  The influential work of Bravo et al. 2018 shows that derivative free play in
strongly monotone games has complexity $O(d^2/\varepsilon^3)$, where
$\varepsilon$ is the target accuracy on the expected squared distance to the
solution. This note shows that the efficiency estimate is actually
$O(d^2/\varepsilon^2)$, which reduces to the known efficiency guarantee for the
method in unconstrained optimization. The argument we present simple interprets
the method as stochastic gradient play on a slightly perturbed strongly
monotone game.
