The problem with statement "as adversarial networks compete against each other repeatedly they eventually will converge on a Nash Equilibrium" is that they often won't, and a big problem with training GANs is to ensure that they converge.
Intuitively, what can happen is that one of the problems is simpler to learn than another, and when one of the "players" becomes overwhelmingly good, then the other part of the network stops receiving useful feedback and is unable to find out a direction for improvement, the learning stops. A "sufficiently smart" method would be able to go to a Nash equilibrium even in this case, but current GAN methods can not, so you need to take steps to ensure that it doesn't happen - e.g. extra normalization or less training for the "simpler to learn" component.
It's not enough to train the "adversarial" networks to compete during each inference, on a meta-level you must ensure a form of cooperation to ensure that they are effective teachers for each other during the learning process. For a real life analogy, there's a difference between effective behavior during combat and effective behavior during sparring.
Intuitively, what can happen is that one of the problems is simpler to learn than another, and when one of the "players" becomes overwhelmingly good, then the other part of the network stops receiving useful feedback and is unable to find out a direction for improvement, the learning stops. A "sufficiently smart" method would be able to go to a Nash equilibrium even in this case, but current GAN methods can not, so you need to take steps to ensure that it doesn't happen - e.g. extra normalization or less training for the "simpler to learn" component.
It's not enough to train the "adversarial" networks to compete during each inference, on a meta-level you must ensure a form of cooperation to ensure that they are effective teachers for each other during the learning process. For a real life analogy, there's a difference between effective behavior during combat and effective behavior during sparring.