We study exchange rate dynamics under cooperative and self-oriented policies in a two-country DSGE model with unconventional monetary and exchange rate policies. The cooperative solution features a large exchange rate adjustment that cushions the impact of negative shocks and a moderate use of unconventional policy instruments. Self-oriented policies (Nash equilibrium), however, entail limited exchange rate movements and an aggressive use of unconventional policies in both countries. Our results highlight the role of international policy cooperation in allowing the exchange rate to play the traditional role of shock absorber.