Honestly the fact that you think there are only four airlines in the domestic US market speaks to your lack of understanding on the subject matter.

There are dozens of regional airlines in the US that own their own fleets and hire their own pilots and carry their own operations. These regionals then fly under big national express banners to take advantage of widespread name recognition, but the pricing of their flights is highly dependent on the individual contracts signed between the big nationals and the regional. The market for these "express" deals are absurdly competitive.

The US ticket prices are fucked up largely because this regional airline model is currently in the process of collapsing in on itself. There's an increased demand for flight with rising employment figures in the US but there's also a shortage of pilots because pilot wage scales fucking suck and the training is outrageously expensive. Regionals literally cannot field enough flights. The correct response would be to dial down the frequency of flights and instead fly bigger planes for regional routes (like A320s and 737s instead of CRJ, ERJ and Dash 8). This is what happens in Europe and is the reason why domestic flights there are cheaper but US regionals don't have the big planes and don't have the capital to get them. So they're just getting crushed right now. The big nationals are eventually going to absorb them, start running regional routes themselves instead of contracting out, and then you'll see a true reduction of competition. It won't be good.

Either way none of this is collusion. The airline market is fucked up. These companies operate with razor thin profit margins. All of them.