Optimal nonlinear income taxation with a finite population

In the standard optimal income taxation problem, tax payments depend only on each consumer's own actions. Piketty [J. Econ. Theory 61 (1993) 23-41] shows that, if one individual's tax schedule depends on others’ actions and the government knows the exact ability distribution, it can implement any undistorted allocation as the unique revelation game outcome. If some individuals misreveal their types, Piketty's mechanism may assign infeasible allocations. We require that tax schedules must balance the government budget for every possible vector of revelations. When individuals reveal their type by simple announcements, all undistorted allocations can be still implemented, even with off-equilibrium feasibility constraints.