A classical algorithm to break through Maskin's theorem for small-scale cases

Quantum mechanics has been applied to game theory for years. A recent work [H. Wu, Quantum mechanism helps agents combat ``bad'' social choice rules. \emph{International Journal of Quantum Information}, 2010 (accepted). Also see http://arxiv.org/pdf/1002.4294v3] has generalized quantum mechanics to the theory of mechanism design (a reverse problem of game theory). Although the quantum mechanism is theoretically feasible, agents cannot benefit from it immediately due to the restriction of current experimental technologies. In this paper, a classical algorithm is proposed to help agents combat ``bad'' social choice rules immediately. The algorithm works well when the number of agents is not very large (e.g., less than 20). Since this condition is acceptable for small-scale cases, it can be concluded that the Maskin's sufficiency theorem has been broken through for small-scale cases just right now. In the future, when the experimental technologies for quantum information are commercially available, the Wu's quantum mechanism will break through the Maskin's sufficiency theorem completely.Quantum games; Prisoners' Dilemma; Mechanism design.