Dynamic Online Pricing with Incomplete Information Using Multiarmed Bandit Experiments
Abstract
We propose an alternative dynamic price experimentation policy that extends multiarmed bandit (MAB) algorithms from statistical machine learning to include microeconomic choice theory.
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“2019) • Multiarmed bandit algorithms from statistical machine learning dynamically adjusted online prices with incomplete price information (Misra et al. 2019) • Machine learning based on Bayesian inference optimize online pricing with sparse and noisy data (Bauer and Jannach 2018) • Consumers’ private information for…”
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“[32] exploit that, in many practical settings, the demand function is monotonically decreasing in the price to design novel algorithms outperforming the classical MAB policies empirically.”
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“Contextual bandit algorithms aims to seek a balance between exploration and exploitation, which have been used in several applications, such as recommender systems [21], dynamic pricing [22], quantitative finance [31] and so on.”
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“Finally, in dynamic pricing tasks [15], a key problem for businesses is to learn online the market demands to set prices for products or services dynamically.”
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“…variables that can include, for example, user and publisher characteristics, with P being the total number of different combinations of values across all elements of Z. Consumer segmentation of user characteristics in this manner is common in the literature; see, for instance, Misra et al. (2019).”
BackgroundResultInfluentialDynamic Pricing with Parametric Demand Learning and Reference-Price Effects
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“To address this, some scholars have proposed parametric demand learning [7–9].”
Selective Reviews of Bandit Problems in AI via a Statistical View
Zhou, P., Wei, H., & Zhang, H. (2025) · Mathematics · doi:10.3390/math13040665 · Cited by 11 · see citing works
Pantano, E., Pizzi, G., Bilotta, E., & Pantano, P. (2021) · Journal of Marketing Management · doi:10.1080/0267257x.2021.2003422 · Cited by 11 · see citing works
“To this end, we employ an approach based on agents’ simulations using the Montecarlo method to reflect the nature of consumers’ movements within the store (Hidalgo, 2015; Misra et al., 2019).”
MethodTajik, M., Tosarkani, B. M., Makui, A., & Ghousi, R. (2023) · Expert Systems with Applications · doi:10.1016/j.eswa.2023.123060 · Cited by 11 · see citing works
Effective Adaptive Exploration of Prices and Promotions in Choice-Based Demand Models
Jain, L., Li, Z., Loghmani, E., Mason, B., & Yoganarasimhan, H. (2024) · Marketing Science · doi:10.1287/mksc.2023.0322 · Cited by 11 · see citing works
Diffusion and Pricing Over the Product Life CyclePreprint
Nair, H. S. (2019) · SSRN Electronic Journal · doi:10.2139/ssrn.3380744 · Cited by 9 · see citing works
Mahi, R., Alam, F., & Hasan, M. (2024) · GLOBAL MAINSTREAM JOURNAL · doi:10.62304/jieet.v3i3.159 · Cited by 22 · see citing works
Contextual Restless Multi-Armed Bandits with Application to Demand Response Decision-Making
Chen, X., & Hou, I.-H. (2024) · IEEE Conference on Decision and Control (CDC) · doi:10.1109/cdc56724.2024.10886713 · Cited by 8 · see citing works
“It has found extensive applications across a broad spectrum of domains [2], such as dynamic pricing [3], demand response [4], [5], clinical trials [6], and recommendation systems [7].”
Amazon's Artificial Intelligence in Retail Novelty - Case Study
Manasa, R., & Devi, A. J. (2022) · International Journal of Case Studies in Business IT and Education · doi:10.47992/ijcsbe.2581.6942.0233 · Cited by 11 · see citing works
Nonparametric multi-product dynamic pricing with demand learning via simultaneous price perturbation
Yang, X., Zhang, J., Hu, J.-Q., & Hu, J.-Q. (2024) · European Journal of Operational Research · doi:10.1016/j.ejor.2024.06.017 · Cited by 8 · see citing works
Advancement of human-machine collaboration in manufacturing: A review on industry 1.0 - 6.0
Oladele, I. O., Okoro, C. J., Falana, S. O., Olanrewaju, O. F., Adelani, S. O., & Onuh, L. N. (2024) · JOURNAL OF MECHANICAL ENGINEERING AND SCIENCES · doi:10.15282/jmes.18.4.2024.7.0813 · Cited by 8 · see citing works
“…align price points with rivals in pricing environments that are undergoing rapid change, such as e-commerce claims that to optimize dynamic pricing strategies, advanced pricing algorithms, such as best response pricing, considering customer preferences, rival strategy, and supply networks [92, 93].”
Dynamic Data Transaction in Crowdsensing Based on Multi-Armed Bandits and Shapley Value
Xu, C. L., Si, Y., Zhu, L., Zhang, C., Sharif, K., & Wu, H. (2021) · IEEE Transactions on Sustainable Computing · doi:10.1109/tsusc.2021.3128388 · Cited by 7 · see citing works
“Some studies have researched the transaction between the service provider as the seller and customers as the buyer, and give respective pricing scheme [13], [14], [15].”
BackgroundReinforcement learning for content's customization: a first step of experimentation in Skyscanner
Giachino, C., Bollani, L., Bonadonna, A., & Bertetti, M. (2021) · Industrial Management & Data Systems · doi:10.1108/imds-12-2019-0722 · Cited by 6 · see citing works
Pricing Prediction Services for Profit Maximization with Incomplete Information
Peng, H., Miao, X., Chen, L., Gao, Y., & Yin, J. (2023) · IEEE International Conference on Data Engineering (ICDE) · doi:10.1109/icde55515.2023.00108 · Cited by 6 · see citing works
“The other one is to online learn the real valuation from the posted price and the demand history [21], [22], [41], [42].”
BackgroundLearning to Set PricesPreprint
Huang, Y., Ellickson, P. B., & Lovett, M. J. (2018) · SSRN Electronic Journal · doi:10.2139/ssrn.3267701 · Cited by 6 · see citing works
Diffusion Approximations for Thompson Sampling in the Small Gap RegimePreprint
Fan, L., & Glynn, P. W. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2105.09232 · Cited by 6 · see citing works
Dynamic pricing of regulated field services using reinforcement learning
Mandania, R., & Oliveira, F. S. (2022) · IISE Transactions · doi:10.1080/24725854.2022.2151672 · Cited by 5 · see citing works
“Misra et al. (2019) modeled the problem with incomplete information using multi-armed bandits with statistical machine learning to identify consumer demand functions.”
BackgroundPredictive Analytics in Marketing Using Artificial Intelligence
Shukla, R. P., Juneja, D., & Monga, S. (2024) · Lecture notes in networks and systems · doi:10.1007/978-981-99-9531-8_17 · Cited by 5 · see citing works
Ni, Y., & Yang, D. (2025) · IEEE Transactions on Engineering Management · doi:10.1109/tem.2025.3576279 · Cited by 5 · see citing works
Multi-Armed-Bandit-based Shilling Attack on Collaborative Filtering Recommender Systems
Sundar, A. P., Li, F., Zou, X., Hu, Q., & Gao, T. (2020) · IEEE International Conference on Mobile Ad-Hoc and Sensor Systems (MASS) · doi:10.1109/mass50613.2020.00050 · Cited by 5 · see citing works
“In [26], the authors make an algorithm to choose between earning an immediate profit and learning for future profit when the demand information is incomplete.”
BackgroundGroup Fairness in Bandit Arm SelectionPreprint
Schumann, C., Lang, Z., Mattei, N., & Dickerson, J. P. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1912.03802 · Cited by 5 · see citing works
“Examples include algorithms for selecting what advertisements to display to users on a webpage [28], systems for dynamic pricing [29], and content recommendation services [24].”
BackgroundNonparametric Estimation of Price Elasticities: A Heterogeneous Treatment Effect ApproachPreprint
Wang, J., & Huang, Y. (2019) · SSRN Electronic Journal · doi:10.2139/ssrn.3557359 · Cited by 5 · see citing works
Liu, L., Wang, Y., Fang, Z. Y., & Wu, S. (2021) · SSRN Electronic Journal · doi:10.2139/ssrn.3920764 · Cited by 5 · see citing works
A Scalable Recommendation Engine for New Users and ItemsPreprint
Xu, B., Deng, Y., & Mela, C. F. (2022) · SSRN Electronic Journal · doi:10.2139/ssrn.4202543 · Cited by 5 · see citing works
Survey of dynamic pricing based on Multi-Armed Bandit algorithms
Qu, J. (2024) · Applied and Computational Engineering · doi:10.54254/2755-2721/37/20230497 · Cited by 4 · see citing works
Personalized Dynamic Pricing Based on Improved Thompson Sampling
Bi, W.-J., Wang, B., & Liu, H. (2024) · Mathematics · doi:10.3390/math12081123 · Cited by 2 · see citing works
“Recently, the MAB framework has gained widespread application in various fields, such as recommendation systems [36,37], healthcare [38], and dynamic pricing [39–42].”
BackgroundMulti-Task Neural Linear Bandit for Exploration in Recommender Systems
Su, Y., Lu, H.-K., Li, Y.-N., Liu, L., Bi, S., Chi, E. H., & Chen, M.-M. (2024) · Knowledge Discovery and Data Mining · doi:10.1145/3637528.3671649 · Cited by 8 · see citing works
Lopez-Pastor, M., de Madariaga, J. G., Sánchez-Herrera, J., & Figueiredo, J. (2020) · International Review of Management and Marketing · doi:10.32479/irmm.10683 · Cited by 4 · see citing works
“International Review of Management and Marketing | Vol 10 • Issue 6 • 2020 72 of products in real time without the option of conducting market research or calculating price elasticity (Baker et al., 2014; Misra et al., 2019), which depending on the sales model may even escape their control (Chen et al.”
BackgroundInfluential(Private) Kernelized Bandits with Distributed Biased Feedback
Li, F., Zhou, X., & Ji, B. (2023) · Proceedings of the ACM on Measurement and Analysis of Computing Systems · doi:10.1145/3579318 · Cited by 4 · see citing works
Dynamic Pricing with Volume Discounts in Online Settings
Mussi, M., Genalti, G., Nuara, A., Trovò, F., Restelli, M., & Gatti, N. (2023) · Proceedings of the AAAI Conference on Artificial Intelligence · doi:10.1609/aaai.v37i13.26845 · Cited by 4 · see citing works
SPECTS: Price Elasticity Computation Model Using Thompson Sampling
Sethuraman, S., Maheswari, G. U., & Ramanan, S. (2022) · International Conference on Computational Science and Computational Intelligence (CSCI) · doi:10.1109/csci58124.2022.00118 · Cited by 4 · see citing works
“In [7], the authors present a scalable distribution-free algorithm for dynamic pricing in an online setting.”
BackgroundData-Driven Dynamic Pricing: Sticky Fairness Concerns and the Exploitation-Exploration Trade-Off
Rathore, H., & Tiwari, S. (2025) · Journal of the Operational Research Society · doi:10.1080/01605682.2025.2571064 · Cited by 4 · see citing works
“Auer et al. (2002), Misra et al. (2019) and Zhong et al. (2021) exhibit adaptive experimentation in DPWL policies for similar reasons.”
InfluentialSetting Reserve Prices in Second-Price Auctions with Unobserved Bids
Rhuggenaath, J., Akçay, A., Zhang, Y., & Kaymak, U. (2022) · INFORMS journal on computing · doi:10.1287/ijoc.2022.1199 · Cited by 3 · see citing works
“This assumption is also fairly common in the literature on multi-armed bandits and dynamic pricing (Cheung et al. 2017, Trovò et al. 2018, Misra et al. 2019).”
BackgroundMethodRethinking the role of uncertainty and risk in Marketing
Grimaldi, D., Sallan, J. M., Arboleda, H., & Sehgal, S. (2023) · Journal of Decision System · doi:10.1080/12460125.2023.2232570 · Cited by 3 · see citing works
PAC-Bayes Bounds for Bandit Problems: A Survey and Experimental Comparison
Flynn, H., Reeb, D., Kandemir, M., & Peters, J. (2023) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2023.3305381 · Cited by 3 · see citing works
“Bandit problems are frequently encountered in real-world problems, including clinical trials [15], [30], dynamic pricing [71], [72] and recommendation systems [65], to name just a few.”
BackgroundBialkova, S. (2024) · Springer eBooks · doi:10.1007/978-3-031-56471-0_10 · Cited by 3 · see citing works
МАРКЕТИНГОВІ МОЖЛИВОСТІ ПІДПРИЄМСТВ НА ОСНОВІ ШТУЧНОГО ІНТЕЛЕКТУ
Заячковська, Г. А. (2024) · Трансформаційна економіка · doi:10.32782/2786-8141/2024-7-3 · Cited by 3 · see citing works
Modeling Dynamic Consumer Preferences from Few-Shot Data: A Meta-Learning Approach
Yin, M., Boughanmi, K., & Mukherjee, A. (2026) · Journal of Marketing Research · doi:10.1177/00222437261458290 · Cited by 3 · see citing works
Managing Crowding and Consumers' Perceived Store Density
Pantano, E., & Willems, K. (2022) · Emerald Group Publishing Limited eBooks · doi:10.1108/978-1-80117-846-420221007 · Cited by 3 · see citing works
Runge, J., & Nair, H. S. (2021) · SSRN Electronic Journal · doi:10.2139/ssrn.3794028 · Cited by 3 · see citing works
Wang, C., Cui, S., Wu, R., & Wang, Z. (2022) · IET Collaborative Intelligent Manufacturing · doi:10.1049/cim2.12050 · Cited by 2 · see citing works
Dynamic Pricing with Demand Learning: Emerging Topics and State of the Art
den Boer, A. V., & Keskin, N. B. (2022) · Springer series in supply chain management · doi:10.1007/978-3-031-01926-5_4 · Cited by 2 · see citing works
الأسدودی, ن. (2023) · مجلة البحوث الإعلامیة · doi:10.21608/jsb.2023.230616.1633 · Cited by 4 · see citing works
Aktaş, M., & Çavuşoğlu, S. (2023) · Özgür Yayınları eBooks · doi:10.58830/ozgur.pub398.c1662 · Cited by 3 · see citing works
Jamieson, S., How, J. P., & Girdhar, Y. (2024) · Artificial Intelligence · doi:10.1016/j.artint.2024.104096 · Cited by 2 · see citing works
Sengupta, A., Kohar, A., Rathore, H., & Jakhar, S. K. (2024) · Journal of Revenue and Pricing Management · doi:10.1057/s41272-024-00505-6 · Cited by 2 · see citing works
Online Learning and Pricing for Multiple Products With Reference Price Effects
Ji, S., Shi, C., & Yang, Y. (2025) · Naval Research Logistics (NRL) · doi:10.1002/nav.22240 · Cited by 4 · see citing works
“…pricing setting, we can view a price as an “arm" and the revenue resulting from that price as a “reward", and apply multi-armed-type algorithms to dynamic pricing problems (see, e.g., Cheung, Simchi-Levi, and Wang 2017, Ferreira, Simchi-Levi, and Wang 2018, Misra, Schwartz, and Abernethy 2019).”
Improving network dynamic pricing policies through offline reinforcement learning
Hausenblas, P., Eichhorn, D., Brieden, A., Soppert, M., & Steinhardt, C. (2025) · OR Spectrum · doi:10.1007/s00291-025-00821-2 · Cited by 2 · see citing works
“We refer to Raju et al. (2006); Ferreira et al. (2018); Misra et al. (2019); Bu et al. (2020), and those not discussed above but summarized in Kastius and Schlosser (2022).”
Nonparametric Pricing Bandits Leveraging Informational Externalities to Learn the Demand Curve
Weaver, I. C., Kumar, V., & Jain, L. (2025) · Marketing Science · doi:10.1287/mksc.2022.0247 · Cited by 2 · see citing works
Secure Best Arm Identification in the Presence of a Copycat
Cohen, A., & Günlü, O. (2025) · IEEE Information Theory Workshop (ITW) · doi:10.1109/itw62417.2025.11240381 · Cited by 2 · see citing works
“MAB problems have diverse applications across various fields, including clinical trials [1], finance (such as portfolio selection [2] and dynamic pricing [3]), recommendation systems [4], influence maximization in social networks [5], and even routing [6].”
How Effective Is Suggested Pricing? Experimental Evidence from an E-Commerce Platform
Fong, J., Manchanda, P., & Song, Y. (2026) · Journal of Marketing Research · doi:10.1177/00222437261432198 · Cited by 3 · see citing works
“This stream of literature covers a variety of topics, including personalized pricing (Misra, Schwartz, and Abernethy 2019; Smith, Seiler, and Aggarwal 2023), pricing frictions (Aparicio and Simester 2022; Huang 2022; Pan and Wang 2021; Williams 2022), and selling mechanisms (Filippas, Jagabathula,…”
- Authors
- Misra, K., Schwartz, E. M., & Abernethy, J.
- Affiliations
- University of California San Diego (US)
- University of Michigan (US)
- Georgia Institute of Technology (US)
- Corresponding author
- Misra, Kanishka
- Venue
- Marketing Science
- Published
- 2019-03
- Volume
- 38
- Issue
- 2
- Pages
- 226-252
- ISSN
- 0732-2399 (ISSN-L)
- 1526-548X
- OpenAlex
- W2725896932
- Cited by
- 183
- References
- 59
- Citations by year
- 2026: 17 · 2025: 22 · 2024: 39 · 2023: 38 · 2022: 24 · 2021: 25 · 2020: 8 · 2019: 8 · 2018: 2
- FWCI
- 11.59
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Marketing Science (publishedVersion)
- Topics
- Social Sciences › Decision Sciences › Management Science and Operations Research › Advanced Bandit Algorithms Research
- Social Sciences › Business, Management and Accounting › Marketing › Consumer Market Behavior and Pricing
- Social Sciences › Business, Management and Accounting › Management Information Systems › Supply Chain and Inventory Management
- Keywords
- dynamic pricing, online pricing, incomplete information, multi-armed bandits, choice theory, pricing policy
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