Maskin meets Abreu and Matsushima
统一了完全实施理论中两种正交的方法，证明马斯金单调性是有限机制实现精确混合策略纳什实施的充要条件，且机制无需整数或模博弈，均衡中无不良结果或转移支付。
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 (1977, 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.