It's already happening in the US with RealPage, the company that uses AI to set the rent for tenants.
RealPage, owned by the private equity firm Thoma Bravo, includes a tool called "AI Revenue Management" that provides recommendations for rental prices based on data from competitors. The feature, according to the CEA, the Department of Justice (DOJ), and class action lawsuits, facilitates "price coordination." It allows individual landlords to "act as if they are a single dominant landlord, and use their collective market power to increase profits by setting higher prices."
https://popular.info/p/ai-costs-american-renters-over-36
Using AI to set prices is just price fixing with some extra steps.