Do algorithms collude?

Yes, in short.  Emilio Calvano, Giacomo Calzolari, Vincenzo Denicolò and Sergio Pastorello cover this topic in the latest issue of the American Economic Review:

Increasingly, algorithms are supplanting human decision-makers in pricing goods and services. To analyze the possible consequences, we study experimentally the behavior of algorithms powered by Artificial Intelligence (Q-learning) in a workhorse oligopoly model of repeated price competition. We find that the algorithms consistently learn to charge supracompetitive prices, without communicating with one another. The high prices are sustained by 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, changes in the number of players, and various forms of uncertainty.

Here is the paper.