The outcome of a trade war (with import tariffs and export subsidies) between two countries is analysed in a Cournot duopoly and in a Bertrand duopoly with differentiated products. The model allows for asymmetries between the countries in terms of competitiveness. When the two countries are similar, both countries will be worse off in a trade war than under free trade, but the country with the uncompetitive firm may win the trade war when the asymmetries are sufficiently great. Hence, in an infinitely -repeated game, cost asymmetries make it difficult to sustain free trade using infinite Nash reversion. However, it is shown that both countries minimaxing each other by setting prohibitive import tariffs and export taxes is also a Nash equilibrium in trade policies that results in each country obtaining autarky welfare. In an infinitely-repeated game, it is much easier to sustain free trade using infinite minimax reversion when there are cost asymmetries than with infinite Nash reversion. In fact, free trade can be sustained even if the punishment phase lasts for only a few rounds. Since there are two Nash equilibria of the trade policy game, free trade can also be sustained in a finitely-repeated game.