In the light of the recent adoption of social responsible activities by large exporters, this paper sets up a strategic trade policy model in which two national champions compete à la Cournot in a third country and both governments can tax or subsidise the production of its local champion and reconsiders the well-known result of the Prisoner’s Dilemma game structure in which governments set subsidies for their exporters. We show that (1) multiple sub-game perfect equilibria emerge in which one government taxes, while the other one allows free trade, provided that firms’ social concerns are sufficiently large and (2) the social welfare of both countries in the latter asymmetric equilibrium is higher than that under free trade. Our findings suggest that a free-trade regime is always the less efficient policy in industries characterised by large social concerns. Moreover, we analyse the impact of the firms’ social concerns interacting with strategic trade policies on welfare effects, showing that the welfares of consumers and the world as a whole (resp., total welfare of producing countries) are a U-shaped (resp., an inverted U-shaped) function of the intensity of social concerns: this suggests that in some cases, rather unexpectedly, producing countries (resp. consumers) benefit (resp. are harmed) by raising firms’ social concerns.