We build a simple international trade model to study how the interaction between imperfect market selection and technological learning jointly shapes trade patterns as well as firm and industry dynamics. The model features two countries populated by firms heterogeneous in their productivity and size. Market selection is driven by a finite pairwise Pólya urn process, while a geometric random walk characterizes the idiosyncratic cumulative firm learning process. We show that the model is able to jointly reproduce a wide ensemble of stylized facts concerning intra-industry trade, industry and firm dynamics as well as realistic dynamics of export and productivity leadership at the country level. A series of sensitivity exercises on the degree of trade openness and the tightness of the market selection process allow us to draw interesting policy insights on concentration, volatility and the dynamics of international leadership in both export shares and aggregate productivity.