On amending the sufficient conditions for Nash implementation

Mechanism design, a reverse problem of game theory, is an important branch of economics. Nash implementation is the cornerstone of the theory of mechanism design. The well-known Maskin's theorem describes the sufficient conditions for Nash implementation when the number of agents are at least three. A recent work [H. Wu, Quantum mechanism helps agents combat ``bad'' social choice rules. International Journal of Quantum Information, 2010 (accepted) http://arxiv.org/abs/1002.4294 ] shows that when an additional condition is satisfied, the Maskin's theorem will no longer hold by using a quantum mechanism. Although quantum mechanisms are theoretically feasible, agents cannot benefit from them 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 leads to the same results as quantum mechanisms do. Consequently, the sufficent conditions for Nash implementation are amended not only in the quantum world, but also in the real world