First off, lets go over regional airlines in the Real world because they DO NOT operate like majors for the most part.
Great lakes, ASA, Pinnacle, whoever... Any carrier flying regional aircraft for the majors are doing so as the major's flight (ASA flight x operating Delta flight Y). On every route the regional is flying for the major, they are being paid X amount of money whether the flight has one person on board or full. That amount doesnt change too much either if at all until the contract has to be renegociated. So if fuel prices rocket, the regional carrier is the one that has to make the flights work.
Now some regionals like Colgan and Gulf Stream(if they ever operate again) and a few others operate(s)(d) their own flights under their own name. Those flights, they are fully open to the competitive markets.
Then there are "regionals" like GO! who are niche and operate completely on their own.
Now the first type, there really is no point in having players do that. It however, should be easier for an airline to do that in house, but commonality right now screws that all up.
The second I think could be possible since its a mix of both and the third is how it currently is.
Now as for advertising, If the route is for a major carrier, then they should be paying the costs. If the Regional is operating flights inhouse, then they need to be paying the advertising. Its that simple.