  Motivated by Generative Adversarial Networks, we study the computation of
Nash equilibrium in concave network zero-sum games (NZSGs), a multiplayer
generalization of two-player zero-sum games first proposed with linear payoffs.
Extending previous results, we show that various game theoretic properties of
convex-concave two-player zero-sum games are preserved in this generalization.
We then generalize last iterate convergence results obtained previously in
two-player zero-sum games. We analyze convergence rates when players update
their strategies using Gradient Ascent, and its variant, Optimistic Gradient
Ascent, showing last iterate convergence in three settings -- when the payoffs
of players are linear, strongly concave and Lipschitz, and strongly concave and
smooth. We provide experimental results that support these theoretical
findings.
