  Adversarial deep learning is to train robust DNNs against adversarial
attacks, which is one of the major research focuses of deep learning. Game
theory has been used to answer some of the basic questions about adversarial
deep learning such as the existence of a classifier with optimal robustness and
the existence of optimal adversarial samples for a given class of classifiers.
In most previous work, adversarial deep learning was formulated as a
simultaneous game and the strategy spaces are assumed to be certain probability
distributions in order for the Nash equilibrium to exist. But, this assumption
is not applicable to the practical situation. In this paper, we give answers to
these basic questions for the practical case where the classifiers are DNNs
with a given structure, by formulating the adversarial deep learning as
sequential games. The existence of Stackelberg equilibria for these games are
proved. Furthermore, it is shown that the equilibrium DNN has the largest
adversarial accuracy among all DNNs with the same structure, when
Carlini-Wagner's margin loss is used. Trade-off between robustness and accuracy
in adversarial deep learning is also studied from game theoretical aspect.
