We study the impact of trade liberalization on the international strategy of firms (to export and/or invest abroad as well as the number of products to be produced) when product differentiation is endogenous. By considering product differentiation as a strategic variable, our analysis sheds new light on the impact of trade barriers on the decision to produce abroad and on the choice of product range, in accordance with recent empirical evidence. Indeed, we show, even though technology exhibits the same productivity for each variety, firms drop some of varieties with trade integration. In addition, our results reveal that, contrary to the standard theoretical literature, the relationship between the decision to export and trade costs is non-linear. When trade costs are relatively high, each firm export and is multi-product. Then, when trade costs take intermediate values, firms may invest abroad and the choice of producing abroad results from a prisoner's dilemma game. Finally, when trade costs are low, firms export, but become single-product.