Dominant Strategy Implementability and Zero Length Cycles
37 Pages Posted: 24 May 2017 Last revised: 19 May 2018
Date Written: May 15, 2018
Necessary conditions for dominant strategy implementability of an allocation function on a restricted type space are identified when utilities are quasilinear and the set of alternatives is finite. For any one-person mechanism obtained by fixing the other individuals’ types, the geometry of the partition of the type space into subsets that are allocated the same alternative is used to identify situations in which it is necessary for all of the cycle lengths in the corresponding allocation graph to be zero. It is shown that when all cycle lengths are zero, the set of all implementing payment functions can be characterized and computed quite simply using the lengths of the directed arcs between pairs of nodes in the allocation graph.
Keywords: Dominant Strategy Incentive Compatibility, Implementation Theory, Mechanism Design, Roberts' Theorem, Rochet's Theorem
JEL Classification: D71, D82
Suggested Citation: Suggested Citation