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The Implementation Duality

Author

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  • Nöldeke, Georg

    () (University of Basel)

  • Samuelson, Larry

Abstract

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.

Suggested Citation

  • Nöldeke, Georg & Samuelson, Larry, 2015. "The Implementation Duality," Working papers 2015/01, Faculty of Business and Economics - University of Basel.
  • Handle: RePEc:bsl:wpaper:2015/01
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    References listed on IDEAS

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    1. Kahn Charles M., 1993. "Existence and Characterization of Optimal Employment Contracts on a Continuous State Space," Journal of Economic Theory, Elsevier, vol. 59(1), pages 122-144, February.
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    Cited by:

    1. Pierre-Andr'e Chiappori & Robert McCann & Brendan Pass, 2016. "Multidimensional matching," Papers 1604.05771, arXiv.org.

    More about this item

    Keywords

    Implementation; Duality; Galois Connection; Imperfectly Transferable Utility; Principal-Agent Model; Two-Sided Matching;

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • 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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