Reconsidering two-agent Nash implementation

In this paper, we reconsider the full characterization of two-agent Nash implementation provided in the celebrated papers byMoore and Repullo (Econometrica 58:1083\u20131099, 1990) and Dutta and Sen (Rev Econ Stud 58:121\u2013128, 1991), since we are able to show that the characterizing conditions are not logically independent. We prove that an amended version of the conditions proposed in these papers is still necessary and sufficient for Nash implementability. Then, by using our necessary and sufficient condition, we show that Maskin\u2019s impossibility result can be avoided under restrictions on the outcomes and the domain of preferences much weaker than those previously imposed by Moore and Repullo (Econometrica 58:1083\u20131099, 1990) and Dutta and Sen (Rev Econ Stud 58:121\u2013128, 1991)