Dominant strategy implementation with a convex product space of valuations
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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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