On amending the sufficient conditions for Nash implementation

The Maskin's theorem on Nash implementation is a fundamental work in the theory of mechanism design. A recent work [Wu, Quantum mechanism helps agents combat ``bad'' social choice rules. Intl. J. of Quantum Information 9 (2011) 615-623] shows that when an additional condition is satisfied, the Maskin's theorem will not hold if agents use quantum strategies. Although quantum mechanisms are theoretically feasible, they are not applicable immediately due to the restriction of current experimental technologies. In this paper, we will go beyond the obstacle of how to realize quantum mechanisms, and propose an algorithmic mechanism which amends the sufficient conditions of the Maskin's theorem immediately just in the macro world (i.e., computer or Internet world)