I believe that the key point here is that as adversarial networks compete against each other repeatedly they eventually will converge on a Nash Equilibrium.

Nash Equilibrium from Wikipedia: "Amy is making the best decision she can, taking into account Phil's decision while Phil's decision remains unchanged, and Phil is making the best decision he can, taking into account Amy's decision while Amy's decision remains unchanged."

At the point this happens, a stable solution exists which is almost like saying that we have made the most rational decision given the information we had. Nash was novel in this theory to say that if the participants were rational they would converge on an equilibrium and not get lost in endless recursion. Endless recursion being something like participants endlessly guessing the other opponent move... If Amy knows Phil knows Amy knows Phil knows Amy knows Phil... Obviously it would be problematic for DL to plunge into infinite recursion.

I like to think of the Nash Equilibrium as a balanced teeter totter. When the teeter totter becomes off balanced rational systems will relearn to balance the odds again based the properties of risk (what Nash referred to as utility I believe). Once they do so, they once again converge on an equilibrium.