Since everyone here seems to misunderstand how collusion works: Monitoring your competitor‘s prices to undercut them is the opposite of collusion - that‘s how competition is supposed to work, everyone trying to give the better price!

It is similar to a prisoner‘s dilemma, with a Nash equilibrium at consumer-friendly prices. Tacit collusion, on the other hand, makes use of the iterated nature of the "game“, and utilizes a tit-for-tat strategy: If you undercut me, I‘ll set prices even lower at uneconomical levels for some time, to punish you for it. If you take the hint and set a high price, I‘ll reward you by matching it and we both rake in that sweet margin.

Of course, a real-world tacit collusion strategy is more complex, and algorithmic pricing certainly helps with implementing it - especially as it makes it easier to commit to a strategy ahead of time, which is very useful from a game theoretic standpoint.