Lawyer here. Hard disagree. The software is sold for the purpose of reducing competition, and gives advice on how to best achieve that. Everyone colluding is buying and using the software with a goal of not competing with each other.
That is just about a textbook case.
You can remove the software. Imagine you all pay someone to write a number on a piece of paper that gets posted on a light pole once a month. You don't get a say what the number is, but you all agree to set prices at that number 80% of the time.
This is illegal. Even if you remove the 80% and say "we recommend you use this number 80% of the time to maximize your non competition", it would be illegal
This is not a close case. Fixing the price this way is illegal.
Agreeing not to compete at all is illegal.
It does not matter if you get someone else to set the price. At the point you all agree not to compete, you've clearly violated the act.
As for whether it's per-se illegal, per-se illegal went out the window on basically all illegal acts under the sherman act over the past few decades, except a few remaining forms of price-fixing.
But you would still win the cases under the rule of reason anyway, and it would not be close there either.
People seem really hung up on whether they agreed with each other explicitly.
They don't have to. Conspiracy suffices. Tacit agreement is not illegal, but it has to be truly tacit. This is not. As I said elsewhere: it is illegal for them to conspire to not compete matter what the form of the conspiracy.
However if they just aren't competing, you can't order them to compete.
This is a clear case of the former - they are conspiring towards a common non competition goal. They knew what would happen if they conspired this way.
It's like trying to avoid a conspiracy to commit murder charge by saying you never explicitly agreed to hire a particular hitman, you instead just followed the directions some software gave you when it said "in order to maximize the possibility of your husband being dead, we recommend depositing at least five million at the following address". Good luck with your claim that you didn't agree to anything with anyone - you were just maximizing some probabilities.
Hell, i bet when they do discovery the company has not been as careful as they think, and there are chats/emails about how successfully they've been able to destroy competition or raise prices or whatever.
Because there always is.