We study the strategic interaction between two firms competing in quantites which decide whether exporting into each other market. The product is homogeneous and production entails constant returns to scale. Scope effects are present. By dealing with two types of trade costs, namely per unit and ad valorem trade costs, we characterize the set of Nash equilibria showing that one way trade is a possible outcome of the trade game. In particular, despite the assumption on symmetry between firms, unilateral trade arises provided trade costs are sufficiently high. The private incentives towards one way trade are then compared with the social ones.