Price fixing is when competitors agree to set prices. If AirBnb and Hilton and Marriott started agreeing on prices, then it would be price fixing.

This isn't price fixing because companies aren't considered their own competitors.

It might be a little fuzzy if the people posting rooms on AirBnb are considered competitors, but even then it's not price fixing because there's no requirement to use the algorithm's suggested price, and no single owner can influence the general price of rooms, because there's still hotels, motels, non-AirBnb rooms, etc.

For one, because AirBnB has multiple competitors. HomeAway is the closest thing, but traditional BnBs and hotels are playing in largely the same space.

For two, they're not actually setting the prices, the property owners are doing that. They're recommending prices, which is very different.

Feels kinda weird to be defending AirBnB, since I work for Homeaway.

ETA: Probably the closest analogy would be the infamous Manufacturer Suggested Retail Price, which is quite legal as long as they don't actually force the retailers to stick to it.