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The consensus in recent literature is that gains from international monetary cooperation are likely to be small. We show that, while this is true near the steady state, the emergence of global imbalances and adverse domestic trade-offs along the dynamic evolution of the global economy can substantially magnify the incentives to pursue nationally-oriented, strategic monetary policies—raising the risk of “exchange rate wars.” Using the workhorse two-country, two-good monetary model with nominal rigidities, we find that the welfare effects of deviating from cooperative policies in favor of nationally-oriented policies are sizable when conditioned on empirically-relevant dynamic developments of the global economy. Under incomplete markets, the key development is the level of net foreign assets. Under complete markets or financial autarky, a key development consists of real wage distortions reflecting different price and wage rigidities. In both cases, the costs of nationally-oriented policies can climb to several times the costs associated with business cycle fluctuations. We also show that flexible inflation targeting comes close to replicating the cooperative policies, and thus it is just as fragile.