Correlated jamming on MIMO Gaussian fading channels

We consider a zero-sum mutual information game on multiple-input multiple-output (MIMO) Gaussian Rayleigh-fading channels. The players are an encoder-decoder pair as the maximizer, and a jammer as the minimizer, of the mutual information between the input and the output of the channel. There are total power constraints on both the jammer and the encoder. Also, the jammer has access to the encoder output. We find the unique saddle point of this game, and prove the somewhat surprising result that the knowledge of the channel input is useless to the jammer.