# Self-Play Q-learners Can Provably Collude in the Iterated Prisoner's Dilemma

arXiv: https://arxiv.org/abs/2312.08484 · HTML: https://mlsanity.com/paper/2312.08484/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Dec 2023.

## Built on by (most cited first, 3 of 3)

- [Solipsistic Superintelligence is Unlikely to be Cooperative](https://mlsanity.com/paper/2606.03237/) (2026)
- [Mitigating Retaliatory Algorithmic Collusion in Repeated Games](https://mlsanity.com/paper/2609.20548/) (2026)
- [Beyond Supra-Competitive Outcomes: Collusive Behaviour in Deep Reinforcement Learning for Optimal Execution Games](https://mlsanity.com/paper/2610.00619/) (2026)

## Abstract (arXiv)

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.