Pith. sign in

REVIEW 3 major objections 4 minor 96 references

Algorithmic collusion under asynchronous price updating

T0 review · 3 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Asynchrony in price-update timing hampers algorithmic collusion; the effect is strongest for stateless algorithms and weakest when algorithms condition on their rival's current price.

desk verdict Genuinely new angle on algorithmic collusion—update timing—with a solid stateless result and a suggestive but under-powered stateful contrast. read the letter →

arxiv 2608.01406 v1 pith:LVYCCSLL submitted 2026-08-02 econ.TH cs.GT

Ivan Conjeaud , Gaspard Abel , Argyris Kalogeratos This is my paper
classification econ.THcs.GT
keywords algorithmiccollusionQ-learningasynchronouspriceupdatingBertrandduopolyreward-punishmentschemesindexPoissonclockpricingregulation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper argues that the timing of price updates—whether two pricing algorithms move at the same instant or at independent random moments—is a previously overlooked factor in whether algorithmic collusion emerges. It sets up a continuous-time Bertrand duopoly in which two Q-learning, price-setting reinforcement-learning algorithms revise prices at Poisson-timed moments, with a parameter q controlling the chance that the rival updates at the same moment. Across numerical experiments, higher synchrony yields more collusion, and the effect is largest for stateless algorithms, whose collusive behavior collapses at low q. When algorithms condition on the rival's price, the result depends on information: conditioning on the current price supports collusion even under full asynchrony, while conditioning on the average price since the last update does not. The paper's point is that asynchrony is not a neutral detail in algorithmic-collusion models, and that regulators should focus on the price information algorithms receive.

What carries the argument

The controlling object is a single parameter q in [0,1] embedded in two independent Poisson clocks: each firm is scheduled by its own clock of rate λ/2, and whenever one firm updates, the rival also updates with probability q. q=1 reproduces a single synchronous clock and q=0 reproduces two independent clocks. The conclusions ride on how this timing process interacts with the Q-learning update rule and with the state definition: no state (NOSTATE), the average opponent price since the last own update (AVGPRICE), or the opponent's current price (CURRENTPRICE). Collusion is measured by a normalized collusion index and by a pattern-detection pipeline that records reactions to unilateral price c

What would settle it

Run the same two-firm Q-learning Bertrand model with deterministic alternating updates or fixed business-hour schedules at the same average update frequency, then measure the collusion index and reward-punishment detection across q. If collusion appears at low q or disappears at high q under these schedules, then the Poisson timing assumption, rather than synchrony itself, is producing the result.

Watch

Extended reading notes

Core claim

The paper's central claim is that update timing is a first-order determinant of algorithmic collusion. In a continuous-time Bertrand duopoly with logistic demand, two firms use Q-learning to choose prices at revision times generated by independent Poisson clocks, with q the probability that a rival joins an update; q=1 replicates synchronous updating and q=0 makes the clocks fully independent. The paper reports three results. Stateless algorithms (no memory of the rival's price) reach near-Nash prices at q=0 and collude only as q approaches 1, because the coupling mechanism that sustains this spurious collusion requires simultaneous updates. When algorithms condition on the rival's average p

Load-bearing premise

The load-bearing premise is that real pricing algorithms get their update opportunities from independent memoryless Poisson clocks with a fixed probability q that the rival updates at the same moment; if update timing in real markets follows deterministic schedules or demand-triggered events instead, the paper's synchrony-collusion link may not transfer.

Editorial extensions

If this is right

  • Synchronous-update models overstate algorithmic collusion risk in markets where firms update at independent random times; the common timing assumption is not neutral.
  • Stateless 'spurious' collusion requires simultaneous updating; without it, collusion indices fall to competitive levels, so this class of collusion is unlikely in asynchronous retail settings.
  • Algorithms that condition on a rival's current price can collude even with fully asynchronous updates, making observability of the rival's live price a key enabler.
  • Algorithms that see only average prices since their last update need high synchrony to collude; low-synchrony markets with such information are near-competitive.
  • Regulatory measures that impose simultaneous updates, as in fuel-price transparency rules, can increase algorithmic collusion risk, while adding noise to update timing can mitigate it.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • An implication the paper leaves implicit: in the CURRENTPRICE specification, q also changes how often a fresh rival price is observed, so part of the robustness to asynchrony could be information freshness rather than timing per se; an experiment varying observation frequency and update frequency independently would separate the two channels.
  • The DTW-plus-DBSCAN detector could be reused as a regulatory screen: record price reactions to a test price cut in a live market and compare cluster separation against an untrained baseline, extending the method beyond simulation.
  • The paper models timing as exogenous; if firms can deliberately choose update schedules, equilibrium timing choices could amplify or offset the collusion effects reported here—for example, a firm might synchronize to collude or desynchronize to avoid triggering punishment.
  • A testable policy extension: comparing aggregated historical competitor statistics versus real-time price feeds in a field experiment on a retail platform would directly test the AVGPRICE-versus-CURRENTPRICE gap outside the simulated environment.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper studies algorithmic collusion in a continuous-time Bertrand duopoly in which two Q-learning firms update prices at times governed by a Poisson clock, with a parameter q controlling the probability that the other firm joins an update. Three algorithm specifications are compared: stateless Q-learning (NOSTATE), Q-learning conditioning on the opponent's average price since the firm's last update (AVGPRICE), and Q-learning conditioning on the opponent's current price (CURRENTPRICE). Collusion is measured by a payoff-based collusion index and by a novel DTW/DBSCAN detection of reward-punishment reaction patterns. The main finding is that asynchrony (lower q) hampers collusion, strongly so for stateless algorithms; stateful collusion is robust to asynchrony only when the algorithm observes the opponent's current price, not when it observes only an average price. The authors draw regulatory conclusions about synchronous price-update mandates and access to competitor price information.

Significance. If the result holds, it is an important contribution: the synchrony assumption in previous algorithmic-collusion models (Calvano et al. 2020b, Klein 2021) is shown to be consequential, and the paper identifies access to real-time competitor prices as a key determinant of collusion persistence. The stateless result is supported by a larger simulation campaign (100 runs per (q, ε) in Figure 2) and by a clean switching experiment (Figure 3). The collusion index is standard and independent of the detection method, so the main q-CI relationship is not an artifact of the DTW/DBSCAN pipeline. The paper also offers concrete, falsifiable predictions about the effect of update synchrony and information structure, which is a strength. However, the stateful results rest on only 10 runs per q with no uncertainty quantification, and the general claim about asynchrony is tested only under a specific Poisson timing process.

major comments (3)
  1. [§3.1 and Appendix A] The central claim 'asynchrony hampers the emergence of algorithmic collusion' is tested exclusively under the Poisson-with-join-probability timing model. Appendix A correctly states that the three motivating interpretations are mathematically equivalent to this Poisson process, but the introduction motivates the model with deterministic business hours, event-triggered inventory updates, and FuelWatch's daily simultaneous updates. Under a fixed alternating or deterministic schedule, q=0 does not correspond to a small probability of simultaneous updates but to exactly zero simultaneous updates, and the age of the opponent's observed price is constant rather than exponentially distributed. The load-bearing mechanism in Section 4 (simultaneous updating is needed for coupling) may survive, but the quantitative q-CI relationship could differ or reverse. I request re-running the key experiments
  2. [§5.4, Figure 7, and Appendix C] All stateful results use 10 independent runs per q, with no error bars, confidence intervals, or per-q dispersion measures. The difference between AVGPRICE and CURRENTPRICE at low q is large, but the ARI curves are visibly non-monotonic and could be driven by sampling noise; 10 runs can also miss rare collusive outcomes. Please report standard errors or bootstrap intervals for both CI and ARI, or increase the number of runs. This is particularly important because the policy conclusion that CURRENTPRICE collusion is 'very robust to asynchrony' is a quantitative claim about the level of CI at q=0, not just a qualitative ordering.
  3. [§5.3 and Appendix C] The DBSCAN radius η=10 is described as chosen 'a priori on the scale of the DTW distances, without optimization,' but the next sentence justifies it by reporting that average trained-trained distances at q=1 are about 13 versus 22 across groups. If the q=1 data were inspected before fixing η, then the ARI at q=1 is a selected result, and the comparison across q is not out-of-sample. A sensitivity analysis over η (e.g., 5, 10, 15, 20) is needed to show that the ARI-q relationship is not an artifact of this fixed threshold. The collusion-index results are not affected, but the ARI is used to support the claim about reward-punishment schemes.
minor comments (4)
  1. [§4, Figure 2] The text says 'hardly any collusion for low enough values of q,' but at ε=0.001 and q=0 the reported CI is 0.06, which is above the discrete-Nash threshold of 0.043. Please either rephrase the claim or explain why this point is considered non-collusive.
  2. [§3.2, Eq. (4)] The 'average payoff π collected between update times' is not formally defined. It should be stated explicitly as the time-integrated profit divided by the interval length, since the units of Q and the discounting in Eq. (4) depend on this normalization.
  3. [Appendix B and §3.2] The cited convergence proposition (Singh et al., 2000) requires Σ α_t = ∞ and Σ α_t^2 < ∞, but the experiments use a constant learning rate α=0.1. Moreover, the exponentially decaying exploration rate in Eq. (5) may not satisfy the infinite-visitation requirement. The authors should either use a decreasing learning-rate schedule or explicitly state that the convergence theorem is invoked only heuristically.
  4. [§5.1, Figure 4] The response-graph analysis is informative but only illustrated for n=4 prices and one run per configuration. Since the graph structure is central to the explanation of the AVGPRICE vs CURRENTPRICE difference, consider reporting how often the described structures appear across runs.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: results are simulation outputs, not fitted inputs or definitional identities.

full rationale

The paper's central claim that asynchrony hampers algorithmic collusion is an empirical finding from numerical simulations, not a consequence of a definition or a fitted parameter. The synchrony parameter q is an exogenous controlled input of the update process (Section 3.1), and the two collusion metrics—the payoff-based collusion index CI (Eq. 3) and the ARI from DTW/DBSCAN clustering of reactions to price cuts (Sections 5.2–5.3)—are evaluation tools that are not fitted to reproduce the q-effect. The DTW radius is chosen a priori and the paper explicitly notes it is conservative. There are no load-bearing self-citations; the cited prior work (Calvano et al. 2020b, Banchio and Mantegazza 2023) is external and provides baselines, not the paper's result. No uniqueness theorem from the authors is invoked. The only notable scope limitation is that 'asynchrony' is modeled as Poisson update times with a join probability q, and the paper does not test non-memoryless timing processes; this is an external-validity concern, not a circularity. No equation or fitted parameter reduces the conclusion to its own inputs.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The model imports standard demand and Q-learning components from Calvano et al. and Banchio and Mantegazza. The paper's own additions are the Poisson timing rule, the q-dependent exploration and horizon scaling, and the DTW/DBSCAN detection method; these are modeling choices rather than fitted constants, but several are chosen by hand and not sensitivity-tested.

free parameters (6)
  • β1 (baseline exploration decay rate) = 1e-5
    Section 5: β1=1e-5; Appendix C scales it as β=(q+1)/2 β1 to keep final exploration rate constant across q. The scaling is chosen by hand, not derived.
  • T1 (baseline episode count) = 1e6
    Appendix C: T=2T1/(q+1). Chosen to keep expected number of updates per player constant across q; arbitrary scale.
  • α (learning rate) = 0.1
    From Calvano et al. (2020b); constant, which violates the learning-rate conditions of the Singh et al. convergence theorem cited in Appendix B.
  • γ (discount factor) = 0.95
    From Calvano et al. (2020b) baseline.
  • DBSCAN radius η = 10
    Appendix C: chosen 'a priori' but with reported distance scale; appears informed by the trained-trained distances.
  • DBSCAN minimum neighborhood size m = 4
    Appendix C: chosen for clustering.
assumptions (5)
  • domain assumption Update times are generated by independent Poisson clocks plus synchronous updates with probability q
    Section 3.1; the central timing model is never validated against deterministic or event-driven updating.
  • ad hoc to paper The Q-learning update rule (Eq. 4) is a valid asynchronous learning rule
    Section 3.2; the rule bootstraps on the state at update time and is not derived from a continuous-time Bellman equation.
  • domain assumption AVGPRICE and CURRENTPRICE state encodings capture the relevant information environments
    Section 3.2; the policy conclusion about restricting scraping depends on this dichotomy.
  • domain assumption The learning process reaches a reliable long-run Q-matrix despite constant α
    Appendix B cites Singh et al. (2000) convergence conditions, which require decreasing α and infinite exploration; neither holds. Yet the response graph and final Q-matrix analyses assume stable learned behavior.
  • domain assumption The collusion index and DTW/DBSCAN metrics measure algorithmic collusion
    Eq. (3) and Sections 5.2-5.4; the main conclusions are expressed in terms of these metrics.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Algorithmic collusion under asynchronous price updating." pith.science (2026). https://pith.science/paper/LVYCCSLL

@misc{pith2026260801406,
  author       = {Pith},
  title        = {Pith review of: Algorithmic collusion under asynchronous price updating},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LVYCCSLL}},
  note         = {Machine review of arXiv:2608.01406}
}
abstract

This paper investigates the effect of asynchrony in agents' updates in the emergence of algorithmic collusion. We present a continuous-time model for algorithmic collusion in which two firms use $Q$-learning algorithms to set prices asynchronously in a Bertrand duopoly. The firms update their prices at times dictated by a Poisson clock. By controlling the extent of agents' asynchrony, we run extensive numerical experiments with three specifications of the algorithm to investigate the emergence of algorithmic collusion. The strength of collusion is measured by a standard collusion index, as well as by automatically detecting the reward-punishment schemes. This is done by recording a large number of algorithms' reactions to unilateral price cuts and comparing them with the reactions of untrained algorithms. Our findings indicate that asynchrony hampers collusion, especially when the algorithms are stateless. When they condition on their competitor's previous prices, the sensitivity of algorithmic collusion to asynchrony varies depending on the type of information they have access to. The implications of these results for the regulation of algorithmic pricing are discussed.

Figures

Figures reproduced from arXiv: 2608.01406 by the authors.

Figure 1
Figure 1. Illustration of the timing of updates for different values of q ∈ [0, 1], which controls the updating synchrony from independent to totally synchronized updates. regular Q-learning, each algorithm keeps in memory and updates a matrix of values, called the Q-matrix, which is given by Q : P × P 2 → R. We denote by Qt(p, s) the Q-value associated with price p and state s at time t. The state is an ordered pair of price… view at source ↗
Figure 2
Figure 2. Collusion indices with stateless algorithms [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Switching regime experiment. We start the experiment with full synchrony (q = 1) and exogenously change it to full asynchrony (q = 0; the time is indicated by a black vertical line). Following the change, the algorithms fail to synchronize on mutually beneficial actions. behavior. We keep track of the Q-values and the actions selected by the algorithms (C for high price, D for low price). The results for one represe… view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Response graphs for different values of q in the two specifications. The color of the nodes represents the collusion index of the associated pair of prices. While AVGPRICE for q = 1 and CURRENTPRICE show structure indicating reward-punishment schemes, it is not the cas…
Figure 5
Figure 5. Figure 5: Reactions to price cuts and corresponding DTW matches [PITH_FULL_IMAGE:figures/full_fig_p014_5.png]
Figure 6
Figure 6. Figure 6: PCoA of DTW distances in the AVGPRICE specification. Colors represent the ground truth. As q decreases, the two types of points become hardly distinguishable. own. In order to measure the performance of the clustering algorithms in distinguishing the two, the Adjusted …
Figure 7
Figure 7. Figure 7: Collusion index and ARI score for the AVGPRICE (top) and CURRENTPRICE (bottom) specifications. results in Section 4 show that this type of “collusion” disappears without synchronized updates as it precisely relies on a mechanism that needs them. Without a way for the a…
Figure 8
Figure 8. Figure 8: Comparison of Euclidean (point-to-point) and DTW distance for two reaction profiles sharing the same reward-punishment structure but differing in the speed of adjustment. E DBSCAN Once pairwise DTW distances between reaction profiles have been computed, we use the DB￾S…

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

96 extracted references · 71 canonical work pages

  1. [1]

    Artificial intelligence: Can seemingly collusive outcomes be avoided? Management Science, 69 0 (9): 0 5042--5065, 2023

    Ibrahim Abada and Xavier Lambin. Artificial intelligence: Can seemingly collusive outcomes be avoided? Management Science, 69 0 (9): 0 5042--5065, 2023

    2023

  2. [2]

    Collusion by mistake: Does algorithmic sophistication drive supra-competitive profits? European Journal of Operational Research, 318 0 (3): 0 927--953, 2024

    Ibrahim Abada, Xavier Lambin, and Nikolay Tchakarov. Collusion by mistake: Does algorithmic sophistication drive supra-competitive profits? European Journal of Operational Research, 318 0 (3): 0 927--953, 2024

    2024

  3. [3]

    Impact of post and hold regulation on retail petroleum prices

    Christopher P Adams. Impact of post and hold regulation on retail petroleum prices. Australian Economic Review, 58 0 (2): 0 109--114, 2025

    2025

  4. [4]

    The rise of AI pricing: Trends, driving forces, and implications for firm performance

    Jonathan J Adams, Min Fang, Zheng Liu, and Yajie Wang. The rise of AI pricing: Trends, driving forces, and implications for firm performance. Journal of Monetary Economics, page 103875, 2025

    2025

  5. [5]

    Artificial intelligence, algorithm design, and pricing

    John Asker, Chaim Fershtman, and Ariel Pakes. Artificial intelligence, algorithm design, and pricing. AEA Papers and Proceedings, 112: 0 452--456, 2022

    2022

  6. [6]

    Algorithmic pricing and competition: Empirical evidence from the German retail gasoline market

    Stephanie Assad, Robert Clark, Daniel Ershov, and Lei Xu. Algorithmic pricing and competition: Empirical evidence from the German retail gasoline market. Journal of Political Economy, 132 0 (3): 0 723--771, 2024

    2024

  7. [8]

    Algorithmic collusion under sequential pricing and stochastic costs

    Gonzalo Ballestero. Algorithmic collusion under sequential pricing and stochastic costs. International Journal of Industrial Organization, page 103281, 2026

    2026

  8. [9]

    Adaptive algorithms and collusion via coupling

    Martino Banchio and Giacomo Mantegazza. Adaptive algorithms and collusion via coupling. In ACM Conference on Economics and Computation, page 208, 2023

    2023

Show all 96 references
  1. [10]

    Artificial intelligence and auction design

    Martino Banchio and Andrzej Skrzypacz. Artificial intelligence and auction design. In ACM Conference on Economics and Computation, pages 30--31, 2022

    2022

  2. [11]

    Using dynamic time warping to find patterns in time series

    Donald J Berndt and James Clifford. Using dynamic time warping to find patterns in time series. In AAAI Workshop on Knowledge Discovery in Databases, pages 359--370, 1994

    1994

  3. [12]

    Learning to coordinate: A study in retail gasoline

    David P Byrne and Nicolas De Roos. Learning to coordinate: A study in retail gasoline. American Economic Review, 109 0 (2): 0 591--619, 2019

    2019

  4. [13]

    Protecting consumers from collusive prices due to AI

    Emilio Calvano, Giacomo Calzolari, Vincenzo Denicol \`o , Joseph E Harrington Jr, and Sergio Pastorello. Protecting consumers from collusive prices due to AI . Science, 370 0 (6520): 0 1040--1042, 2020 a

    2020

  5. [14]

    Artificial intelligence, algorithmic pricing, and collusion

    Emilio Calvano, Giacomo Calzolari, Vincenzo Denicol \`o , and Sergio Pastorello. Artificial intelligence, algorithmic pricing, and collusion. American Economic Review, 110 0 (10): 0 3267--3297, 2020 b

    2020

  6. [15]

    Algorithmic collusion with imperfect monitoring

    Emilio Calvano, Giacomo Calzolari, Vincenzo Denicol \`o , and Sergio Pastorello. Algorithmic collusion with imperfect monitoring. International Journal of Industrial Organization, 79: 0 102712, 2021

    2021

  7. [16]

    Algorithmic collusion: Genuine or spurious? International Journal of Industrial Organization, 90: 0 102973, 2023

    Emilio Calvano, Giacomo Calzolari, Vincenzo Denicol \`o , and Sergio Pastorello. Algorithmic collusion: Genuine or spurious? International Journal of Industrial Organization, 90: 0 102973, 2023

    2023

  8. [18]

    Intertemporal price discrimination via randomized promotions

    Hongqiao Chen, Ming Hu, and Jiahua Wu. Intertemporal price discrimination via randomized promotions. Manufacturing & Service Operations Management, 25 0 (3): 0 1176--1194, 2023

    2023

  9. [19]

    An empirical analysis of algorithmic pricing on Amazon Marketplace

    Le Chen, Alan Mislove, and Christo Wilson. An empirical analysis of algorithmic pricing on Amazon Marketplace . In International Conference on World Wide Web, pages 1339--1349, 2016

    2016

  10. [21]

    Learning and pricing with models that do not explicitly incorporate competition

    William L Cooper, Tito Homem-de Mello, and Anton J Kleywegt. Learning and pricing with models that do not explicitly incorporate competition. Operations Research, 63 0 (1): 0 86--103, 2015

    2015

  11. [22]

    Secret econometric business: Watching FuelWatch and the ACCC

    Sinclair Davidson. Secret econometric business: Watching FuelWatch and the ACCC . Agenda: A Journal of Policy Analysis and Reform, 15 0 (4): 0 5--18, 2008

    2008

  12. [23]

    A dynamic theory of random price discounts

    Francesc Dilm \'e and Daniel F Garrett. A dynamic theory of random price discounts. Review of Economic Studies, page rdaf074, 2025

    2025

  13. [25]

    Dynamic pricing in the presence of inventory considerations: Research overview, current practices, and future directions

    Wedad Elmaghraby and P nar Keskinocak. Dynamic pricing in the presence of inventory considerations: Research overview, current practices, and future directions. Management Science, 49 0 (10): 0 1287--1309, 2003

    2003

  14. [26]

    On algorithmic collusion and reward-punishment schemes

    Andr \'e a Epivent and Xavier Lambin. On algorithmic collusion and reward-punishment schemes. Economics Letters, 237: 0 111661, 2024

    2024

  15. [28]

    A density-based algorithm for discovering clusters in large spatial databases with noise

    Martin Ester, Hans-Peter Kriegel, J \"o rg Sander, and Xiaowei Xu. A density-based algorithm for discovering clusters in large spatial databases with noise. In International Conference on Knowledge Discovery and Data Mining, pages 226--231, 1996

    1996

  16. [29]

    Artificial intelligence & collusion: When computers inhibit competition

    Ariel Ezrachi and Maurice E Stucke. Artificial intelligence & collusion: When computers inhibit competition. University of Illinois Law Review, 2017, 2017

    2017

  17. [30]

    Some distance properties of latent root and vector methods used in multivariate analysis

    John C Gower. Some distance properties of latent root and vector methods used in multivariate analysis. Biometrika, 53 0 (3--4): 0 325--338, 1966

    1966

  18. [31]

    Frontiers: Algorithmic collusion: Supra-competitive prices via independent algorithms

    Karsten T Hansen, Kanishka Misra, and Mallesh M Pai. Frontiers: Algorithmic collusion: Supra-competitive prices via independent algorithms. Marketing Science, 40 0 (1): 0 1--12, 2021

    2021

  19. [32]

    FoolWatch : A case study of econometric analysis and evidenced-based-policy making in the Australian Government

    Don Harding. FoolWatch : A case study of econometric analysis and evidenced-based-policy making in the Australian Government . MPRA Paper 16041, University Library of Munich, 2008

    2008

  20. [33]

    Developing competition law for collusion by autonomous artificial agents

    Joseph E Harrington. Developing competition law for collusion by autonomous artificial agents. Journal of Competition Law & Economics, 14 0 (3): 0 331--363, 2018

    2018

  21. [34]

    Regulation of algorithmic collusion

    Jason D Hartline, Sheng Long, and Chenhao Zhang. Regulation of algorithmic collusion. In ACM Symposium on Computer Science and Law, pages 98--108, 2024

    2024

  22. [35]

    Regulation of algorithmic collusion, refined: Testing pessimistic calibrated regret

    Jason D Hartline, Chang Wang, and Chenhao Zhang. Regulation of algorithmic collusion, refined: Testing pessimistic calibrated regret. In ACM Symposium on Computer Science and Law, pages 108--120, 2025

    2025

  23. [36]

    Dynamic pricing and consumer fairness perceptions

    Kelly L Haws and William O Bearden. Dynamic pricing and consumer fairness perceptions. Journal of Consumer Research, 33 0 (3): 0 304--311, 2006

    2006

  24. [37]

    Algorithmic collusion: Insights from deep learning

    Matthias Hettich. Algorithmic collusion: Insights from deep learning. CQE Working Paper 94, University of M \"u nster , 2021

    2021

  25. [38]

    Exact indexing of dynamic time warping

    Eamonn Keogh and Chotirat Ann Ratanamahatana. Exact indexing of dynamic time warping. Knowledge and Information Systems, 7 0 (3): 0 358--386, 2005

    2005

  26. [39]

    Autonomous algorithmic collusion: Q -learning under sequential pricing

    Timo Klein. Autonomous algorithmic collusion: Q -learning under sequential pricing. The RAND Journal of Economics, 52 0 (3): 0 538--558, 2021

    2021

  27. [40]

    Retail price optimization at InterContinental Hotels Group

    Dev Koushik, Jon A Higbie, and Craig Eister. Retail price optimization at InterContinental Hotels Group . Interfaces, 42 0 (1): 0 45--57, 2012

    2012

  28. [41]

    Less than meets the eye: Simultaneous experiments as a source of algorithmic seeming collusion

    Xavier Lambin. Less than meets the eye: Simultaneous experiments as a source of algorithmic seeming collusion. Preprint SSRN:4498926, 2024

    2024

  29. [42]

    Antitrust and the robo-seller: Competition in the time of algorithms

    Salil K Mehra. Antitrust and the robo-seller: Competition in the time of algorithms. Minnesota Law Review, 100 0 (4): 0 1323--1375, 2016

    2016

  30. [43]

    When does mandatory price disclosure lower prices? Evidence from the German fuel market

    Felix Montag, Alina Sagimuldina, and Christoph Winter. When does mandatory price disclosure lower prices? Evidence from the German fuel market. Journal of Political Economy Microeconomics, 4 0 (1): 0 106--146, 2026

    2026

  31. [44]

    Algorithms and collusion: Competition policy in the digital age

    OECD . Algorithms and collusion: Competition policy in the digital age. OECD Report, Paris, 2017

    2017

  32. [45]

    Carlson Rezidor Hotel Group maximizes revenue through improved demand management and price optimization

    Pelin Pekg \"u n, Ronald P Menich, Suresh Acharya, Phillip G Finch, Frederic Deschamps, Kathleen Mallery, Jim Van Sistine, Kyle Christianson, and James Fuller. Carlson Rezidor Hotel Group maximizes revenue through improved demand management and price optimization. Interfaces, ...

    2013

  33. [46]

    Convergence results for single-step on-policy reinforcement-learning algorithms

    Satinder Singh, Tommi Jaakkola, Michael L Littman, and Csaba Szepesv \'a ri. Convergence results for single-step on-policy reinforcement-learning algorithms. Machine Learning, 38 0 (3): 0 287--308, 2000

    2000

  34. [47]

    Q -learning agents in a Cournot oligopoly model

    Ludo Waltman and Uzay Kaymak. Q -learning agents in a Cournot oligopoly model. Journal of Economic Dynamics and Control, 32 0 (10): 0 3275--3293, 2008

    2008

  35. [48]

    (Mixed) strategy in oligopoly pricing: Evidence from gasoline price cycles before and under a timing regulation

    Zhongmin Wang. (Mixed) strategy in oligopoly pricing: Evidence from gasoline price cycles before and under a timing regulation. Journal of Political Economy, 117 0 (6): 0 987--1030, 2009

    2009

  36. [50]

    The rise of

    Adams, Jonathan J and Fang, Min and Liu, Zheng and Wang, Yajie , journal=. The rise of. 2025 , publisher=

    2025

  37. [51]

    Algorithmic pricing and competition: Empirical evidence from the

    Assad, Stephanie and Clark, Robert and Ershov, Daniel and Xu, Lei , journal=. Algorithmic pricing and competition: Empirical evidence from the. 2024 , publisher=

    2024

  38. [52]

    2024 , publisher=

    Algorithmic pricing and consumer sensitivity to price variability , author=. 2024 , publisher=

    2024

  39. [53]

    Information Economics and Policy , volume=

    Algorithms in the marketplace: An empirical analysis of automated pricing in e-commerce , author=. Information Economics and Policy , volume=. 2024 , publisher=

    2024

  40. [54]

    American Economic Review , volume=

    Artificial intelligence, algorithmic pricing, and collusion , author=. American Economic Review , volume=. 2020 , publisher=

    2020

  41. [55]

    An empirical analysis of algorithmic pricing on

    Chen, Le and Mislove, Alan and Wilson, Christo , booktitle=. An empirical analysis of algorithmic pricing on

  42. [56]

    Protecting consumers from collusive prices due to

    Calvano, Emilio and Calzolari, Giacomo and Denicol. Protecting consumers from collusive prices due to. Science , volume=. 2020 , publisher=

    2020

  43. [57]

    Algorithms and Collusion: Competition Policy in the Digital Age , author=

  44. [58]

    Robert Schuman Centre for Advanced Studies Research Paper , number=

    Collusion by pricing algorithms in competition law and economics , author=. Robert Schuman Centre for Advanced Studies Research Paper , number=

  45. [59]

    International Journal of Industrial Organization , volume=

    Algorithmic collusion with imperfect monitoring , author=. International Journal of Industrial Organization , volume=. 2021 , publisher=

    2021

  46. [60]

    ACM Conference on Economics and Computation , pages=

    Adaptive algorithms and collusion via coupling , author=. ACM Conference on Economics and Computation , pages=

  47. [61]

    CQE Working Paper 94, University of M

    Algorithmic collusion: Insights from deep learning , author=. CQE Working Paper 94, University of M

  48. [62]

    Biometrika , volume=

    Some distance properties of latent root and vector methods used in multivariate analysis , author=. Biometrika , volume=. 1966 , publisher=

    1966

  49. [63]

    Machine Learning , volume=

    Convergence results for single-step on-policy reinforcement-learning algorithms , author=. Machine Learning , volume=. 2000 , publisher=

    2000

  50. [64]

    2008 , publisher=

    Waltman, Ludo and Kaymak, Uzay , journal=. 2008 , publisher=

    2008

  51. [65]

    AAAI Workshop on Knowledge Discovery in Databases , pages=

    Using dynamic time warping to find patterns in time series , author=. AAAI Workshop on Knowledge Discovery in Databases , pages=

  52. [66]

    International Conference on Knowledge Discovery and Data Mining , pages=

    A density-based algorithm for discovering clusters in large spatial databases with noise , author=. International Conference on Knowledge Discovery and Data Mining , pages=

  53. [67]

    Management Science , volume=

    Dynamic pricing in the presence of inventory considerations: Research overview, current practices, and future directions , author=. Management Science , volume=. 2003 , publisher=

    2003

  54. [68]

    Management Science , volume=

    Real-time dynamic pricing with minimal and flexible price adjustment , author=. Management Science , volume=. 2016 , publisher=

    2016

  55. [69]

    Retail price optimization at

    Koushik, Dev and Higbie, Jon A and Eister, Craig , journal=. Retail price optimization at. 2012 , publisher=

    2012

  56. [70]

    Interfaces , volume=

    Pekg. Interfaces , volume=. 2013 , publisher=

    2013

  57. [71]

    Journal of Consumer Research , volume=

    Dynamic pricing and consumer fairness perceptions , author=. Journal of Consumer Research , volume=. 2006 , publisher=

    2006

  58. [72]

    Review of Economic Studies , pages=

    A dynamic theory of random price discounts , author=. Review of Economic Studies , pages=. 2025 , publisher=

    2025

  59. [73]

    Manufacturing & Service Operations Management , volume=

    Intertemporal price discrimination via randomized promotions , author=. Manufacturing & Service Operations Management , volume=. 2023 , publisher=

    2023

  60. [74]

    Autonomous algorithmic collusion:

    Klein, Timo , journal=. Autonomous algorithmic collusion:. 2021 , publisher=

    2021

  61. [75]

    Knowledge and Information Systems , volume=

    Exact indexing of dynamic time warping , author=. Knowledge and Information Systems , volume=. 2005 , publisher=

    2005

  62. [76]

    Preprint arXiv:2502.15084 , year=

    Algorithmic collusion under observed demand shocks , author=. Preprint arXiv:2502.15084 , year=

  63. [77]

    International Journal of Industrial Organization , pages=

    Algorithmic collusion under sequential pricing and stochastic costs , author=. International Journal of Industrial Organization , pages=. 2026 , publisher=

    2026

  64. [78]

    Journal of Competition Law & Economics , volume=

    Developing competition law for collusion by autonomous artificial agents , author=. Journal of Competition Law & Economics , volume=. 2018 , publisher=

    2018

  65. [79]

    International Journal of Industrial Organization , volume=

    Algorithmic collusion: Genuine or spurious? , author=. International Journal of Industrial Organization , volume=. 2023 , publisher=

    2023

  66. [80]

    ACM Conference on Economics and Computation , pages=

    Artificial intelligence and auction design , author=. ACM Conference on Economics and Computation , pages=

  67. [81]

    AEA Papers and Proceedings , volume=

    Artificial intelligence, algorithm design, and pricing , author=. AEA Papers and Proceedings , volume=. 2022 , publisher=

    2022

  68. [82]

    Preprint arXiv:2411.16574 , year=

    The illusion of collusion , author=. Preprint arXiv:2411.16574 , year=

  69. [83]

    Preprint arXiv:2403.07177 , year=

    Collusive outcomes without collusion , author=. Preprint arXiv:2403.07177 , year=

    arXiv

  70. [84]

    Operations Research , volume=

    Learning and pricing with models that do not explicitly incorporate competition , author=. Operations Research , volume=. 2015 , publisher=

    2015

  71. [85]

    Marketing Science , volume=

    Frontiers: Algorithmic collusion: Supra-competitive prices via independent algorithms , author=. Marketing Science , volume=. 2021 , publisher=

    2021

  72. [86]

    Preprint arXiv:2605.16064 , year=

    Misspecified explore-then-exploit leads to supra-competitive prices , author=. Preprint arXiv:2605.16064 , year=

    arXiv

  73. [87]

    Preprint SSRN:4498926 , year=

    Less than meets the eye: Simultaneous experiments as a source of algorithmic seeming collusion , author=. Preprint SSRN:4498926 , year=

  74. [88]

    European Journal of Operational Research , volume=

    Collusion by mistake: Does algorithmic sophistication drive supra-competitive profits? , author=. European Journal of Operational Research , volume=. 2024 , publisher=

    2024

  75. [89]

    Economics Letters , volume=

    On algorithmic collusion and reward-punishment schemes , author=. Economics Letters , volume=. 2024 , publisher=

    2024

  76. [90]

    Preprint arXiv:2201.00345 , year=

    Robust algorithmic collusion , author=. Preprint arXiv:2201.00345 , year=

    arXiv

  77. [91]

    Management Science , volume=

    Artificial intelligence: Can seemingly collusive outcomes be avoided? , author=. Management Science , volume=. 2023 , publisher=

    2023

  78. [92]

    Preprint arXiv:2508.14766 , year=

    Algorithmic collusion is algorithm orchestration , author=. Preprint arXiv:2508.14766 , year=

  79. [93]

    Minnesota Law Review , volume=

    Antitrust and the robo-seller: Competition in the time of algorithms , author=. Minnesota Law Review , volume=

  80. [94]

    ACM Symposium on Computer Science and Law , pages=

    Regulation of algorithmic collusion, refined: Testing pessimistic calibrated regret , author=. ACM Symposium on Computer Science and Law , pages=

  81. [95]

    ACM Symposium on Computer Science and Law , pages=

    Regulation of algorithmic collusion , author=. ACM Symposium on Computer Science and Law , pages=

  82. [96]

    University of Illinois Law Review , volume=

    Artificial intelligence & collusion: When computers inhibit competition , author=. University of Illinois Law Review , volume=

  83. [97]

    Harding, Don , institution=

  84. [98]

    Secret econometric business: Watching

    Davidson, Sinclair , journal=. Secret econometric business: Watching

  85. [99]

    2009 , publisher=

    Wang, Zhongmin , journal=. 2009 , publisher=

    2009

  86. [100]

    American Economic Review , volume=

    Learning to coordinate: A study in retail gasoline , author=. American Economic Review , volume=. 2019 , publisher=

    2019

  87. [101]

    Australian Economic Review , volume=

    Impact of post and hold regulation on retail petroleum prices , author=. Australian Economic Review , volume=. 2025 , publisher=

    2025

  88. [102]

    When does mandatory price disclosure lower prices?

    Montag, Felix and Sagimuldina, Alina and Winter, Christoph , journal=. When does mandatory price disclosure lower prices?. 2026 , publisher=

    2026

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.