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Algorithmic Collusion: Insights from Deep Learning

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  • Matthias Hettich

Abstract

Increasingly, firms use algorithms powered by artificial intelligence to set prices. Previous research simulated interactions among Q-learning algorithms in an oligopoly model of price competition. The algorithms learn collusive strategies but require a long time that corresponds to several years to do so. We show that pricing algorithms using deep learning (DQN) can collude significantly faster. The availability of these more powerful pricing algorithms enables simulations in larger markets. Collusion disappears in wide oligopolies with up to 10 firms. However, incorporating knowledge of the learning behavior by reformulating the state representation increases the ability to collude effectively.

Suggested Citation

  • Matthias Hettich, 2021. "Algorithmic Collusion: Insights from Deep Learning," CQE Working Papers 9421, Center for Quantitative Economics (CQE), University of Muenster.
    • Handle: RePEc:cqe:wpaper:9421
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    File URL: https://www.wiwi.uni-muenster.de/cqe/sites/cqe/files/CQE_Paper/cqe_wp_94_2021.pdf
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    References listed on IDEAS

    as
    1. Calzolari, Giacomo & Calvano, Emilio & Denicolo, Vincenzo & Pastorello, Sergio, 2021. "Algorithmic collusion with imperfect monitoring," CEPR Discussion Papers 15738, C.E.P.R. Discussion Papers.
    2. Calvano, Emilio & Calzolari, Giacomo & Denicoló, Vincenzo & Pastorello, Sergio, 2021. "Algorithmic collusion with imperfect monitoring," International Journal of Industrial Organization, Elsevier, vol. 79(C).
    3. Stephanie Assad & Robert Clark & Daniel Ershov & Lei Xu, 2020. "Algorithmic Pricing and Competition: Empirical Evidence from the German Retail Gasoline Market," Working Paper 1438, Economics Department, Queen's University.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Dolgopolov, Arthur, 2024. "Reinforcement learning in a prisoner's dilemma," Games and Economic Behavior, Elsevier, vol. 144(C), pages 84-103.
    2. Werner, Tobias, 2021. "Algorithmic and human collusion," DICE Discussion Papers 372, Heinrich Heine University Düsseldorf, Düsseldorf Institute for Competition Economics (DICE).
    3. Bernhard Kasberger & Simon Martin & Hans-Theo Normann & Tobias Werner, 2024. "Algorithmic Cooperation," CESifo Working Paper Series 11124, CESifo.
    4. Arnoud V. den Boer & Janusz M. Meylahn & Maarten Pieter Schinkel, 2022. "Artificial Collusion: Examining Supracompetitive Pricing by Q-learning Algorithms," Tinbergen Institute Discussion Papers 22-067/VII, Tinbergen Institute.
    5. Ivan Conjeaud, 2023. "Algorithmic collusion under competitive design," Papers 2312.02644, arXiv.org, revised Sep 2024.
    6. Werner, Tobias, 2023. "Algorithmic and Human Collusion," VfS Annual Conference 2023 (Regensburg): Growth and the "sociale Frage" 277573, Verein für Socialpolitik / German Economic Association.
    7. Aleksei Pastushkov, 2024. "Market efficiency, informational asymmetry and pseudo-collusion of adaptively learning agents," Papers 2411.05032, arXiv.org.
    8. Fabrizio Lillo & Andrea Macr`i, 2024. "Deviations from the Nash equilibrium and emergence of tacit collusion in a two-player optimal execution game with reinforcement learning," Papers 2408.11773, arXiv.org.
    9. Epivent, Andréa & Lambin, Xavier, 2024. "On algorithmic collusion and reward–punishment schemes," Economics Letters, Elsevier, vol. 237(C).
    10. Abada, Ibrahim & Lambin, Xavier & Tchakarov, Nikolay, 2024. "Collusion by mistake: Does algorithmic sophistication drive supra-competitive profits?," European Journal of Operational Research, Elsevier, vol. 318(3), pages 927-953.

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    More about this item

    Keywords

    Algorithmic Pricing; Collusion; Artificial Intelligence; Reinforcement Learning; DQN;
    All these keywords.

    JEL classification:

    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • L12 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Monopoly; Monopolization Strategies
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

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