Journal article: This paper offers a framework to study strategic interactions between private players, national fiscal authorities and a common central bank in monetary unions. We establish general conditions, in terms of restrictions on spillover effects of actions by private and public players, under which games that differ in the degree of cooperation and commitment can admit the same equilibrium outcome. We use these conditions to characterize benchmark results on the irrelevance of cooperation and commitment established in recent literature. Moreover, we show for a general setting, in which the benchmark results do not apply, that gains from fiscal cooperation depend on the number of countries and increase as this number gets larger.