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Recently, antitrust authorities started to worry about the possible consequences of algorithmic pricing. Indeed, we document that pricing algorithms are already widely used and argue that they are likely to become even more prevalent in the future. In particular, authorities worry about data-driven price discrimination and algorithmic collusion. We focus on the latter. It is the contention of this article that algorithmic collusion is a real risk, the seriousness of which is still difficult to assess, but that should not be dismissed lightly by antitrust agencies. First, we discuss various ways in which algorithms may facilitate collusion without creating any genuinely new antitrust issue. Second, we argue that pricing algorithms may learn to collude “autonomously” and without explicitly communicating with one another. In light of this evidence, we discuss the specific new policy challenges that this kind of algorithmic collusion poses.