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We introduce a generalization of zero-sum network multiagent matrix games andprove that alternating gradient descent converges to the set of Nash equilibriaat rate $O(1/T)$ for this set of games. Alternating gradient descent obtainsthis convergence guarantee while using fixed learning rates that are four timeslarger than the optimistic variant of gradient descent. Experimentally, we showwith 97.5% confidence that, on average, these larger learning rates result intime-averaged strategies that are 2.585 times closer to the set of Nashequilibria than optimistic gradient descent.

$O\left(1/T\right)$ Time-Average Convergence in a Generalization of Multiagent Zero-Sum Games