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

Galit Askenazi-Golan (), Domenico Mergoni Cecchelli (), Edward Plumb () and Clemens Possnig ()
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Galit Askenazi-Golan: Department of Mathematics, The London School of Economics and Political Science
Domenico Mergoni Cecchelli: Department of Mathematics, The London School of Economics and Political Science
Edward Plumb: Department of Mathematics, The London School of Economics and Political Science
Clemens Possnig: School of Economics, University of Waterloo

No 26002, Working Papers from University of Waterloo, Department of Economics

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.

Keywords: Q-learning; projected gradient; replicator; log-barrier dynamics (search for similar items in EconPapers)
Pages: 45 pages
Date: 2026-03-03
New Economics Papers: this item is included in nep-mic
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