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

Computer Science and Game Theory 2026-03-04 v2 Theoretical Economics Machine Learning

Abstract

We explore the behaviour emerging from learning agents repeatedly interacting strategically for a wide range of learning dynamics, including QQ-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 QQ-learning algorithms in repeated games.

Keywords

Cite

@article{arxiv.2411.12725,
  title  = {The Bounds of Algorithmic Collusion; $Q$-learning, Gradient Learning, and the Folk Theorem},
  author = {Galit Askenazi-Golan and Domenico Mergoni Cecchelli and Edward Plumb and Clemens Possnig},
  journal= {arXiv preprint arXiv:2411.12725},
  year   = {2026}
}

Comments

This is a new version of a previous paper by the title "Reinforcement Learning, Collusion, and the Folk Theorem" by the three (alphabetically) first authors