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Algorithmic collusion with imperfect monitoring

Author

Listed:
  • Calvano, Emilio
  • Calzolari, Giacomo
  • Denicoló, Vincenzo
  • Pastorello, Sergio

Abstract

We show that if they are allowed enough time to complete the learning, Q-learning algorithms can learn to collude in an environment with imperfect monitoring adapted from Green and Porter (1984), without having been instructed to do so, and without communicating with one another. Collusion is sustained by punishments that take the form of “price wars” triggered by the observation of low prices. The punishments have a finite duration, being harsher initially and then gradually fading away. Such punishments are triggered both by deviations and by adverse demand shocks.

Suggested Citation

  • Calvano, Emilio & Calzolari, Giacomo & Denicoló, Vincenzo & Pastorello, Sergio, 2021. "Algorithmic collusion with imperfect monitoring," International Journal of Industrial Organization, Elsevier, vol. 79(C).
    • Handle: RePEc:eee:indorg:v:79:y:2021:i:c:s0167718721000059
    DOI: 10.1016/j.ijindorg.2021.102712
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    References listed on IDEAS

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    1. Green, Edward J & Porter, Robert H, 1984. "Noncooperative Collusion under Imperfect Price Information," Econometrica, Econometric Society, vol. 52(1), pages 87-100, January.
    2. B. Douglas Bernheim & Erik Madsen, 2017. "Price Cutting and Business Stealing in Imperfect Cartels," American Economic Review, American Economic Association, vol. 107(2), pages 387-424, February.
    3. Maskin, Eric & Tirole, Jean, 1988. "A Theory of Dynamic Oligopoly, II: Price Competition, Kinked Demand Curves, and Edgeworth Cycles," Econometrica, Econometric Society, vol. 56(3), pages 571-599, May.
    4. Johnson, Justin Pappas & Rhodes, Andrew & Wildenbeest, Matthijs, 2020. "Platform Design when Sellers Use Pricing Algorithms," TSE Working Papers 20-1146, Toulouse School of Economics (TSE).
    5. Emilio Calvano & Giacomo Calzolari & Vincenzo Denicolò & Sergio Pastorello, 2020. "Artificial Intelligence, Algorithmic Pricing, and Collusion," American Economic Review, American Economic Association, vol. 110(10), pages 3267-3297, October.
    6. Abreu, Dilip & Pearce, David & Stacchetti, Ennio, 1990. "Toward a Theory of Discounted Repeated Games with Imperfect Monitoring," Econometrica, Econometric Society, vol. 58(5), pages 1041-1063, September.
    7. Abreu, Dilip & Pearce, David & Stacchetti, Ennio, 1986. "Optimal cartel equilibria with imperfect monitoring," Journal of Economic Theory, Elsevier, vol. 39(1), pages 251-269, June.
    8. Kerry Back & C. Henry Cao & Gregory A. Willard, 2000. "Imperfect Competition among Informed Traders," Journal of Finance, American Finance Association, vol. 55(5), pages 2117-2155, October.
    9. Waltman, Ludo & Kaymak, Uzay, 2008. "Q-learning agents in a Cournot oligopoly model," Journal of Economic Dynamics and Control, Elsevier, vol. 32(10), pages 3275-3293, October.
    10. Foster, F Douglas & Viswanathan, S, 1996. "Strategic Trading When Agents Forecast the Forecasts of Others," Journal of Finance, American Finance Association, vol. 51(4), pages 1437-1478, September.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Gonzalo Ballestero, 2022. "Collusion and Artificial Intelligence: A Computational Experiment with Sequential Pricing Algorithms under Stochastic Costs," Working Papers 118, Red Nacional de Investigadores en Economía (RedNIE).
    2. Gonzalo Ballestero, 2021. "Collusion and Artificial Intelligence: A computational experiment with sequential pricing algorithms under stochastic costs," Young Researchers Working Papers 1, Universidad de San Andres, Departamento de Economia, revised Oct 2022.
    3. Martin, Simon & Rasch, Alexander, 2022. "Collusion by algorithm: The role of unobserved actions," DICE Discussion Papers 382, Heinrich Heine University Düsseldorf, Düsseldorf Institute for Competition Economics (DICE).
    4. Simon Martin & Alexander Rasch, 2022. "Collusion by Algorithm: The Role of Unobserved Actions," CESifo Working Paper Series 9629, CESifo.
    5. Gonzalo Ballestero, 2021. "Collusion and Artificial Intelligence: A computational experiment with sequential pricing algorithms under stochastic costs," Asociación Argentina de Economía Política: Working Papers 4433, Asociación Argentina de Economía Política.
    6. Sinziana-Maria Rindasu & Ioan Dan Topor & Liliana Ionescu-Feleaga, 2023. "The Evolution of Management Accountants' Digital Skills in Industry 4.0: A Qualitative Approach," Oblik i finansi, Institute of Accounting and Finance, issue 1, pages 38-48, March.
    7. Lucila Porto, 2022. "Q-Learning algorithms in a Hotelling model," Asociación Argentina de Economía Política: Working Papers 4587, Asociación Argentina de Economía Política.
    8. Aleksandar B. Todorov, 2022. "Algorithmic pricing and concerted behaviour – competitive challenges?," Economic Thought journal, Bulgarian Academy of Sciences - Economic Research Institute, issue 1, pages 90-107.
    9. Normann, Hans-Theo & Sternberg, Martin, 2022. "Human-algorithm interaction: Algorithmic pricing in hybrid laboratory markets," DICE Discussion Papers 392, Heinrich Heine University Düsseldorf, Düsseldorf Institute for Competition Economics (DICE).
    10. Normann, Hans-Theo & Sternberg, Martin, 2023. "Human-algorithm interaction: Algorithmic pricing in hybrid laboratory markets," European Economic Review, Elsevier, vol. 152(C).
    11. Hans-Theo Normann & Martin Sternberg, 2021. "Human-Algorithm Interaction: Algorithmic Pricing in Hybrid Laboratory Markets," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2021_11, Max Planck Institute for Research on Collective Goods, revised 13 Apr 2022.
    12. Daehyeon Park & Doojin Ryu, 2022. "Supply chain ethics and transparency: An agent‐based model approach with Q‐learning agents," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 43(8), pages 3331-3337, December.
    13. Martino Banchio & Giacomo Mantegazza, 2022. "Artificial Intelligence and Spontaneous Collusion," Papers 2202.05946, arXiv.org, revised Sep 2023.
    14. Matthias Hettich, 2021. "Algorithmic Collusion: Insights from Deep Learning," CQE Working Papers 9421, Center for Quantitative Economics (CQE), University of Muenster.
    15. Nicolas Eschenbaum & Filip Mellgren & Philipp Zahn, 2022. "Robust Algorithmic Collusion," Papers 2201.00345, arXiv.org, revised Jan 2022.
    16. W. Benedikt Schmal, 2022. "From Rules to Regs: A Structural Topic Model of Collusion Research," Papers 2210.02957, arXiv.org.

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    More about this item

    Keywords

    Artificial intelligence; Q-Learning; Imperfect monitoring; Collusion;
    All these keywords.

    JEL classification:

    • L41 - Industrial Organization - - Antitrust Issues and Policies - - - Monopolization; Horizontal Anticompetitive Practices
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
    • 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

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