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Monitoring, Market Primitives, and the Stability of Algorithmic Collusion

Author

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  • Possnig, Clemens

    (School of Economics, University of Waterloo)

Abstract

This paper develops an analytical framework to study when sophisticated machine learning algorithms may learn to collude. Algorithms observe a state variable and update policies to maximize long-term payoffs; their long-run policies correspond to the stable equilibria of a tractable differential equation. In a repeated Bertrand game, I derive necessary and sufficient conditions under which Nash equilibria are learned. This reveals how the interplay between monitoring technology (state variables) and market conditions determines whether competitive or collusive outcomes emerge. I apply these insights to evaluate two key regulatory policies: limiting algorithmic data inputs and imposing competition in the software provider market.

Suggested Citation

  • Possnig, Clemens, 2026. "Monitoring, Market Primitives, and the Stability of Algorithmic Collusion," Working Papers 26005, University of Waterloo, Department of Economics.
    • Handle: RePEc:wat:wpaper:26005
    as

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    File URL: https://hdl.handle.net/10012/23580
    File Function: First version, 2026
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    References listed on IDEAS

    as
    1. Timo Klein, 2021. "Autonomous algorithmic collusion: Q‐learning under sequential pricing," RAND Journal of Economics, RAND Corporation, vol. 52(3), pages 538-558, September.
    2. 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.
    3. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-1277, November.
    4. Jacob Palis Jr. & Welington de Melo, 1982. "Geometric Theory of Dynamical Systems," Springer Books, Springer, number 978-1-4612-5703-5, January.
    5. Zach Y. Brown & Alexander MacKay, 2023. "Competition in Pricing Algorithms," American Economic Journal: Microeconomics, American Economic Association, vol. 15(2), pages 109-156, May.
    Full references (including those not matched with items on IDEAS)

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