Self-Play $Q$-Learners Can Provably Collude in the Iterated Prisoner’s Dilemma

Quentin Bertrand, Juan Agustin Duque, Emilio Calvano, Gauthier Gidel
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:3952-3975, 2025.

Abstract

A growing body of computational studies shows that simple machine learning agents converge to cooperative behaviors in social dilemmas, such as collusive price-setting in oligopoly markets, raising questions about what drives this outcome. In this work, we provide theoretical foundations for this phenomenon in the context of self-play multi-agent Q-learners in the iterated prisoner’s dilemma. We characterize broad conditions under which such agents provably learn the cooperative Pavlov (win-stay, lose-shift) policy rather than the Pareto-dominated “always defect” policy. We validate our theoretical results through additional experiments, demonstrating their robustness across a broader class of deep learning algorithms.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-bertrand25a, title = {Self-Play $Q$-Learners Can Provably Collude in the Iterated Prisoner’s Dilemma}, author = {Bertrand, Quentin and Duque, Juan Agustin and Calvano, Emilio and Gidel, Gauthier}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {3952--3975}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/bertrand25a/bertrand25a.pdf}, url = {https://proceedings.mlr.press/v267/bertrand25a.html}, abstract = {A growing body of computational studies shows that simple machine learning agents converge to cooperative behaviors in social dilemmas, such as collusive price-setting in oligopoly markets, raising questions about what drives this outcome. In this work, we provide theoretical foundations for this phenomenon in the context of self-play multi-agent Q-learners in the iterated prisoner’s dilemma. We characterize broad conditions under which such agents provably learn the cooperative Pavlov (win-stay, lose-shift) policy rather than the Pareto-dominated “always defect” policy. We validate our theoretical results through additional experiments, demonstrating their robustness across a broader class of deep learning algorithms.} }
Endnote
%0 Conference Paper %T Self-Play $Q$-Learners Can Provably Collude in the Iterated Prisoner’s Dilemma %A Quentin Bertrand %A Juan Agustin Duque %A Emilio Calvano %A Gauthier Gidel %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-bertrand25a %I PMLR %P 3952--3975 %U https://proceedings.mlr.press/v267/bertrand25a.html %V 267 %X A growing body of computational studies shows that simple machine learning agents converge to cooperative behaviors in social dilemmas, such as collusive price-setting in oligopoly markets, raising questions about what drives this outcome. In this work, we provide theoretical foundations for this phenomenon in the context of self-play multi-agent Q-learners in the iterated prisoner’s dilemma. We characterize broad conditions under which such agents provably learn the cooperative Pavlov (win-stay, lose-shift) policy rather than the Pareto-dominated “always defect” policy. We validate our theoretical results through additional experiments, demonstrating their robustness across a broader class of deep learning algorithms.
APA
Bertrand, Q., Duque, J.A., Calvano, E. & Gidel, G.. (2025). Self-Play $Q$-Learners Can Provably Collude in the Iterated Prisoner’s Dilemma. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:3952-3975 Available from https://proceedings.mlr.press/v267/bertrand25a.html.

Related Material