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The Implementation Duality

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  • Georg Nöldeke
  • Larry Samuelson

Abstract

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.

Suggested Citation

  • Georg Nöldeke & Larry Samuelson, 2018. "The Implementation Duality," Econometrica, Econometric Society, vol. 86(4), pages 1283-1324, July.
    • Handle: RePEc:wly:emetrp:v:86:y:2018:i:4:p:1283-1324
    DOI: 10.3982/ECTA13307
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    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.
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    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

    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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