This paper studies the problem of implementation of taxation methods in one-commodity environments in which the taxable incomes of the (at least two) agents are fixed and not known to the planner. In this problem (unlike most work in implementation theory), the feasible set is unknown to the designer. We first show that feasibility out of equilibrium imposes that the mechanism depend on the environment. Next we present two game forms. In the first one, which requires complete information among the tax payers, each agent reports the incomes of all players to a central agency, and implementation of every taxation method is obtained in Nash, strong and coalition-proof equilibrium. In the second, informational requirements may be somewhat relaxed. One of the agents makes a tax proposal, the others bargain with him, and the services of a central agency are used only to solve disputes between pairs of agents. This game form implements a large class of consistent and monotone taxation methods in subgame perfect equilibrium. Neither mechanism employs the off-equilibrium devices used by the general theory. Partial departures from complete information still allow for implementability. However, under fully private information implementation is not possible.
