We provide new insight on international monetary policy cooperation using a two-country model based on Benigno and Benigno (2006). Assuming symmetry, save for the volatility of (markup) shocks, we show that an incentive feasibility problem exists between the policymakers across national borders: The country faced with a relatively more volatile markup shock has an incentive to deviate from an assumed Cooperation regime to one with Noncooperation. More generally, a similar result obtains if countries differ in size. This motivates our study of a history-dependent Sustainable Cooperation regime which is endogenously sustained by a cross-country, state-contingent contract between policymakers. Under Sustainable Cooperation, the responses of inflation and the output gap in both countries are different from those induced by the Cooperation and Noncooperation regimes reflecting the endogenous welfare redistribution between countries under the state-contingent contract. Such history-contingent welfare redistributions are supported by resource transfers affected through incentive-compatible variations in the terms of trade (or net exports). Such an endogenous cooperative solution may also provide a theoretical rationale for perceived occasional cooperation between national central banks in reality.