We develop a theoretical model to study strategic interactions between
adaptive learning algorithms. Applying continuous-time techniques, we uncover
the mechanism responsible for collusion between Artificial Intelligence
algorithms documented by recent experimental evidence. We show that spontaneous
coupling between the algorithms' estimates leads to periodic coordination on
actions that are more profitable than static Nash equilibria. We provide a
sufficient condition under which this coupling is guaranteed to disappear, and
algorithms learn to play undominated strategies. We apply our results to
interpret and complement experimental findings in the literature and to the
design of learning-robust strategy-proof mechanisms. We show that ex-post
feedback provision guarantees robustness to the presence of learning agents. We
fully characterize the optimal learning-robust mechanisms: they are menu
mechanisms.Comment: 57 pages, 13 figure