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Article
Dominant Strategy Implementation with a Convex Product Space of Valuations
Faculty Articles
  • Katherine Cuff, McMaster University
  • Sunghoon Hong, Vanderbilt University
  • Jesse A. Schwartz, Kennesaw State University
  • Quan Wen, Vanderbilt University
  • John A. Weymark, Vanderbilt University
Document Type
Article
Publication Date
7-1-2012
Disciplines
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.

Citation Information
Katherine Cuff, et al. "Dominant Strategy Implementation with a Convex Product Space of Valuations." Social Choice and Welfare 39.2-3 (2012): 567-97. Print.