Maskin meets Abreu and Matsushima

• Main Authors: CHEN, Yi-Chun, KUNIMOTO, Takashi, SUN, Yifei, XIONG, Siyang
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2018
• Subjects: Economic Theory
• Online Access: https://ink.library.smu.edu.sg/soe_research/2273; https://ink.library.smu.edu.sg/context/soe_research/article/3272/viewcontent/Maskin_meets_Abreu_may_16_2018_wp.pdf
• Institution: Singapore Management University

We study the classical Nash implementation problem due to Maskin (1999), but allow for the use of lottery and monetary transfer as in Abreu and Matsushima (1992, 1994). We therefore unify two well-established but somewhat orthogonal approaches of implementation theory. We first show that Maskin monotonicity is a necessary and sufficient condition for pure-strategy Nash implementation by a direct mechanism. Second, taking mixed strategies into consideration, we show that Maskin monotonicity is a necessary and sufficient condition for mixed-strategy Nash implementation by a finite (albeit indirect) mechanism. Third, we extend our analysis to implementation in rationalizable strategies. In contrast to previous papers, our approach possesses many appealing features simultaneously, e.g., finite mechanisms (with no integer or modulo game) are used; mixed strategies are handled explicitly; neither transfer nor bad outcomes are used on the equilibrium path; our mechanism is robust to information perturbations; and the size of off-equilibrium transfers can be made arbitrarily small. Finally, our result can be extended to continuous settings and ordinal settings.