By diverting and distorting bilateral trade flows, trade wars shift export patterns and market concentration around the globe. In this paper, we estimate parameters in n-country general equilibrium trade model featuring oligopolistic competition with data from a rich panel of firm-level exports from 11 low and middle-income countries to 165 destinations that report bilateral and multilateral tariffs to the World Trade Organization. We show that, by affecting entry/exit decisions of large firms active in export markets, a tariff war between two countries results in a significant rise in market concentration and market power globally, driving down welfare.