We study a policy game between exporting and importing countries in vertically linked industries. In a successive international Cournot oligopoly, we analyse incentives for using tax instruments strategically to shift rents vertically, between exporting and importing countries, and horizontally, between exporting countries. We show that the equilibrium outcome depends crucially on the relative degree of competitiveness in the upstream and downstream parts of the industry. With respect to national welfare, a more competitive upstream industry may benefit an exporting (upstream) country and harm an importing (downstream) country. On the other hand, a more competitive downstream industry may harm exporting countries.