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.
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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
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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
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