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This paper uses two game-theory models, where monetary policy is first ineffective and then effective, to illustrate a delegation scheme that makes consistent policy optimal and controllable. The delegation scheme produces the minimization of both the social and the central bank loss functions. Minimizing the social loss function generates optimality conditions. Minimizing the central bank loss function produces controllability conditions. Optimality conditions depend on specific models, and controllability conditions do not. We propose a concept of consistent targets, which refer to the targets that satisfy both optimality and controllability conditions. Consistent policy proves optimal and controllable in both example models when the government delegates consistent targets to the central bank. Adapted from the source document.