Dominant Strategy Implementation with a Convex Product Space of Valuations
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Date
2011
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Vanderbilt University
Abstract
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.
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Keywords
2-cycle condition, dominant strategy implementation, mechanism design, revenue equivalence, Rockafellar-Rochet Theorem, Saks-Yu Theorem competition, JEL Classification Number: D44, JEL Classification Number: D71, JEL Classification Number: D82