Prices are increasingly set by algorithms. One concern is that intelligent algorithms may learn to collude on higher prices even in the absence of the kind of coordination necessary to establish an antitrust infringement. However, exactly how this may happen is an open question. I show how in simulated sequential competition, competing reinforcement learning algorithms can indeed learn to converge to collusive equilibria when the set of discrete prices is limited. When this set increases, the algorithm considered increasingly converges to supra-competitive asymmetric cycles. I show that results are robust to various extensions and discuss practical limitations and policy implications.