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The Implementation Duality

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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.

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  • Noldeke, Georg & Larry Samuelson, 2015. "The Implementation Duality," Cowles Foundation Discussion Papers 1993, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1993
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    2. Chambers, Christopher P. & Miller, Alan D. & Yenmez, M. Bumin, 2020. "Closure and preferences," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 161-166.
    3. Fernando Tohm'e, 2023. "Dynamic Arrangements in Economic Theory: Level-Agnostic Representations," Papers 2309.06383, arXiv.org.
    4. Demuynck, Thomas & Potoms, Tom, 2020. "Weakening transferable utility: The case of non-intersecting Pareto curves," Journal of Economic Theory, Elsevier, vol. 188(C).
    5. Akira Matsushita & Kei Ikegami & Kyohei Okumura & Yoji Tomita & Atsushi Iwasaki, 2022. "Regulating Matching Markets with Constraints: Data-driven Taxation," Papers 2205.14387, arXiv.org, revised Mar 2023.
    6. Tohmé Fernando, 2023. "Dynamic Arrangements in Economic Theory: Level-Agnostic Representations," Asociación Argentina de Economía Política: Working Papers 4694, Asociación Argentina de Economía Política.
    7. Fernando Tohmé, 2023. "Dynamic Arrangements in Economic Theory: Level-Agnostic Representation," Working Papers 274, Red Nacional de Investigadores en Economía (RedNIE).
    8. Pierre-Andr'e Chiappori & Robert McCann & Brendan Pass, 2016. "Multidimensional matching," Papers 1604.05771, arXiv.org.
    9. Baisa, Brian, 2020. "Efficient multi-unit auctions for normal goods," Theoretical Economics, Econometric Society, vol. 15(1), January.
    10. Alfred Galichon & Larry Samuelson & Lucas Vernet, 2022. "The Existence of Equilibrium Flows," SciencePo Working papers Main hal-03936063, HAL.
    11. Malik, Komal & Mishra, Debasis, 2021. "Pareto efficient combinatorial auctions: Dichotomous preferences without quasilinearity," Journal of Economic Theory, Elsevier, vol. 191(C).
    12. Alfred Galichon & Larry Samuelson & Lucas Vernet, 2022. "The Existence of Equilibrium Flows," Working Papers hal-03936063, HAL.
    13. Alfred Galichon & Larry Samuelson & Lucas Vernet, 2022. "Monotone Comparative Statics for Equilibrium Problems," SciencePo Working papers Main hal-03936102, HAL.
    14. Esteban Peralta, 2022. "Local stability constraints," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(2), pages 273-281, October.
    15. Carlier, Guillaume & Zhang, Kelvin Shuangjian, 2020. "Existence of solutions to principal–agent problems with adverse selection under minimal assumptions," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 64-71.
    16. Alexander V. Kolesnikov & Fedor Sandomirskiy & Aleh Tsyvinski & Alexander P. Zimin, 2022. "Beckmann's approach to multi-item multi-bidder auctions," Papers 2203.06837, arXiv.org, revised Sep 2022.
    17. Yannai A. Gonczarowski & Scott Duke Kominers & Ran I. Shorrer, 2019. "To Infinity and Beyond: A General Framework for Scaling Economic Theories," Papers 1906.10333, arXiv.org, revised Apr 2023.
    18. Alfred Galichon & Larry Samuelson & Lucas Vernet, 2022. "Monotone Comparative Statics for Equilibrium Problems," Working Papers hal-03936102, HAL.
    19. Alfred Galichon & Larry Samuelson & Lucas Vernet, 2022. "The Existence of Equilibrium Flows," Papers 2209.04426, arXiv.org.
    20. Xinyang Wang, 2020. "Cooperation in Small Groups -- an Optimal Transport Approach," Papers 2005.11244, arXiv.org.
    21. Ruodu Wang & Zhenyuan Zhang, 2022. "Simultaneous Optimal Transport," Papers 2201.03483, arXiv.org, revised May 2023.
    22. Alfred Galichon & Larry Samuelson & Lucas Vernet, 2022. "Monotone Comparative Statics for Equilibrium Problems," Papers 2207.06731, arXiv.org.
    23. Alfred Galichon & Robert McCann, 2019. "Special Issue: Optimal Transportation, Equilibrium, and Applications to Economics," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(2), pages 345-347, March.
    24. Kelvin Shuangjian Zhang, 2019. "Existence in multidimensional screening with general nonlinear preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(2), pages 463-485, March.

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    More about this item

    Keywords

    Implementation; Duality; Galois connection; Imperfectly transferable utility; Principal-agent model; Two-sided matching;
    All these keywords.

    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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