Publication Date: March 2015
Revision Date: March 2018
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 Codes: C78, D82, D86