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The Implementation Duality

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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.

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  • Noldeke, Georg & Larry Samuelson, 2015. "The Implementation Duality," Cowles Foundation Discussion Papers 1993R2, Cowles Foundation for Research in Economics, Yale University, revised Mar 2018.
    • Handle: RePEc:cwl:cwldpp:1993r2
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    More about this item

    Keywords

    Implementation; Conjugate Duality; Galois Connection; Optimal Transport; Imperfectly Transferable Utility; Principal-Agent Model;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law

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