My bibliography  Save this paper

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

Listed:
• Wu, Haoyang

## 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.

## Suggested Citation

• Wu, Haoyang, 2010. "Two examples to break through classical theorems on Nash implementation with two agents," MPRA Paper 22670, University Library of Munich, Germany.
• Handle: RePEc:pra:mprapa:22670
as

File URL: https://mpra.ub.uni-muenchen.de/22670/1/MPRA_paper_22670.pdf
File Function: original version

### Keywords

Quantum games; Mechanism design; Implementation theory; Nash implementation; Maskin monotonicity.;

### JEL classification:

• D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
• C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

### NEP fields

This paper has been announced in the following NEP Reports:

## Corrections

All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:22670. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Joachim Winter) or (Rebekah McClure). General contact details of provider: http://edirc.repec.org/data/vfmunde.html .

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

We have no references for this item. You can help adding them by using this form .

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.