The DOJ hasn't made any decision about the gates at DAL (or any other airport where the new AA agreed to give up gates). All they've said is that they want them to go to LCCs to spur competition (i.e. other than UAL, DL. or If it's like the gates at DCA and LGA, I suspect they'll have an auction, where even the DOJ doesn't know who'll get them, because they don't know how much airlines are willing to pay. In the slot auction, we got some; other airlines got the rest. A few years ago, they had an LGA slot auction, and we got none, as JBLU outbid us. Southwest decided they weren't worth bidding anymore than we did.
To be honest, I suspect that Southwest will try harder/bid more for the DAL gates, because we need them to grow service in Dallas, unlike any other airline. Don't know if you knew this or not, but of all the airlines who fly into Dallas, only Southwest is legally constrained on gates. If we take a gate at the other airport (DFW), then we have to give up one at DAL. If any of the airlines based at DFW take a gate at DAL, then they're not required to give anything up.
Short of abandoning DAL completely, and moving our entire operation to DFW, the most gates we're ever allowed to use anywhere in Dallas is the 20 legally allowed to exist at DAL (we have 16 right now). Contrast that to the literally hundreds of gates American has at DFW, and the ability of Delta (or any other airline, for that matter) to fly from DAL and still grow to as many gates at DFW as they want simultaneously.
It's a unique situation, and I doubt that even the DOJ knows what will happen yet.
Bubba