  We introduce a generalization of zero-sum network multiagent matrix games and
prove that alternating gradient descent converges to the set of Nash equilibria
at rate $O(1/T)$ for this set of games. Alternating gradient descent obtains
this convergence guarantee while using fixed learning rates that are four times
larger than the optimistic variant of gradient descent. Experimentally, we show
with 97.5% confidence that, on average, these larger learning rates result in
time-averaged strategies that are 2.585 times closer to the set of Nash
equilibria than optimistic gradient descent.
