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

Galit Askenazi-Golan, Domenico Mergoni Cecchelli, Edward Plumb and Clemens Possnig

Papers from arXiv.org

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.

Date: 2024-11, Revised 2026-03
New Economics Papers: this item is included in nep-gth and nep-mic
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