  The study of learning in games has thus far focused primarily on normal form
games. In contrast, our understanding of learning in extensive form games
(EFGs) and particularly in EFGs with many agents lags far behind, despite them
being closer in nature to many real world applications. We consider the natural
class of Network Zero-Sum Extensive Form Games, which combines the global
zero-sum property of agent payoffs, the efficient representation of graphical
games as well the expressive power of EFGs. We examine the convergence
properties of Optimistic Gradient Ascent (OGA) in these games. We prove that
the time-average behavior of such online learning dynamics exhibits $O(1/T)$
rate convergence to the set of Nash Equilibria. Moreover, we show that the
day-to-day behavior also converges to Nash with rate $O(c^{-t})$ for some
game-dependent constant $c>0$.
