In this paper we present an application of the dynamic tracking games framework to a monetary union. We use a small stylized nonlinear three-country macroeconomic model of a monetary union to analyse the interactions between fiscal (governments) and monetary (common central bank) policy makers, assuming different objective functions of these decision makers. Using the OPTGAME algorithm we calculate solutions for several games: a noncooperative solution where each government and the central bank play against each other (a feedback Nash Equilibrium solution), a fully cooperative solution with all players following a joint course of action (a Pareto optimal solution), and three solutions where various coalitions (subsets of the players) play against coalitions of the other players in a noncooperative way. It turns out that the fully cooperative solution yields the best results, the noncooperative solution fares worst, and the coalition games lie in between, with a broad coalition of the fiscally more responsible countries and the central bank against the less thrifty country coming closest to the Pareto optimum.