In the context of a model of international trade through reciprocal dumping with horizontally differentiated goods, we study the endogenous choice of quantities and prices as strategic variables. We show that while a Cournot outcome prevails under conditions of export rivalry, strategic asymmetry under foreign direct investment rivalry may be observed, especially when it is possible to initially deter FDI by committing to a price contract, and when switching is costly and/or takes time.