[chii]

to me, it's not enough to show that the same algorithm or software is deciding the price.

It has to be that there's some threat of punishment from the cartel against those who would lower their price from the agreed one. For example, the explicit agreement by the landlord to keep the price at the algorithmicaly calculated one, even so far as to leave vacancy (where as there wouldn't have been a vacancy if the price was lowered).

[radicality]

There is. I forget the number, but the landlords are only allowed to disagree with the software (and give lower rent) only ~10% or so of the time. Otherwise they will be kicked off of the price fixing platform.

[samatman]

Why isn't that clearly stated in the FTC brief? That's a hell of an absence of evidence, under the circumstances. If there's a smoking gun, why leave it out?