Jamming in multiple independent Gaussian channels as a game

We study the problem of \emph{jamming} in multiple independent \emph{Gaussian channels} as a zero-sum game. We show that in the unique Nash equilibrium of the game the best-response strategy of the transmitter is the \emph{waterfilling} to the sum of the jamming and the noise power in each channel and the best-response strategy of the jammer is the \emph{waterfilling} only to the noise power.