Dominant strategy implementation with a convex product space of valuations

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 …