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Increasingly, pricing algorithms are supplanting human decision making in real marketplaces. To inform the competition policy debate on the possible consequences of this development, we experiment with pricing algorithms powered by Artificial Intelligence (AI) in controlled environments (computer simulations), studying the interaction among a number of Q-learning algorithms in a workhorse oligopoly model of price competition with Logit demand and constant marginal costs. In this setting the algorithms consistently learn to charge supra-competitive prices, without communicating with one another. The high prices are sustained by classical collusive strategies with a finite phase of punishment 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.