Quantum mechanism helps agents combat Pareto-inefficient social choice rules

Wu, Haoyang (2010): Quantum mechanism helps agents combat Pareto-inefficient social choice rules.

Abstract

Quantum strategies have been successfully applied in game theory for years. However, as a reverse problem of game theory, the theory of mechanism design is ignored by physicists. In this paper, we generalize the classical theory of mechanism design to a quantum domain and obtain two results: 1) We find that the mechanism in the proof of Maskin's sufficiency theorem is built on the Prisoners' Dilemma. 2) By virtue of a quantum mechanism, agents who satisfy a certain condition can combat Pareto-inefficient social choice rules instead of being restricted by the traditional mechanism design theory.

• Item Type: MPRA Paper
• Language: English
• Keywords: Quantum games; Mechanism design; Implementation theory; Nash implementation; Maskin monotonicity
• Subjects: D - Microeconomics > D7 - Analysis of Collective Decision-Making > D71 - Social Choice ; Clubs ; Committees ; Associations; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games

References

J. von Neumann, O. Morgenstern, Theory of Games and Economic Behavior, Princeton University Press, Princeton, 1944.

R. Serrano, SIAM Review \textbf{46}, 377 (2004).

E. Maskin, Rev.Econom.Stud. \textbf{66}, 23 (1999).

E. Maskin, T. Sj\"{o}str\"{o}m, Implementation theory, in: K.J.Arrow, A.Sen, K.Suzumura (Eds.), Handbook of Social Choice and Welfare, Vol.1, Elsevier Science, New York, 2002, pp. 237-288.

J. Eisert, M. Wilkens, M. Lewenstein, Phys. Rev. Lett. \textbf{83}, 3077 (1999).

D. Meyer, Phys. Rev. Lett. \textbf{82}, 1052 (1999).

S.C. Benjamin, P.M. Hayden, Phys. Rev. A \textbf{64}, 030301(R) (2001).

J. Du, H. Li, X. Xu et al, Phys. Lett. A \textbf{302}, 229 (2002).

A.P. Flitney, L.C.L. Hollenberg, 2007, Phys. Lett. A \textbf{363}, 381 (2007).

S. J. van Enk, R. Pike, Phys. Rev. A \textbf{66}, 024306 (2002).