Dominant Strategy Implementability and Zero Length Cycles

37 Pages Posted: 24 May 2017 Last revised: 19 May 2018

See all articles by Paul H. Edelman

Paul H. Edelman

Vanderbilt University - Law School

John A. Weymark

Vanderbilt University - College of Arts and Science - Department of Economics

Date Written: May 15, 2018

Abstract

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

Edelman, Paul H. and Weymark, John A., Dominant Strategy Implementability and Zero Length Cycles (May 15, 2018). Available at SSRN: https://ssrn.com/abstract=2972177 or http://dx.doi.org/10.2139/ssrn.2972177

Paul H. Edelman (Contact Author)

Vanderbilt University - Law School ( email )

131 21st Avenue South
Nashville, TN 37203-1181
United States
615-322-0990 (Phone)
615-322-6631 (Fax)

John A. Weymark

Vanderbilt University - College of Arts and Science - Department of Economics ( email )

Box 1819 Station B
Nashville, TN 37235
United States
1-615-322-1437 (Phone)
1-615-343-8495 (Fax)

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