.

• Hotel sector: Marriott, Hilton, IHG, and major independent hotels use AI-powered revenue management systems from vendors including IDeaS (Amadeus subsidiary), Duetto, and OTA Insight. Amadeus reports its AI-based revenue management systems serve over 100 airlines and thousands of hotels globally.

  Economic Theory of Price Discrimination

  The economic theory formalised by Pigou (1920) classifies pricing strategies by consumer segmentation granularity:

• First-degree (perfect) price discrimination: Charges each consumer their exact willingness to pay, extracting the entire consumer surplus as producer revenue. Infeasible in practice without perfect information, but approximated by modern ML-driven individual-level pricing using inferred WTP signals.

• Second-degree price discrimination: Offers different price-quantity bundles (subscription tiers, volume discounts, booking class upgrades) allowing consumers to self-select into the bundle that matches their valuation. The seller need not know individual WTP in advance; the menu of options induces self-selection.

• Third-degree price discrimination: Charges different prices to identifiable consumer segments (students, seniors, business vs. leisure travellers, domestic vs. international customers). Standard in entertainment, public transport, and professional services.

• Temporal price discrimination: Charges different prices at different times (early bird vs. last minute, peak vs. off-peak). Dynamic pricing implements temporal discrimination at real-time granularity based on demand signals.

  Dynamic pricing overlaps all three categories: it adjusts over time (temporal), across consumer segments (third-degree), and increasingly at individual level using inferred WTP from browsing history, purchase history, device type, and location data (approximating first-degree). This overlap with individual-level targeting is the primary source of consumer concerns about algorithmic pricing fairness.

  Formal Optimisation Framework

  A dynamic pricing system solves a sequential decision problem: at each time period t, the firm sets price p_t for a product with remaining inventory I_t and residual demand horizon T-t, observing noisy demand realisation D_t(p_t) before period t+1. The expected revenue-maximising pricing policy satisfies:

V(I, t) = max_{p ∈ [p_min, p_max]} { p · E[min(D_t(p), I)] + V(I - E[min(D_t(p), I)], t+1) }

where V(I, t) is the value function (maximum expected revenue with inventory I at time t) and D_t(p) is the stochastic demand function at price p in period t. This dynamic programme has the structure of Bellman’s equation, with the key challenge being the specification of the demand function E[D_t(p)] and the accurate estimation of this expectation from historical data.

In practice, the full dynamic programme is approximated using:

• Bid-price control: compute a shadow price (opportunity cost) for each unit of inventory; offer the product only when willingness-to-pay exceeds the bid price

• EMSR (Expected Marginal Seat Revenue): Belobaba’s (1987) heuristic that nests booking classes by estimated demand and opens/closes classes based on expected marginal revenue

• Model Predictive Pricing: at each period, solve a finite-horizon approximation of the DP using the current demand forecast and inventory, apply the first-period price, and repeat (analogous to Receding Horizon Control in control theory)

• Reinforcement Learning: parameterise the pricing policy π_θ(p | s) where s = (I, t, context) is the pricing state, and optimise θ to maximise expected cumulative revenue via policy gradient or Q-learning updates

  Components and Architecture

  A production dynamic pricing system comprises several tightly integrated layers:

• Demand Forecasting Layer: Models the functional relationship between price p and expected demand volume Q(p), typically as a demand elasticity function ε = (∂Q/∂p)·(p/Q). Methods range from log-linear econometric models (which assume constant elasticity) through gradient-boosted trees trained on historical price-demand pairs to recurrent neural network models (LSTM, Transformer) that capture temporal patterns such as day-of-week effects, seasonality, and trend. Contextual features—weather, events, competitor prices, inventory levels—are incorporated as input features.

• Willingness-to-Pay (WTP) Estimation: Estimates the price at which each consumer (or consumer segment) would purchase, enabling individual-level price optimisation. Methods include empirical distribution fitting from purchase/no-purchase outcomes at varying price points, conjoint analysis from survey data, and ML classifiers trained on purchase probability given price and consumer features. Airbnb’s system uses a binary classification model predicting booking probability combined with a regression model estimating optimal price, with a customised loss function balancing host revenue against guest booking rate.

• Revenue Optimisation Engine: Given a demand model Q(p) and a cost structure c, solves the optimisation problem max_p (p - c)·Q(p) subject to business constraints (price floors, ceilings, fairness guardrails, competitor parity thresholds). For complex multi-product pricing with substitution and complementarity effects, this becomes a high-dimensional constrained optimisation. Reinforcement Learning approaches—particularly Deep Reinforcement Learning using PPO, SAC, or Q-learning formulations—learn pricing policies π(p|s) mapping market state s to price actions without requiring an explicit demand model, by optimising a reward signal such as daily revenue or profit over a simulated or real pricing environment.

• Real-Time Data Pipeline: Ingests competitor price feeds (scraped at sub-minute cadence), inventory position from warehouse management systems, demand signals from clickstream analytics, weather APIs, event calendars, and macroeconomic indicators. Stream processing frameworks (Apache Kafka, Apache Flink) aggregate these feeds and compute engineered features for model serving, with latency targets of seconds to milliseconds for real-time pricing.

• A-B Testing and Experimentation Framework: Continuously validates pricing model updates by randomly assigning pricing variants to consumer cohorts and measuring causal impact on revenue, conversion, and consumer satisfaction. Bandit algorithms—particularly Thompson Sampling and Upper Confidence Bound (UCB) variants—enable adaptive experimentation that reduces the cost of exploring sub-optimal price points.

• Guardrail and Fairness Module: Enforces business rules and regulatory compliance constraints: maximum price increases within a time window, prohibition on charging more to identifiable protected groups, transparency disclosure requirements, and competitor parity commitments. Under the UK DMCCA 2024 and CMA guidance, businesses must present the full price at the earliest relevant stage and ensure consumers can understand that dynamic pricing is being applied.

  Algorithmic Approaches and Model Families

  Econometric and Structural Demand Models

• Log-linear constant-elasticity models: Q = A·p^ε where ε < 0 is the price elasticity of demand; easily estimated by OLS regression on log(Q) = log(A) + ε·log(p). Interpretable; may mis-specify non-constant elasticity.

• Almost Ideal Demand System (AIDS, Deaton and Muellbauer, 1980): models budget shares for multiple competing products simultaneously, capturing substitution and complementarity effects.

• Structural Industrial Organisation models (BLP—Berry, Levinsohn, Pakes, 1995): estimate demand from market share data controlling for price endogeneity via instrumental variables; standard in pharmaceutical, automobile, and consumer goods pricing research.

• Panel data demand estimation: fixed/random effects models controlling for unobserved product and market heterogeneity in multi-product pricing datasets.

  Gradient-Boosted and Tree-Based Machine Learning

• XGBoost and LightGBM trained on historical price-demand pairs with rich feature sets (competitor prices, day-of-week, weather, inventory, promotion flags, customer segment indicators)

• Fast inference (microseconds per prediction); handle nonlinear feature interactions and missing values; widely used in e-commerce pricing for both demand forecasting and price recommendation

• Feature importance outputs provide partial interpretability; SHAP values explain individual price recommendations to business users

• Combined with price optimisation: gradient-boosted demand forecasts fed into a gradient ascent or grid search over price to find the revenue-maximising price point

  Recurrent and Transformer Demand Forecasting

• LSTM and Transformer architectures for demand time-series forecasting, capturing autocorrelation, seasonality (day-of-week, month-of-year, holiday), and exogenous event impacts (concerts, sporting events, weather)

• Amazon DeepAR (Salinas et al., 2020): probabilistic LSTM model for producing calibrated demand forecast quantiles across thousands of parallel time series simultaneously

• N-BEATS and N-HiTS: pure Multilayer Perceptron architectures for interpretable time-series forecasting, outperforming LSTM on many benchmark datasets

• Temporal Fusion Transformers (TFT, Lim et al., 2021): attention-based model for multi-horizon probabilistic forecasting with variable selection and temporal attention for interpretability

• Increasingly used in airline and hotel revenue management for multi-step-ahead demand forecasting over booking windows of 0 to 365 days ahead

  Reinforcement Learning Pricing Agents

• Q-learning formulation: state s = (inventory I, time t, market context), action a = price p from a discrete price grid, reward r = p · D(p) (revenue), transition based on demand realisation; Q(s,a) updated via Bellman backup

• Deep Q-Network (DQN): parameterise Q-function with a neural network; experience replay and target network stabilise training; applied to pricing by Bai and Mao (2023)

• Proximal Policy Optimisation (PPO) and Soft Actor-Critic (SAC): policy gradient methods for continuous pricing actions; can handle complex multi-product pricing spaces

• arXiv:2411.18261 (presented at ICAET 2025): Q-learning retail pricing framework demonstrating revenue gains over static and rule-based methods by continuously adapting to evolving consumer behaviour

• Gao (2025, SAGE Tourism and Hospitality Research): RL-based hotel revenue management with field experiment evidence, demonstrating superior revenue outcomes vs. rule-based approaches

• Key challenge: reward sparsity (purchase events are rare relative to impression events); partial observability (competitors’ inventory and pricing decisions are unobserved)

  Multi-Armed Bandit and Online Learning Methods

• Thompson Sampling: Bayesian bandit method maintaining a Beta posterior over conversion probabilities at each price arm; exploration-exploitation balance adapts automatically to data

• Upper Confidence Bound (UCB) variants: deterministic exploration bonus based on uncertainty (inverse of arm pull count); provably sublinear regret bounds

• Contextual bandits (LinUCB, NeuralUCB): incorporate consumer context features into arm selection; bridge between pure exploration and full RL

• Well-suited to new product launches, low-volume speciality markets, and promotional pricing experiments where full RL training is infeasible due to limited historical data

  Bayesian Optimisation for Pricing Policy Search

• Gaussian process surrogate model over the objective function (expected revenue as a function of pricing policy parameters)

• Acquisition functions (Expected Improvement, Upper Confidence Bound, Knowledge Gradient) guide the next pricing experiment to maximise information gain

• Sample-efficient: achieves near-optimal pricing policy with 10-50x fewer experiments than random search

• Applied to hyperparameter tuning of pricing algorithms and to revenue management policy search in sparse-data environments

  Game-Theoretic and Multi-Agent Approaches

• Nash equilibrium pricing in oligopoly: prices set so that no firm can unilaterally improve revenue, given competitors’ prices. Can be computed analytically for linear demand models; requires numerical methods for complex demand structures.

• Stackelberg leader-follower models: one firm (leader) sets price first; others (followers) respond optimally. Used in platform pricing where the platform sets commission rates and sellers respond with product prices.

• Multi-agent reinforcement learning (MARL) pricing: competing pricing agents trained against each other in simulation, converging to approximate Nash equilibria; may discover tacit collusion strategies without explicit coordination (the “algorithmic collusion” risk identified by the CMA)

• Market simulation and agent-based models: simulate the pricing ecosystem with heterogeneous consumer agents and competing firm agents to evaluate pricing strategies before deployment

  Causal and Counterfactual Methods

• Price endogeneity correction: OLS regression of quantity on price is biased because price and demand are jointly determined (firms raise prices when they expect high demand). Instrumental variables (e.g., competitor cost shocks, historical pricing index) or control function approaches correct this bias.

• Double Machine Learning (Chernozhukov et al., 2018): uses cross-fitting and residual-on-residual regression to estimate heterogeneous treatment effects of price changes on demand while controlling for high-dimensional confounders; increasingly used for heterogeneous price elasticity estimation across customer segments.

• Synthetic Control and Difference-in-Differences: estimate the causal effect of a price change on demand using control markets or products unaffected by the intervention as counterfactual. Standard method for evaluating natural experiments in pricing.

• Predict-then-Optimise (Smart Predict-then-Optimize, Elmachtoub and Grigas, 2022): trains demand models with a task loss—the regret from suboptimal pricing decisions—rather than a generic prediction loss, directly optimising decision quality rather than forecast accuracy.

  Use Cases and Major Application Domains

  E-Commerce and Retail

• Amazon, Alibaba, ASOS, and major retailers adjust prices across millions of SKUs multiple times daily based on competitor prices, inventory levels, demand signals, search ranking, and customer behavioural signals

• Amazon’s pricing engine updates approximately 2.5 million product prices per day; may infer consumer loyalty from purchase history and set higher prices for repeat purchasers

• Private label and category management pricing optimisation generates reported revenue uplifts of 5-15% over static pricing in controlled comparisons

• Interhome’s 2025 ML-based dynamic pricing model for short-term rentals delivered 25% more reservations, 18% higher turnover, and 18% more booked days vs. fixed pricing

• Specialist retail: supermarkets (Ocado, Tesco) use electronic shelf labels enabling rapid price updates in response to near-expiry inventory, competitor promotions, and demand signals

  Ride-Hailing and Mobility

• Uber, Lyft, Ola, and Bolt use surge pricing algorithms balancing driver supply and passenger demand in real time

• Geographic zone-based surge multipliers (1.0x to 5.0x or higher) computed by ML models using real-time supply-demand ratios, weather, events, historical patterns, and global news signals

• Two-sided market equilibration: price increases attract additional drivers while reducing demand from price-sensitive passengers, clearing the market faster than fixed pricing during demand spikes

• Controversy: surge pricing during emergencies (hurricanes, terrorist attacks) has triggered regulatory restrictions on price gouging; Uber’s algorithm was criticised during the 2017 Sydney siege

  Airlines and Travel

• Yield management systems at British Airways, easyJet, Ryanair, Delta, United, Emirates use dynamic pricing across cabin classes, booking windows, and ancillary services (seat selection, baggage, priority boarding)

• Amadeus AI-powered revenue management systems serve over 100 airlines globally; Impact on Airline Revenue Management report (2024) describes AI-driven seat inventory optimisation

• Ancillary revenue: dynamic pricing of extras (baggage, meals, seat upgrades) has become a significant revenue stream; Ryanair generates substantial ancillary revenue per passenger partly through optimised ancillary pricing

• Airbnb Smart Pricing: hosts using the recommendation are approximately four times more likely to receive a booking; system incorporates last-minute demand signals and local event announcements

  Hotels and Short-Term Rentals

• Revenue management systems at major chains (Marriott, Hilton, IHG) use demand forecasting and competitive rate intelligence to dynamically set room rates across distribution channels (OTA, direct booking, GDS)

• IDeaS (Amadeus subsidiary), Duetto, and OTA Insight provide AI-powered revenue management to thousands of independent hotels; ML models incorporate forward-looking events calendar, booking pace, and competitor rate intelligence

• Research: Gao (2025, SAGE Tourism and Hospitality Research) demonstrated RL-based hotel revenue management generating superior outcomes to rule-based approaches in field experiments

• Short-term rental platforms (Vrbo, Booking.com): Interhome’s 2025 case study demonstrated 25% reservation uplift from ML dynamic pricing

  Energy Markets and Smart Grids

• Time-of-use (TOU) electricity tariffs and real-time pricing programs adjust consumer electricity prices to reflect wholesale market costs and grid congestion, incentivising Demand Response

• Dynamic pricing is a key mechanism for smart grid load flexibility: variable tariffs signal consumers and automated devices (EV chargers, heat pumps, washing machines) to shift consumption to off-peak periods

• UK Octopus Agile tariff: 30-minute interval electricity pricing linked to half-hourly wholesale prices, enabling consumers with smart meters to benefit from negative prices during oversupply events

• Wholesale electricity market clearing prices are determined dynamically in energy-only markets (EPEX Spot, N2EX in the UK); balancing mechanism and intraday market prices provide dynamic incentives for flexible generation and storage

  Healthcare and Pharmaceutical Pricing

• Hospital capacity management: dynamic pricing for elective procedure scheduling adjusts out-of-pocket costs based on appointment demand and capacity availability

• Pharmaceutical pricing: value-based pricing for new drugs uses dynamic rebate structures tied to real-world evidence outcomes; PBM (Pharmacy Benefit Manager) rebate negotiations involve dynamic pricing components

• Regulatory constraints: NHS drug pricing in the UK is governed by the Voluntary Scheme for Branded Medicines Pricing and Access (VPAS); dynamic pricing by pharmaceutical companies is constrained by these agreements and the ABPI code

• Medical device supply chain: dynamic pricing for high-demand devices (ventilators, PPE) during public health emergencies has raised significant ethical and regulatory concerns

  Logistics Optimisation and Supply Chain

• Dynamic freight rates in trucking (spot rate APIs from DAT, Spot Market Intelligence), ocean shipping (Freightos Baltic Index, BCO negotiations), and air cargo respond to capacity utilisation, fuel costs, seasonal demand patterns, and port congestion

• Real-time lane pricing APIs (Flexport, C.H. Robinson Navisphere) enable shippers to optimise carrier selection and contract vs. spot market procurement dynamically

• Last-mile delivery: Amazon Logistics and DHL use dynamic surcharges for peak period delivery capacity management

• Cold chain and pharmaceutical logistics: temperature-controlled capacity has specific demand patterns and spoilage risks that inform dynamic pricing of refrigerated transport capacity

  Fairness, Ethics, and Consumer Trust

  Dynamic pricing systems that adjust prices at individual consumer level based on inferred willingness-to-pay generate substantial fairness and equity concerns that have become a major focus of regulatory attention, consumer advocacy, and academic research:

  Consumer Trust Research

• Research published in 2026 (Qin et al., ScienceDirect): consumer scepticism of AI-enabled pricing is high:

  • 85.96% of consumers cite concerns about biases in AI pricing recommendations
  • 79% raise concerns about data privacy in pricing systems
  • 62% report concerns about algorithmic opacity (inability to understand why they received a particular price)

• UK survey (cited in CMA guidance): 91% of consumers oppose dynamic pricing when applied to entertainment events

• Consumer perception that dynamic pricing penalises loyalty—Amazon’s alleged higher prices for repeat purchasers—erodes brand trust and may increase price comparison behaviour

• Price fairness theory (Kahneman, Knetsch, and Thaler, 1986): consumers judge prices unfair when they cannot identify a justifying principle; algorithmic pricing without explanation triggers fairness violations

  UK Regulatory Enforcement and Guidance

• CMA Dynamic Pricing Project (2024): Launched to investigate how dynamic pricing is used across different sectors of the economy. Preliminary findings published and tips for businesses issued June 2025.

• Ticketmaster case (2024-2025): CMA launched a consumer protection case against Ticketmaster in September 2024 concerning opaque surge pricing for Oasis Live ‘25 concert tour. In September 2025, CMA secured undertakings from Ticketmaster to improve pricing transparency and fairness, requiring disclosure of dynamic pricing before ticket selection.

• Hotel sector investigation (February 2026): CMA launched investigation into suspected exchange of competitively sensitive pricing information between competing hotel chains via a shared hotel data analytics tool, raising algorithmic collusion concerns. Further case updates expected in the second half of 2026.

• CMA 2026-2027 Regulatory Priorities: Explicitly include algorithmic pricing as an enforcement focus; CMA blog post (March 2026) on “AI and Collusion: Frontiers, Opportunities and Challenges” identifies algorithmic pricing as a frontier competition concern.

• CMA Price Transparency Guidance (November 2025): Guidance under DMCCA 2024 requires businesses to present the full price payable at the earliest relevant stage of the consumer journey and ensure consumers can understand when dynamic pricing is being applied.

  Legal and Regulatory Framework

• UK Digital Markets, Competition and Consumers Act 2024 (DMCCA): Enhanced consumer protection requirements applicable to dynamic pricing. Businesses must not present prices misleadingly or omit material pricing information. Algorithmic pricing decisions must be consistent with fair commercial practice standards.

• EU Digital Services Act (DSA): Requires platform transparency about algorithmic recommendation systems, potentially extending to algorithmic pricing. Very Large Platforms (VLPs) subject to enhanced transparency and audit requirements.

• EU AI Act (effective 2026): High-risk AI classification may apply to AI systems making individualised price discrimination decisions with significant economic impact on consumers. Affected systems would require conformity assessments, algorithmic impact documentation, and transparency obligations. Edinburgh Law School analysis (Andreangeli, 2025) examines how pricing algorithms must be redesigned to comply.

• UK Financial Conduct Authority (FCA): PS21/5 (2022) prohibited renewal price discrimination in home and motor insurance, prohibiting insurers from charging existing customers more than equivalent new customers—a sector-specific anti-dynamic-pricing measure.

• OECD Report (October 2025): Documents algorithmic pricing and competition issues across G7 jurisdictions; notes competition authorities have prioritised market studies and guidance over enforcement to date, but enforcement activity is increasing.

  Algorithmic Collusion Risk

• Competing firms using pricing algorithms may independently converge to supra-competitive equilibrium prices through iterated best-response dynamics without explicit coordination—this constitutes “algorithmic collusion” that may be illegal under competition law even without human intent

• The CMA blog (March 2026) identifies algorithmic collusion as a frontier challenge: standard competition enforcement requires demonstrating agreement between firms, but algorithmic equilibria may emerge from independent algorithmic optimisation

• Academic literature (Calvano et al., 2020, “Artificial Intelligence, Algorithmic Pricing, and Collusion”, American Economic Review): shows that Q-learning pricing algorithms in duopoly simulations spontaneously discover supra-competitive pricing without explicit communication

• Regulatory responses under development: market monitoring tools, algorithmic audits, data-sharing obligations to enable competition authority oversight of pricing algorithm behaviour

  Mitigation Approaches

• Explainable pricing: natural-language justifications for price changes (“Prices are higher due to increased demand in your area”), aligned with DMCCA transparency requirements

• Fairness constraints: price optimisation subject to group fairness constraints (max price ratio between demographic groups), price floor constraints, and price volatility limits

• Consumer controls: opt-out mechanisms for personalised pricing; price lock options; advance purchase price guarantees

• Algorithmic impact assessments: pre-deployment evaluation of dynamic pricing systems for disparate impact across demographic groups

• External audit: third-party algorithmic pricing audits to assess fairness and regulatory compliance, analogous to financial statement audits

  Academic Context

  The academic study of dynamic pricing spans economics, operations research, computer science, marketing, law, and behavioural science:

• Operations Research foundations: Gallego and van Ryzin (1994) established the continuous-time dynamic pricing framework for perishable inventory under stochastic Poisson demand, proving the optimality of monotone pricing policies. Belobaba (1987) introduced EMSR for airline revenue management. Talluri and van Ryzin (2004) produced the definitive textbook systematising revenue management theory across airlines, hotels, and retail.

• Economics of price discrimination: Pigou (1920) introduced the first/second/third-degree classification. Mussa and Rosen (1978) developed the theory of quality discrimination (second-degree), foundational to menu design. Myerson (1981, Nobel Laureate 2007) derived the optimal mechanism for revenue-maximising auction/pricing under asymmetric information.

• Demand estimation with endogeneity: Berry, Levinsohn, and Pakes (1995)—the “BLP” model—addressed price endogeneity in demand estimation using instruments and random coefficients, becoming the standard approach in structural industrial organisation.

• Online learning and exploration-exploitation: Besbes and Zeevi (2009) established minimax-optimal policies for dynamic pricing without knowledge of the demand function, introducing the “price dithering” concept. Thompson (1933) introduced Thompson Sampling for bandit problems; Auer, Cesa-Bianchi, and Fischer (2002) derived UCB with provable regret bounds.

• Reinforcement learning for pricing: Bai and Mao (2023) formulated deep RL pricing for perishable inventory. arXiv:2411.18261 (Subramanian et al., 2024, ICAET 2025) demonstrated Q-learning retail pricing. Gao (2025, SAGE) demonstrated RL hotel revenue management with field experiments.

• Algorithmic collusion: Calvano, Calzolari, Denicolò, and Pastorello (2020, American Economic Review): Q-learning algorithms in duopoly simulations spontaneously reach supra-competitive prices. Andreangeli (2025, Edinburgh Law School): implications for AI Act compliance. Michigan Journal of Economics (2025): “Algorithmic Pricing: Colluding Without Breaking the Rules.”

• Consumer behaviour and fairness: Kahneman, Knetsch, and Thaler (1986): dual entitlement theory of price fairness. Bolton, Warlop, and Alba (2003): consumer judgements of price unfairness. Qin et al. (2026, ScienceDirect): ethics, transparency, and consumer trust in AI-enabled pricing.

• Causal pricing: Chernozhukov et al. (2018): double machine learning for heterogeneous treatment effects, applicable to heterogeneous price elasticity estimation. Elmachtoub and Grigas (2022, Management Science): Smart Predict-then-Optimize (SPO) framework for decision-optimised demand models.

• Marketing science: Ailawadi, Lehmann, and Neslin (2003): revenue premium as brand value measure. Nagle, Hogan, and Zale (2016): “The Strategy and Tactics of Pricing”—comprehensive practitioner-facing textbook covering value-based, competitive, and dynamic pricing strategies.

  Current Landscape (2026)

  Dynamic pricing is now pervasive across digital commerce, travel, mobility, and energy markets by mid-2026:

  Industry Adoption

• Amazon updates approximately 2.5 million product prices per day using AI and ML models

• Airbnb Smart Pricing updates nightly rates dynamically; hosts using the system receive ~4x more bookings

• Ride-hailing (Uber, Lyft, Bolt, Ola): real-time surge pricing fully operationalised globally

• Hotel sector: majority of major hotel chains and independent properties now use AI-powered revenue management systems (IDeaS, Duetto, OTA Insight)

• Short-term rentals: Interhome’s 2025 ML model delivered 25% more reservations, 18% higher turnover

• Electricity retail: Octopus Agile and similar dynamic tariffs in UK; Tibber and Voltalis expanding across Europe

• Report: Airbnb, Amazon and Uber dominate dynamic pricing adoption metrics (Hotel News Resource, 2025)

  Regulatory Tightening

• UK DMCCA 2024: enhanced consumer protection and price transparency obligations; CMA guidance issued November 2025

• CMA enforcement: Ticketmaster undertakings (September 2025); hotel sector investigation launched (February 2026)

• CMA 2026-2027 strategic priorities: algorithmic pricing explicitly included as enforcement focus

• EU AI Act (full effect 2026): potential high-risk classification for individualised pricing AI systems

• EU Digital Fairness Act (forthcoming): expected to introduce additional algorithmic price transparency requirements

• OECD report (October 2025): documents increasing regulatory activity across G7; identifies algorithmic collusion as the leading frontier concern

  Technology Advances

• Causal machine learning for demand elasticity estimation: separating price effects from confounders using double ML and IV methods, improving pricing model reliability

• Foundation model-based pricing agents: LLM-powered pricing systems that can be configured with natural language objectives and constraints, synthesising market intelligence from unstructured text

• Explainability: SHAP-based price explanation systems being deployed to meet DMCCA transparency requirements

• Real-time personalisation: individual-level WTP estimation at transaction scale becoming economically feasible as inference costs decline

• Dynamic pricing platforms: Revionics (Aptos), Symson, Omnia, Prisync serve mid-market retailers; PriceLabs and Beyond serve short-term rental operators

• Perkins Coie (2025) legal update and Lexology (2026) guidance documents the rapidly evolving compliance landscape for UK businesses deploying algorithmic pricing

  Ongoing Controversies

• Surge pricing at entertainment events: 91% of UK consumers oppose dynamic pricing for entertainment; Ticketmaster/Oasis case triggered parliamentary debate

• Algorithmic collusion risks from algorithm-mediated price signalling in oligopolistic markets (hotels, airlines, petrol stations)

• Personalised pricing at individual level: fairness, data privacy, and equity concerns when prices vary by inferred consumer characteristics

• Price walking in insurance: though banned in UK home/motor insurance by FCA PS21/5 (2022), concerns persist in other financial services categories

  UK Context

  The UK is both a major deployment context for dynamic pricing and among the world’s most active regulatory and academic hubs for algorithmic pricing research and enforcement:

  Regulatory Leadership

• Competition and Markets Authority (CMA): Among the world’s most active regulators of algorithmic pricing. Launched dynamic pricing market study (2024), published guidance (June and November 2025), secured Ticketmaster undertakings (September 2025), initiated hotel algorithmic collusion investigation (February 2026). CMA 2026-2027 strategy explicitly prioritises algorithmic pricing enforcement.

• Financial Conduct Authority (FCA): PS21/5 (2022) prohibited renewal price discrimination in home and motor insurance—a sector-specific ban on a form of dynamic pricing. FCA’s Consumer Duty (2023) imposes broader fairness obligations on financial services pricing.

• Ofcom: Reviews pricing practices of telecoms providers; digital markets and algorithmic pricing increasingly relevant to its regulatory scope under DMCCA 2024.

• Grant Thornton (2025): Published “Playing Fair on Pricing Practices: CMA Updates Its Guidance”—industry guidance on DMCCA compliance for businesses using dynamic pricing.

  Academic Research

• University of Edinburgh (Law School, Economics): Andreangeli (2025) analysed pricing algorithms under the EU AI Act. Edinburgh economics department works on mechanism design and digital market competition. Edinburgh Business School contributes revenue management and service operations research.

• London School of Economics (Department of Economics, Management): Research on platform economics, algorithmic pricing competition, and digital markets regulation. Abi Adams-Prassl (Oxford, formerly LSE) works on algorithmic labour market platforms and pricing.

• University of Oxford (Said Business School, Economics): Research on digital markets, behavioural economics of price fairness, and antitrust economics of algorithmic pricing. The Oxford Internet Institute contributes digital governance perspectives.

• University of Manchester (Alliance Manchester Business School): Revenue management and dynamic pricing research in retail and service operations. Centre for Digital Business has active research on e-commerce pricing strategies.

• King’s College London: Competition law and digital markets regulation research group; analysis of algorithmic pricing under UK and EU competition law.

  Industry Deployment

• Airlines: British Airways (oneworld yield management system), easyJet (full-dynamic-pricing model, no booking classes), Ryanair (highly aggressive dynamic pricing with yield-optimised ancillaries), Virgin Atlantic

• Transport and ticketing: Trainline (rail fare optimisation and ticket availability management), Uber UK (surge pricing in London and major cities), National Express (dynamic coach pricing)

• Retail: ASOS (competitor-based pricing algorithms), Ocado (grocery dynamic pricing, electronic pricing signals), The Hut Group (THG) (multi-brand e-commerce dynamic pricing), Boots (personalised member pricing)

• Hospitality: Premier Inn and other UK hotel chains use IDeaS and similar revenue management systems; Yotel, citizenM deploy algorithmic room pricing

• Energy: Octopus Energy (Agile tariff with 30-minute interval dynamic pricing), OVO Energy, Bulb (now Octopus) have pioneered dynamic electricity tariffs linked to wholesale prices

  Northern England Industrial Context

• Manchester: THG (The Hut Group, Trafford Park) operates large-scale algorithmic pricing across beauty, sports nutrition, and lifestyle brands. Manchester Metropolitan University and University of Manchester research on e-commerce pricing and demand forecasting.

• Leeds: Asda (Stonewall, Morley) uses ML-based grocery pricing; Leeds City Region has growing tech sector with pricing analytics firms.

• Sheffield: Retail technology firms and supply chain analytics companies in the Digital Creative Cluster use ML-based pricing tools. University of Sheffield AMRC works on pricing models for advanced manufacturing contracts.

• Newcastle: Sage Group (Newcastle Quayside) provides cloud ERP with pricing optimisation modules for UK SMEs. NewcastleGateshead tech cluster includes e-commerce businesses using dynamic pricing platforms.

  Future Directions (2026–2030)

• Causal and Counterfactual Pricing: Mainstream adoption of double ML, IV regression, and synthetic control methods for demand elasticity estimation that disentangle price effects from confounders, enabling more accurate and legally defensible revenue optimisation models that withstand regulatory scrutiny.

• Multi-Stakeholder Objective Pricing: Pricing systems explicitly balancing revenue, consumer welfare, fairness, and sustainability through multi-objective Pareto optimisation or constrained optimisation frameworks—moving beyond pure revenue maximisation in response to regulatory mandates and reputational pressure from consumers and investors.

• Algorithmic Collusion Detection and Prevention: Competition authorities (CMA, DG Competition) will develop real-time monitoring tools to detect supra-competitive equilibria emerging from competing pricing algorithms without explicit coordination. Platforms may be required to run algorithmic impact assessments before deploying new pricing models in concentrated markets.

• Explainable Pricing AI: Consumer-facing explanation systems generating natural-language justifications for price changes (“Prices are higher this weekend due to a local festival”), aligned with EU AI Act transparency requirements and CMA guidance. Standardised price explanation formats may emerge as a regulatory requirement.

• Federated and Privacy-Preserving Demand Modelling: Demand elasticity models trained across retailer consortia using federated learning and differential privacy, pooling training signals without exposing commercially sensitive individual price-demand data. Relevant for supply chain pricing where multiple players share inventory and logistics costs.

• Foundation Model Pricing Agents: LLM-powered pricing agents configured with natural language business objectives and constraints, synthesising real-time market intelligence from news, social media, and unstructured data sources, and generating dynamic pricing recommendations across novel product categories without domain-specific feature engineering.

• Real-Time Personalisation with Consent Frameworks: As inference costs decline, individually calibrated WTP estimation at transaction level will become widespread. Regulatory frameworks requiring explicit informed consent for personalised pricing—analogous to GDPR consent for personal data processing—may emerge, creating new compliance requirements for dynamic pricing systems.

• Sustainability-Linked Dynamic Pricing: Carbon pricing signals, energy market dynamics, and supply chain sustainability costs will increasingly be incorporated into dynamic pricing models, aligning commercial pricing incentives with sustainability objectives.

• Central Bank Digital Currency (CBDC) Programmable Pricing: If CBDC technology enables programmable payment conditions, it may enable new forms of conditional pricing where payments are automatically adjusted based on post-purchase product performance, creating a merger between dynamic pricing and performance-based contracting.

  Key Terminology

• Price Elasticity of Demand (PED): The percentage change in quantity demanded resulting from a 1% change in price; ε = (ΔQ/Q) / (ΔP/P). Elastic demand (|ε| > 1) means price increases reduce total revenue; inelastic demand (|ε| < 1) means price increases increase total revenue.

• Willingness to Pay (WTP): The maximum price a consumer would pay for a unit of a good. Dynamic pricing attempts to estimate and extract WTP through price-quantity tradeoffs and personalisation.

• Consumer Surplus: The difference between a consumer’s WTP and the price paid. Dynamic pricing with price discrimination reduces consumer surplus by extracting more of the value consumers place on products.

• Yield Management: Revenue management practice originating in the airline industry; adjusts prices of perishable capacity (seat inventory) to maximise revenue given demand forecasts and booking pace.

• Surge Pricing: Form of dynamic pricing in two-sided markets (ride-hailing, food delivery) that raises prices during periods of excess demand to incentivise additional supply and reduce excess demand.

• Price Discrimination: Charging different prices to different consumers for the same product, based on their WTP or segment membership. Distinguished from cost-based price differences (which are not discrimination).

• Algorithmic Collusion: When competing pricing algorithms independently discover and maintain supra-competitive pricing without explicit coordination, raising antitrust concerns similar to cartel behaviour.

• Price Walking (Insurance): The practice of charging existing customers progressively higher renewal prices compared to equivalent new customers; banned in UK home and motor insurance by FCA PS21/5 (2022).

  Research and Literature

  1. Pigou, A.C. (1920). The Economics of Welfare. Macmillan. (Foundational classification of price discrimination degrees.)
  2. Gallego, G. and van Ryzin, G. (1994). “Optimal dynamic pricing of inventories with stochastic demand over finite horizons.” Management Science, 40(8), 999-1020. https://doi.org/10.1287/mnsc.40.8.999
  3. Myerson, R.B. (1981). “Optimal Auction Design.” Mathematics of Operations Research, 6(1), 58-73. https://doi.org/10.1287/moor.6.1.58
  4. Talluri, K. and van Ryzin, G. (2004). The Theory and Practice of Revenue Management. Kluwer Academic Publishers. https://doi.org/10.1007/b139000
  5. Aydin, G. and Porteus, E. (2008). “Joint inventory and pricing decisions for an assortment.” Operations Research, 56(5), 1247-1255.
  6. den Boer, A.V. (2015). “Dynamic pricing and learning: historical origins, current research, and new directions.” Surveys in Operations Research and Management Science, 20(1), 1-18. https://doi.org/10.1016/j.sorms.2015.03.001
  7. Elmaghraby, W. and Keskinocak, P. (2003). “Dynamic Pricing in the Presence of Inventory Considerations: Research Overview, Current Practices, and Future Directions.” Management Science, 49(10), 1287-1309.
  8. Phillips, R.L. (2005). Pricing and Revenue Optimization. Stanford University Press.
  9. Bitran, G. and Caldentey, R. (2003). “An overview of pricing models for revenue management.” Manufacturing and Service Operations Management, 5(3), 203-229.
  10. Besbes, O. and Zeevi, A. (2009). “Dynamic pricing without knowing the demand function: Risk bounds and near-optimal algorithms.” Operations Research, 57(6), 1407-1420.
  11. Barto, A.G., Sutton, R.S., and Anderson, C.W. (1983). “Neuronlike adaptive elements that can solve difficult learning control problems.” IEEE Transactions on Systems, Man, and Cybernetics, 13(5), 834-846. (Foundation for RL pricing.)
  12. Watkins, C.J.C.H. and Dayan, P. (1992). “Q-learning.” Machine Learning, 8(3), 279-292. https://doi.org/10.1007/BF00992698
  13. Mnih, V. et al. (2015). “Human-level control through deep reinforcement learning.” Nature, 518, 529-533. https://doi.org/10.1038/nature14236
  14. Subramanian, J. et al. (2024). “Dynamic Retail Pricing via Q-Learning: A Reinforcement Learning Framework for Enhanced Revenue Management.” arXiv:2411.18261. https://arxiv.org/abs/2411.18261
  15. Gao, J. (2025). “Optimizing hotel revenue management through dynamic pricing algorithms and data analysis.” Tourism and Hospitality Research. https://journals.sagepub.com/doi/abs/10.1177/14727978241298467
  16. Andreangeli, A. (2025). “Pricing Algorithms and the Artificial Intelligence Act.” Law, Innovation and Technology, Edinburgh Law School. https://www.research.ed.ac.uk/files/539254973/AndreangeliA2025LIEIPricingAlgorithms.pdf
  17. Qin, M. et al. (2026). “Ethics, Transparency, and Consumer Trust in AI-Enabled Pricing: Implications for Sustainable Technology Entrepreneurship and Economic Policy.” ScienceDirect. https://www.sciencedirect.com/science/article/pii/S2773032826000040
  18. OECD (2025). “Algorithmic Pricing and Competition: A Review of G7 Jurisdictions.” OECD Policy Report, October 2025.
  19. Competition and Markets Authority (2025). “Price Transparency and Unfair Commercial Practices Guidance under the DMCCA.” CMA Guidance Note, November 2025.
  20. Competition and Markets Authority (2024). “Dynamic Pricing: CMA Project Launch and Preliminary Findings.” CMA Report. https://www.competitionandmarkets.blog.gov.uk/
  21. Competition and Markets Authority (2026). “AI and Collusion: Frontiers, Opportunities and Challenges.” CMA Blog, March 2026. https://competitionandmarkets.blog.gov.uk/2026/03/04/ai-and-collusion-frontiers-opportunities-and-challenges/
  22. Perkins Coie (2025). “Recent Algorithmic Pricing Developments in the UK and the EU.” Legal Update. https://perkinscoie.com/insights/update/recent-algorithmic-pricing-developments-uk-and-eu
  23. Lexology (2026). “Dynamic Pricing under the DMCCA: 10 Lessons in How to Achieve Transparency, Fairness and Compliance in 2026.” https://www.lexology.com/library/detail.aspx?g=3876c8af-79e0-411b-a4b0-c7784900bef3
  24. Akin Gump (2025). “When Bots Set Prices: CMA Highlights Real World Risks of Algorithmic Pricing.” https://www.akingump.com/en/insights/alerts/when-bots-set-prices-cma-highlights-real-world-risks-of-algorithmic-pricing
  25. Financial Conduct Authority (2022). “General Insurance Pricing Practices Market Study: PS21/5.” FCA Policy Statement. https://www.fca.org.uk/publications/policy-statements/ps21-5-general-insurance-pricing-practices
  26. Boer, A.V. and Zwart, B. (2015). “Simultaneously learning and optimizing using controlled variance pricing.” Management Science, 61(6), 1339-1355.
  27. Misra, K. et al. (2019). “Dynamic Online Pricing with Incomplete Information Using Multi-Armed Bandit Experiments.” Marketing Science, 38(2), 226-252.
  28. Elmachtoub, A.N. and Grigas, P. (2022). “Smart Predict, then Optimize.” Management Science, 68(1), 9-26. https://doi.org/10.1287/mnsc.2020.3922

Provenance