We investigate how potential tax-driven migrations modify the Mirrlees income tax schedule when two countries play Nash. The social objective is the maximin and preferences are quasilinear in income. Individuals differ both in skills and migration costs, which are continuously distributed. We derive the optimal marginal income tax rates at the equilibrium, extending the Diamond-Saez formula. The theory and numerical simulations on the US case show that the level and the slope of the semi-elasticity of migration on which we lack empirical evidence are crucial to derive the shape of optimal marginal income tax. Our simulations show that potential migrations result in a welfare drop between 0.4% and 5.3% for the worst-off and an average gain between 18.9% and 29.3% for the top 1%.