[Quicksilvre]

I think the reason for why rakes will stay the same is a little simpler.

Assuming reasonable consumers, as soon as the rake goes down at one site, players will flood that site and all the others would lose business. Therefore, all the other sites would have to cut rake, and there would be less profit for all. Obviously, then, rake won't go down.

If the rake goes up at a site, the other sites would simply keep their rakes the same, and the rake-boosting site would lose business. Obviously, then, rake won't go up. This sort of thing is very typical for oligopolies.

Of course, consumers are not reasonable. Still, there are enough sites out there, that if one site hikes the rake by a large degree, it would lose business.