The Implementation Duality

69 Pages Posted: 6 Apr 2018

See all articles by Georg Nöldeke

Georg Nöldeke

University of Basel; University of Basel

Larry Samuelson

Yale University - Department of Economics; Yale University - Cowles Foundation

Multiple version iconThere are 3 versions of this paper

Date Written: March 29, 2018

Abstract

Conjugate duality relationships are pervasive in matching and implementation problems and provide much of the structure essential for characterizing stable matches and implementable allocations in models with quasilinear (or transferable) utility. In the absence of quasilinearity, a more abstract duality relationship, known as a Galois connection, takes the role of (generalized) conjugate duality. While weaker, this duality relationship still induces substantial structure. We show that this structure can be used to extend existing results for, and gain new insights into, adverse-selection principal-agent problems and two-sided matching problems without quasilinearity.

Keywords: Implementation, Conjugate Duality, Galois Connection, Optimal Transport, Imperfectly Transferable Utility, Principal-Agent Model

JEL Classification: C78, D82, D86

Suggested Citation

Nöldeke, Georg and Samuelson, Larry, The Implementation Duality (March 29, 2018). Cowles Foundation Discussion Paper No. 1993R2. Available at SSRN: https://ssrn.com/abstract=3155345 or http://dx.doi.org/10.2139/ssrn.3155345

Georg Nöldeke

University of Basel ( email )

Peter Merian-Weg 6
Basel, 4002
Switzerland

HOME PAGE: http://sites.google.com/site/georgnoldeke/

University of Basel ( email )

Peter Merian-Weg 6
Basel, 4002
Switzerland

HOME PAGE: http://sites.google.com/site/georgnoldeke/

Larry Samuelson (Contact Author)

Yale University - Department of Economics ( email )

28 Hillhouse Ave
New Haven, CT 06520-8268
United States

Yale University - Cowles Foundation

Box 208281
New Haven, CT 06520-8281
United States

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