Pricing algorithms are increasingly replacing human decision making in real marketplaces. To inform the competition policy debate on possible consequences, we run experiments with pricing algorithms powered by Artificial Intelligence in controlled environments (computer simulations). In particular, we study the interaction among a number of Q-learning algorithms in the context of a workhorse oligopoly model of price competition with Logit demand and constant marginal costs. We show that the algorithms consistently learn to charge supra-competitive prices, without communicating with each other. The high prices are sustained by classical collusive strategies with a finite punishment phase followed by a gradual return to cooperation. This finding is robust to asymmetries in cost or demand and to changes in the number of players.