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We study the international monetary policy design problem within an optimizing two-country sticky price model, where each country faces a short run trade-off between output and inflation. The model is sufficiently tractable to solve analytically. We find that in the Nash equilibrium, the policy problem for each central bank is isomorphic to the one it would face if it were a closed economy. Gains from co-operation arise, however, that stem from the impact of foreign economic activity on the domestic marginal cost of production. While under Nash central banks need only adjust the interest rate in response to domestic inflation, under co-operation they should respond to foreign inflation as well. In either scenario, flexible exchange rates are desirable.