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The Bounds of Algorithmic Collusion: Q-learning, Gradient Learning, and the Folk Theorem

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  • Askenazi-Golan, Galit

    (Department of Mathematics, The London School of Economics and Political Science)

  • Mergoni Cecchelli, Domenico

    (Department of Mathematics, The London School of Economics and Political Science)

  • Plumb, Edward

    (Department of Mathematics, The London School of Economics and Political Science)

  • Possnig, Clemens

    (School of Economics, University of Waterloo)

Abstract

We explore the behaviour emerging from learning agents repeatedly interacting strategically for a wide range of learning dynamics, including Q-learning, projected gradient, replicator and log-barrier dynamics. Going beyond the better understood classes of potential games and zero-sum games, we consider the setting of a general repeated game with finite recall under different forms of monitoring. We obtain a Folk Theorem-style result and characterise the set of payoff vectors that can be obtained by these dynamics, discovering a wide range of possibilities for the emergence of algorithmic collusion. Achieving this requires a novel technical approach, which, to the best of our knowledge, yields the first convergence result for multi-agent Q-learning algorithms in repeated games.

Suggested Citation

  • Askenazi-Golan, Galit & Mergoni Cecchelli, Domenico & Plumb, Edward & Possnig, Clemens, 2026. "The Bounds of Algorithmic Collusion: Q-learning, Gradient Learning, and the Folk Theorem," Working Papers 26002, University of Waterloo, Department of Economics.
    • Handle: RePEc:wat:wpaper:26002
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    File URL: https://hdl.handle.net/10012/23583
    File Function: First version, 2026
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