Actually up until this year when the NFL gave up their tax exempt status their books were opened and we knew quite a bit of the details of the agreements. And since no new contracts have been signed since then we actually DO know how payments to the NFL are structured and what obligation the NFL is under at the halftime show. And actually quite a bit of this was discussed in the aftermath of the wardrobe malfunction. Simple put, the NFL does not participate in the halftime show. It’s for the network and the stadium to work out, the network does most of the design and sign up, the stadium tells them whether or not that could actually work. The artists don’t get paid, and they also don’t pay (there was some talk by the league last year about making the artists pay, but that sunk fast).
The halftime show can’t actually generate enough money for the NFL to actually care. That’s part of why last year’s talk about making the artists pay died. The NFL pulls in 5 BILLION dollars a year on the TV contracts alone, and part of how they pull that off is the prize of the SB. It’s a big revenue and self promotion opportunity for the networks, it’s pretty much the only way they turn a profit on their NFL contracts. So the league leaves it alone, and lets the networks use it for themselves. That’s a big part of why CBS had The Who (providers of the theme songs for 4 CBS shows) a few years ago, it was a massive act of self promotion.
Of necessity, that influences the choice of halftime acts, and behind those decisions is a legion of marketing experts and a mass of sophisticated audience studies. That is part of the fundamental expertise that sustains broadcast networks, knowing how to get eyeballs to watch TV shows and their ads, with advertisers assured that the owners of those eyeballs are their desired target audience.