This paper proposes a simple framework that generalizes the timing structure of macroeconomic (as well as other) games. Building on alternating move games and models of ‘rational inattention’ the players’ actions may be rigid, ie optimally chosen to be infrequent. This rigidity makes the game more dynamic/asynchronous and by linking successive periods it can serve as commitment. Therefore, it can enhance cooperation and often eliminate inefficient equilibrium outcomes. We apply the framework to the Kydland-Prescott-Barro-Gordon monetary policy game and derive the conditions - the sufficient degree of commitment - under which the influential time-inconsistency problem disappears. Interestingly, (i) this can happen even in a finite game (possibly as short as two periods), (ii) the required degree of commitment may be rather (even infinitesimally) low and (iii) the policymaker’s commitment may substitute for his conservatism and/or patience in achieving credibility. The analysis makes several predictions about explicit inflation targeting and central bank independence (and their relationship) that we show to be empirically supported. In doing so we show that our theoretical results reconcile some conflicting empirical findings of the literature.