This paper revisits optimal monetary policy in open economies, in particular, focusing on the noncooperative policy game under local currency pricing in a two-country dynamic stochastic general equilibrium model. We first derive the quadratic loss functions which noncooperative policy makers aim to minimize. Then, we show that noncooperative policy makers face extra trade-offs regarding stabilizing the real marginal costs induced by deviations from the law of one price under local currency pricing. As a result of the increased number of stabilizing objectives, welfare gains from cooperation emerge even when two countries face only technology shocks, which usually leads to equivalence between cooperation and noncooperation. Still, gains from cooperation are not large, implying that frictions other than nominal rigidities are necessary to strongly recommend cooperation as an important policy framework to increase global welfare.