  Many recent AI architectures are inspired by zero-sum games, however, the
behavior of their dynamics is still not well understood. Inspired by this, we
study standard gradient descent ascent (GDA) dynamics in a specific class of
non-convex non-concave zero-sum games, that we call hidden zero-sum games. In
this class, players control the inputs of smooth but possibly non-linear
functions whose outputs are being applied as inputs to a convex-concave game.
Unlike general zero-sum games, these games have a well-defined notion of
solution; outcomes that implement the von-Neumann equilibrium of the "hidden"
convex-concave game. We prove that if the hidden game is strictly
convex-concave then vanilla GDA converges not merely to local Nash, but
typically to the von-Neumann solution. If the game lacks strict convexity
properties, GDA may fail to converge to any equilibrium, however, by applying
standard regularization techniques we can prove convergence to a von-Neumann
solution of a slightly perturbed zero-sum game. Our convergence guarantees are
non-local, which as far as we know is a first-of-its-kind type of result in
non-convex non-concave games. Finally, we discuss connections of our framework
with generative adversarial networks.
