Arnoud V. den Boer

I am associate professor at the Mathematics department of the University of Amsterdam. This page lists my scientific publications.

In my early career, my research focused on the development and analysis of algorithms that learn optimal prices and product assortments from data. Recently I have started to focus more on societally relevant consequences of price algorithms: their potential to reduce waste, and their ability to harm consumer welfare by forming cartels.

These publications are joint work with colleagues, friends, and students: Ali Aouad (London Business School), Athanassios Avramidis (University of Southampton), Richard Boucherie (University of Twente), Boxiao Chen (University of Illinois Chicago), Ruben van de Geer, Marijn Jansen, Bora Keskin (Duke University), Thomas Loots, Michel Mandjes (Leiden University), Benedikt Meylahn, Janusz Meylahn (University of Twente), Yannik Peeters, Ohad Perry (Northwestern University), Maarten Pieter Schinkel (University of Amsterdam), Dirk Sierag, Yining Wang (University of Texas at Dallas), Andreas Weiermann (Ghent University), Jinglong Zhao (Boston University), Bert Zwart (Eindhoven University of Technology).

Almost all my publications are publicly available, and can be accessed via the [url] links below.

Contact information

Can algorithms learn to form a cartel?

A question among competition regulators is whether data-driven algorithms are able to learn to collude instead of compete against each other. There has been debate about the question whether such `algorithmic collusion' is really possible or merely science fiction. The following paper contributes to this debate by providing a formal definition, a set of requirements that an algorithm should satisfy before one should properly call it collusive.

A (mathematical) definition of algorithmic collusion. [url] Working paper. With J. M. Meylahn.

These three papers show that algorithmic collusion is possible in several market models:

Learning to Collude in a Pricing Duopoly. [url1] [url2] Manufacturing & Service Operations Management 24(5), 2577-2594, 2022. With J. M. Meylahn.
Data-driven collusion and competition in a pricing duopoly with multinomial logit demand. [url1] [url2] Production and Operations Management 32(4), 1169-1186, 2023. With T. Loots.
Algorithmic Collusion in Assortment Games. [url] With Ali Aouad. Under revision.

An assessment of claims that Q-learning algorithms autonomously learn to collude:

Artificial Collusion: Examining Supracompetitive Pricing by Q-learning Algorithms. [url] With Janusz Meylahn and Maarten Pieter Schinkel.

Can dynamic pricing reduce waste?

Can giving markdowns at expiry dates simultaneously reduce waste and increase profit of perishable products?

Waste Reduction of Perishable Products through Markdowns at Expiry Dates. [url] With H.M. Jansen and Jinglong Zhao.

Can algorithms learn optimal prices and assortments from data?

These fifteen papers are about algorithms that learn optimal prices and product assortments from data:

Pricing and Positioning of Horizontally Differentiated Products with Incomplete Information. [url1] [url2] Operations Research, 2024. With Boxiao Chen and Yining Wang.
Dynamic Pricing with Demand Learning: Emerging Topics and State of the Art. [url] In: The Elements of Joint Learning and Optimization in Operations Management. X. Chen, S. Jasin, C. Shi (Eds.), Springer Series in Supply Chain Management vol. 18, Springer, Cham, 2022. With N.B. Keskin.
Pricing in a Non-stationary Environment. [url] In: The Elements of Joint Learning and Optimization in Operations Management. X. Chen, S. Jasin, C. Shi (Eds.), Springer Series in Supply Chain Management vol. 18, Springer, Cham, 2022. With N.B. Keskin.
Stochastic Approximation for Uncapacitated Assortment Optimization under the Multinomial Logit Model. [url1] [url2] Naval Research Logistics 69(7), 927-938, 2022. With Y. Peeters.
Continuous Assortment Optimization with Logit Choice Probabilities under Incomplete Information. [url1] [url2] Operations Research 70(3), 1613-1628, 2022. With Y. Peeters and M. Mandjes.
Dynamic Pricing with Demand Learning and Reference Effects. [url1] [url2] Management Science 68(10), 7112-7130, 2022. With N.B. Keskin.
A Regret Lower Bound for Assortment Optimization under the Capacitated MNL Model with Arbitrary Revenue Parameters. [url] Probability in the Engineering and Informational Sciences 36(4), 1266-1274, 2022. With Y. Peeters.
Dynamic Pricing with Finite Price Sets: a Non-Parametric Approach. [url] Mathematical Methods of Operations Research 94, 1-34, 2021. With A. Avramidis.
Discontinuous Demand Functions: Estimation and Pricing. [url1] [url2] Management Science 66(10), 4516-4534, 2020. With N.B. Keskin.
Dynamic Pricing and Learning with Competition: Insights from the Dynamic Pricing Challenge at the 2017 INFORMS RM & Pricing Conference. [url] [pdf] Journal of Revenue and Pricing Management, 2018. With R. van de Geer and 11 others.
Dynamic Pricing and Learning: Historical Origins, Current Research, and New Directions. [url1] [url2] Surveys in Operations Research and Management Science 20(1), 1-18, 2015.
Dynamic pricing and learning with finite inventories. [url] [pdf] Operations Research 63(4), 965-978, 2015. With B. Zwart.
Tracking the market: dynamic pricing and learning in a changing environment. [url] [pdf] European Journal of Operational Research 247(3), 914-927, 2015.
Dynamic pricing with multiple products and partially specified demand distribution. [url] [pdf] Mathematics of Operations Research 39(3), 863-888, 2014.
Simultaneously learning and optimizing using controlled variance pricing. [url] [pdf] Management Science 60(3), 770-783, 2014. With B. Zwart.

Various papers on optimal pricing

Succinct description of the time it takes to sell a dynamically priced product:

How long does it take to sell a product? [url] Under review.

A method to compute optimal prices under the finite-mixture logit demand model:

Price Optimization Under the Finite-Mixture Logit Model. [url1] [url2] Management Science 68(10), 7480-7496, 2022. With R. van de Geer.

An optimal policy for a continuous-time price optimization problem:

Dynamic Pricing Policies for an Inventory Model with Random Windows of Opportunities. [url] Naval Research Logistics (NRL) 65(8), 660-675, 2018. With O. Perry and B. Zwart.

Some statistical papers

Can a simple model lead to better decisions than a complex model? How to choose between the two?

Decision-based model selection. [url] [url2] European Journal of Operational Research 290(2), 671-686, 2021. With D.D. Sierag.

Estimation of e.g. queueing related quantities via Laplace transforms:

Convergence rates of Laplace-transform based estimators. [url] Bernoulli 23(4A), 2533-2557, 2017. With M. Mandjes.

Rates of convergence for maximum (quasi-)likelihood estimators in certain generalized linear models:

Mean square convergence rates for maximum quasi-likelihood estimators. [url] Stochastic Systems 4(2), 375-403, 2014. With B. Zwart.

More data is not always better, sometimes it can be worse:

Does adding data always improve linear regression estimates? [url] [pdf] Statistics & Probability Letters 83(3), 829-835, 2013.

PhD thesis

Dynamic Pricing and Learning. PhD Thesis, VU University Amsterdam, 2013.

Master's thesis

My `doctoraalscriptie' (Master's thesis) written in 2006, later turned into a paper. The topic is queueing networks with time-dependent (`transient') product-form probability distribution:

Transient detailed balance and product-form for reaction networks. [url] [pdf] Stochastic Models 33(2), 322-341, 2017. With R.J. Boucherie.

Bachelor's thesis

My `kleine scriptie' (bachelor's thesis), written in 2004/5:

A sharp phase transition threshold for elementary descent recursive functions. [url] Journal of Logic and Computation 17(6), 1083-1098, 2007. With A. Weiermann.