Social Choice and Welfare

, Volume 39, Issue 2–3, pp 567–597 | Cite as

Dominant strategy implementation with a convex product space of valuations

  • Katherine Cuff
  • Sunghoon Hong
  • Jesse A. Schwartz
  • Quan Wen
  • John A. Weymark
Original Paper

Abstract

A necessary and sufficient condition for dominant strategy implementability when preferences are quasilinear is that, for every individual i and every 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), pp 286–293, 2005) 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 full-dimensional 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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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Katherine Cuff
    • 1
  • Sunghoon Hong
    • 2
  • Jesse A. Schwartz
    • 3
  • Quan Wen
    • 2
  • John A. Weymark
    • 2
  1. 1.Department of EconomicsMcMaster UniversityHamiltonCanada
  2. 2.Department of EconomicsVanderbilt UniversityNashvilleUSA
  3. 3.Department of EconomicsFinance, and Quantitative Analysis, Kennesaw State UniversityKennesawUSA

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