Dynamic controllability with overlapping targets: Or why target independence may not be good for you

We generalize some recent results developed in static policy games with multiple players, to a dynamic context. We find that the classical theory of economic policy, static or dynamic, can be usefully applied to a strategic context of difference games: if one player satisfies the Golden Rule, then either all other players' policies are ineffective with respect to the dynamic target variables shared with that player. Or no Nash Feedback Equilibrium can exist, unless they all share target values for those variables. We extend those results to the case in which there are also nondynamic targets, to show that policy effectiveness (a Nash equilibrium) can continue to exist if some players satisfy the Golden Rule but target values differ between players in their nondynamic targets. We demonstrate the practical importance of these results by showing how policy effectiveness (a policy equilibrium) can appear or disappear with small variations in the expectations process or policy rule in a widely used model of monetary policy with the possibility of target independence.