We consider the existence and structure of (zero-sum game) Nash equilibria for a two-way network in the presence of an intelligent jammer capable of tapping the channel signals in both directions. We assume that the source and channel noise signals are all Gaussian random variables, where the source signals are independent of each other, while the noise signals are arbitrarily correlated. We show that for fixed jammer power constraints, a Nash equilibrium exists with respect to the system wide mean square error, and equilibrium jamming policies are always Gaussian. We derive the equilibrium policies in closed form under various system parameters. Finally for two system scenarios, we analytically determine the optimal power allocation levels the jammer can deploy in each channel link, when allowed to operate under an overall power constraint.