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tl;dr: algorithmic pricing may provide a covert collusion channel, unaddressed by existing law.
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Yep, I have a friend that worked in anti-trust for the French government and she gave the example of "garanteed lowest prices" — looks great on the surface but actually serves to constantly monitor the pricing landscape.
For example I know that some e-commerce sites adjust their prices by using web scrapers. They scrape their competitors' sites and always offer products to 1 USD less than the competitor to make more sales.

I think this should violate competition law, but it somehow doesn't.

Isn't that how competition is supposed to work? Eventually they won't be able to undercut while remaining profitable.
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They also increase prices if competition sells them for a higher price. This happens automatically.
Sounds like a startup idea: find a way to identify this scraper traffic and offer different pricing to the scraper (maybe higher, maybe punitively lower).
> Whether tacit collusion—where firms effectively behave as though they are colluding without any direct communication expressing agreement

Basically the Nash equilibrium.

IMO, tacit collusion is the underlying scheme by which we communicate (transfer meaning between people)
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.

>that‘s how competition is supposed to work, everyone trying to give the better price!

Maybe if the price is being lowered, but raising prices based solely on external signal is only "better" for the companies coordinating the price increase.