The Implementation Duality
56 Pages Posted: 18 Mar 2015
Date Written: March 16, 2015
We use the theory of abstract convexity to study adverse-selection principal-agent problems and two-sided matching problems, departing from much of the literature by not requiring quasilinear utility. We formulate and characterize a basic underlying implementation duality. We show how this duality can be used to obtain a sharpening of the taxation principle, to obtain a general existence result for solutions to the principal-agent problem, to show that (just as in the quasilinear case) all increasing decision functions are implementable under a single crossing condition, and to obtain an existence result for stable outcomes featuring positive assortative matching in a matching model.
Keywords: Implementation, Duality, Galois connection, Imperfectly transferable utility, Principal-agent model, Two-sided matching
JEL Classification: C62, C78, D82, D86
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