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Dominant strategy implementation with a convex product space of valuations

  • Katherine Cuff

    ()

  • Sunghoon Hong

    ()

  • Jesse Schwartz

    ()

  • Quan Wen

    ()

  • John Weymark

    ()

A 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 � 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.

(This abstract was borrowed from another version of this item.)

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File URL: http://hdl.handle.net/10.1007/s00355-011-0604-8
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Article provided by Springer in its journal Social Choice and Welfare.

Volume (Year): 39 (2012)
Issue (Month): 2 (July)
Pages: 567-597

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Handle: RePEc:spr:sochwe:v:39:y:2012:i:2:p:567-597
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  1. 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).
  2. William Vickrey, 1961. "Counterspeculation, Auctions, And Competitive Sealed Tenders," Journal of Finance, American Finance Association, vol. 16(1), pages 8-37, 03.
  3. Berger André & Müller Rudolf & Naeemi Seyed Hossein, 2010. "Path-Monotonicity and Incentive Compatibility," Research Memorandum 035, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  4. 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.
  5. Gui Hongwei & Müller Rudolf & Vohra Rakesh, 2004. "Dominant Strategy Mechanisms with Multidimensional Types," Research Memorandum 047, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  6. 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.
  7. 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.
  8. 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.
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