We provide new insight on international monetary policy cooperation in a familiar two-country setting. A country facing a relatively more volatile markup shock has an incentive to deviate from an assumed Cooperation regime to a Non-cooperation regime. A similar result obtains if countries differ in size, have non-unitary elasticity of substitution between domestic and foreign goods, and have different degrees of trade openness (home bias in consumption). This motivates our study of an endogenous, history-dependent Sustainable Cooperation regime. Its history-contingent welfare redistributions are supported by incentive-compatible variations in resource transfers, through 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.