The theory of full implementation has been criticized for using integer/modulo games which admit no equilibrium (Jackson (1992)). To address the critique, we revisit the classical Nash implementation problem due to Maskin (1999) but allow for the use of lotteries and monetary transfers as in Abreu and Matsushima (1992, 1994). We unify the two well-established but somewhat orthogonal approaches in full implementation theory. We show that Maskin monotonicity is a necessary and sufficient condition for (exact) mixed-strategy Nash implementation by a finite mechanism. In contrast to previous papers, our approach possesses the following features: finite mechanisms (with no integer or modulo game) are used
mixed strategies are handled explicitly
neither undesirable outcomes nor transfers occur in equilibrium
the size of transfers can be made arbitrarily small
and our mechanism is robust to information perturbations. Finally, our result can be extended to infinite/continuous settings and ordinal settings.