This paper develops a three-country Stackelberg-Cournot model to analyse strategic tariff setting under asymmetric market power and timing advantages. One country acts as a tariff-setting leader, followed by simultaneous tariff responses from two follower countries, after which firms compete à la Cournot in quantities across destination markets. The framework incorporates heterogeneous market sizes, tariff incidence between consumers and producers, bilateral trade preferences, and empirically calibrated demand and cost parameters. Calibrating the model to the United States, China, and the European Union, we show that tariff leadership allows the first mover to secure short-term welfare gains through tariff revenues and domestic producer protection, despite higher domestic prices and lower consumer surplus. These gains come at the expense of trading partners and result in lower global welfare and reduced trade volumes. We further show that small deviations from optimal tariff policies yield limited national benefits while substantially increasing global inefficiency. The results characterize a non-cooperative Nash equilibrium that is individually rational but Pareto inferior, highlighting the importance of tariff coordination among large economies and the vulnerability of small open economies indirectly exposed to major trade conflicts.