[This post covers too much ground and stretches my brain too far. I'm trying to put Lipsey-Lancaster and game theory together, and apply it to monetary-fiscal. I blame Brad DeLong for making me think about this.]
"But as long as Nick Rowe recognizes that fixing situations of depressed activity by simply printing money gets us not to the first-best but the second-best in many situations, I can have no quarrel."
I think it is the job of monetary policy to take the world as it is, not as it should be. Monetary policy is always, in practice, about living in a second-best world. And that "world" includes fiscal policy.
And a game-theoretic analysis of monetary and fiscal policy in a second-best world leads to the conclusion that the fiscal authority must ignore the effect of fiscal policy on aggregate demand (NGDP), or else the Nash equilibrium will be far from second-best.