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We scrutinize international trade arising from oligopolistic rivalry (reciprocal dumping) in a model where the goods are horizontally differentiated and where otherwise symmetric firms located in different regions adopt asymmetric strategies—one competing in prices and the other competing in quantities. Unidirectional and intra‐industry trade appear endogenously in our framework. We show that as trade costs decline the equilibrium outcome will transition from autarky through a region of unidirectional trade, before intra‐industry trade ultimately arises. In the unidirectional trade region, potential market entry by the rival has an impact on firm behavior even though the rival is not exporting. The implications of product differentiation and changing trade costs for trade volumes and for the gains from trade are asymmetric in general. Welfare may rise monotonically as trade costs fall for one of the economies, but will necessarily fall initially relative to autarky for the other.