The Implementation Duality - Georg Nöldeke; Larry Samuelson (University of Basel, Center of Business and Economics (WWZ), 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: C62; C78; D82; D86; 330; Implementation; Duality; Galois Connection; Imperfectly Transferable Utility; Principal-Agent Model; Two-Sided Matching