Algorithms have played an increasingly important role in economic activity, as they becoming faster and smarter. Together with the increasing use of ever larger data sets, they may lead to significant changes in the way markets work. These developments have been raising concerns not only over the rights to privacy and consumers’ autonomy, but also on competition. Infringements of antitrust laws involving the use of algorithms have occurred in the past. However, current concerns are of a different nature as they relate to the role algorithms can play as facilitators of collusive behavior in repeated games, and the role increasingly sophisticated algorithms can play as autonomous implementers of pricing strategies, learning to collude without any explicit instructions provided by human agents. In particular, it is recognized that the use of ‘learning algorithms’ can facilitate tacit collusion and lead to an increased blurring of borders between tacit and explicit collusion. Several authors who have addressed the possibilities for achieving tacit collusion equilibrium outcomes by algorithms interacting autonomously, have also considered some form of ex-ante assessment and regulation over the type of algorithms used by firms. By using well-known results in the theory of computation, I show that such option faces serious challenges to its effectiveness due to undecidability results. Ex-post assessment may be constrained as well. Notwithstanding several challenges face by current software testing methodologies, competition law enforcement and policy have much to gain from an interdisciplinary collaboration with computer science and mathematics.