Abstract 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 quasi-linear in consumption. 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. We 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.