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arXiv · 2411.12725

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

Galit Askenazi-Golan·Domenico Mergoni Cecchelli·Edward Plumb·Clemens Possnig
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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.

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Galit Askenazi-Golan, Domenico Mergoni Cecchelli, Edward Plumb, Clemens Possnig. 2024-11-19. The Bounds of Algorithmic Collusion; $Q$-learning, Gradient Learning, and the Folk Theorem. https://arxiv.org/abs/2411.12725

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