Dominant Strategy Implementation with a Convex Product Space of Valuations
AbstractA necessary and sufficient condition for dominant strategy implementability when preferences are quasilinear is that, for any individual i and any choice of the types of the other individuals, all k-cycles in i's allocation graph have nonnegative length for every integer k ï¿½ 2. Saks and Yu (Proceedings of the 6th ACM Conference on Electronic Commerce (EC'05), 2005, 286-293) have shown that when the number of outcomes is finite and i's valuation type space is convex, nonnegativity of the length of all 2-cycles is sufficient for the nonnegativity of the length of all k-cycles. In this article, it is shown that if each individual's valuation type space is a convex product space and a mild domain regularity condition is satisfied, then (i) the nonnegativity of all 2-cycles implies that all k-cycles have zero length and (ii) all 2-cycles having zero length is necessary and sufficient for dominant strategy implementability.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Vanderbilt University Department of Economics in its series Vanderbilt University Department of Economics Working Papers with number 1104.
Date of creation: May 2011
Date of revision:
Contact details of provider:
Web page: http://www.vanderbilt.edu/econ/wparchive/index.html
2-cycle condition; dominant strategy implementation; mechanism design; revenue equivalence; Rockafellar-Rochet Theorem; Saks-Yu Theorem;
Other versions of this item:
- Katherine Cuff & Sunghoon Hong & Jesse Schwartz & Quan Wen & John Weymark, 2012. "Dominant strategy implementation with a convex product space of valuations," Social Choice and Welfare, Springer, vol. 39(2), pages 567-597, July.
- D44 - Microeconomics - - Market Structure and Pricing - - - Auctions
- D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
- D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Rochet, Jean-Charles, 1987. "A necessary and sufficient condition for rationalizability in a quasi-linear context," Journal of Mathematical Economics, Elsevier, vol. 16(2), pages 191-200, April.
- William Vickrey, 1961. "Counterspeculation, Auctions, And Competitive Sealed Tenders," Journal of Finance, American Finance Association, vol. 16(1), pages 8-37, 03.
- Jehiel, Philippe & Moldovanu, Benny & Stacchetti, Ennio, 1999.
"Multidimensional Mechanism Design for Auctions with Externalities,"
Journal of Economic Theory,
Elsevier, vol. 85(2), pages 258-293, April.
- Jehiel, Phillipe & Moldovanu, Benny & Stacchetti, E., 1997. "Multidimensional Mechanism Design for Auctions with Externalities," Sonderforschungsbereich 504 Publications 97-04, Sonderforschungsbereich 504, Universität Mannheim & Sonderforschungsbereich 504, University of Mannheim.
- Müller, Rudolf & Uetz, Marc & Vohra, Rakesh & Heydenreich, Birgit, 2007.
"Characterization of Revenue Equivalence,"
017, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
- First:Birgit Heydenreich & Rudolf Muller & Marc Uetz & Rakesh Vohra, 2007. "Characterization of Revenue Equivalence," Discussion Papers 1448, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Heydenreich, Birgit & Müller, Rudolf & Uetz, Marc & Vohra, Rakesh, 2008. "Characterization of Revenue Equivalence," Research Memorandum 001, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
- Sushil Bikhchandani & Shurojit Chatterji & Ron Lavi & Ahuva Mu'alem & Noam Nisan & Arunava Sen, 2006. "Weak Monotonicity Characterizes Deterministic Dominant-Strategy Implementation," Econometrica, Econometric Society, vol. 74(4), pages 1109-1132, 07.
- Ron Lavi & Ahuva Mu’alem & Noam Nisan, 2009. "Two simplified proofs for Roberts’ theorem," Social Choice and Welfare, Springer, vol. 32(3), pages 407-423, March.
- Debasis Mishra & Anup Pramanik & Souvik Roy, 2013. "Implementation in multidimensional domains with ordinal restrictions," Indian Statistical Institute, Planning Unit, New Delhi Discussion Papers 13-07, Indian Statistical Institute, New Delhi, India.
- Debasis Mishra & Abdul Quadir, 2012. "Deterministic single object auctions with private values," Indian Statistical Institute, Planning Unit, New Delhi Discussion Papers 12-06, Indian Statistical Institute, New Delhi, India.
- Mishra, Debasis & Roy, Souvik, 2013.
"Implementation in multidimensional dichotomous domains,"
Econometric Society, vol. 8(2), May.
- Debasis Mishra & Souvik Roy, 2011. "Implementation in multidimensional dichotomous domains," Indian Statistical Institute, Planning Unit, New Delhi Discussion Papers 11-15, Indian Statistical Institute, New Delhi, India.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (John P. Conley).
If references are entirely missing, you can add them using this form.