  Generative Adversarial Networks (GAN) have become one of the most successful
frameworks for unsupervised generative modeling. As GANs are difficult to train
much research has focused on this. However, very little of this research has
directly exploited game-theoretic techniques. We introduce Generative
Adversarial Network Games (GANGs), which explicitly model a finite zero-sum
game between a generator ($G$) and classifier ($C$) that use mixed strategies.
The size of these games precludes exact solution methods, therefore we define
resource-bounded best responses (RBBRs), and a resource-bounded Nash
Equilibrium (RB-NE) as a pair of mixed strategies such that neither $G$ or $C$
can find a better RBBR. The RB-NE solution concept is richer than the notion of
`local Nash equilibria' in that it captures not only failures of escaping local
optima of gradient descent, but applies to any approximate best response
computations, including methods with random restarts. To validate our approach,
we solve GANGs with the Parallel Nash Memory algorithm, which provably
monotonically converges to an RB-NE. We compare our results to standard GAN
setups, and demonstrate that our method deals well with typical GAN problems
such as mode collapse, partial mode coverage and forgetting.
