TY - JOUR

T1 - Dominant strategy implementation with a convex product space of valuations

AU - Cuff, Katherine

AU - Hong, Sunghoon

AU - Schwartz, Jesse A.

AU - Wen, Quan

AU - Weymark, John A.

PY - 2012/7

Y1 - 2012/7

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84863544067&partnerID=8YFLogxK

U2 - 10.1007/s00355-011-0604-8

DO - 10.1007/s00355-011-0604-8

M3 - Article

AN - SCOPUS:84863544067

SN - 0176-1714

VL - 39

SP - 567

EP - 597

JO - Social Choice and Welfare

JF - Social Choice and Welfare

IS - 2-3

ER -