Two examples to break through classical theorems on Nash implementation with two agents

Wu, Haoyang (2010): Two examples to break through classical theorems on Nash implementation with two agents.

Abstract

[E. Maskin, \emph{Rev. Econom. Stud.} \textbf{66} (1999) 23-38] is a seminal paper in the field of mechanism design and implementation theory. [J. Moore and R. Repullo, \emph{Econometrica} \textbf{58} (1990) 1083-1099] and [B. Dutta and A. Sen, \emph{Rev. Econom. Stud.} \textbf{58} (1991) 121-128] are two fundamental papers on two-player Nash implementation. Recently, [H. Wu, http://arxiv.org/pdf/1004.5327v1 ] proposed a classical algorithm to break through Maskin's theorem for the case of many agents. In this paper, we will give two examples to break through the aforementioned results on two-agent Nash implementation by virtue of Wu's algorithm. There are two main contributions of this paper: 1) A two-player social choice rule (SCR) that satisfies Condition $\mu2$ cannot be Nash implemented if an additional Condition $\lambda'$ is satisfied. 2) A non-dictatorial two-player weakly pareto-optimal SCR is Nash implementable if Condition $\lambda'$ is satisfied. Although the former is negative for the economic society, the latter is just positive. Put in other words, some SCRs which are traditionally viewed as not be Nash implementable may be Nash implemented now.

• 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

1. E. Maskin, \emph{Rev. Econom. Stud.} \textbf{66} (1999) 23-38.

2. J. Moore and R. Repullo, \emph{Econometrica} \textbf{58} (1990) 1083-1099.

3. B. Dutta and A. Sen, \emph{Rev. Econom. Stud.} \textbf{58} (1991) 121-128.

4. F. Busutto and G. Codognato, \emph{Social Choice and Welfare} \textbf{32} (2009) 171-179.

5. H. Wu, Quantum mechanism helps agents combat ``bad'' social choice rules. \emph{International Journal of Quantum Information}, 2010 (accepted). See http://arxiv.org/pdf/1002.4294v3

6. H. Wu, A classical algorithm to break through Maskin's theorem. http://arxiv.org/pdf/1004.5327v1