The Nash equilibria of a tax-setting game between two governments who can set nonlinear income tax schedules for a perfectly mobile workforce whose members differ in unobserved skill levels are examined. Each government maximizes the average utility of its residents. It is shown that while equilibria exist, there do not exist equilibria in which either the most highly skilled pay positive taxes or the lowest skilled receive transfers. It is also shown that it is possible for the most highly skilled to receive a net transfer funded by taxes on lower skilled individuals in equilibrium.Income tax competition, labor mobility, optimal income taxation, race to the bottom