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Duality in Contracting

Author

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  • Peter Bardsley

Abstract

In a linear contracting environment the Fenchel transform provides a complete duality between the contract and the information rent. Through an appropriate generalised convexity this can be extended to provide a complete duality in the supermodular quasilinear contracting environment that covers the majority of applications. Using this framework, we provide a complete characterization of the allocation correspondences that can be implemented by a principal in this environment. We also address the question of when an allocation can be implemented by a menu of simple contracts. Along the way, a supermodular envelope theorem is proved, somewhat different in nature to the Milgrom Segal result.

Suggested Citation

  • Peter Bardsley, 2012. "Duality in Contracting," Department of Economics - Working Papers Series 1141, The University of Melbourne.
    • Handle: RePEc:mlb:wpaper:1141
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    File URL: http://fbe.unimelb.edu.au/__data/assets/pdf_file/0008/784304/1141.pdf
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    References listed on IDEAS

    as
    1. Vohra,Rakesh V., 2011. "Mechanism Design," Cambridge Books, Cambridge University Press, number 9781107004368, January.
    2. Border, Kim C, 1991. "Implementation of Reduced Form Auctions: A Geometric Approach," Econometrica, Econometric Society, vol. 59(4), pages 1175-1187, July.
    3. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
    4. William P. Rogerson, 1987. "On the Optimality of Menus of Linear Contracts," Discussion Papers 714, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    5. Krishna, Vijay & Maenner, Eliot, 2001. "Convex Potentials with an Application to Mechanism Design," Econometrica, Econometric Society, vol. 69(4), pages 1113-1119, July.
    6. Vohra,Rakesh V., 2011. "Mechanism Design," Cambridge Books, Cambridge University Press, number 9780521179461, January.
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    Cited by:

    1. Georg Nöldeke & Larry Samuelson, 2018. "The Implementation Duality," Econometrica, Econometric Society, vol. 86(4), pages 1283-1324, July.

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    More about this item

    Keywords

    mechanism design; contract theory; duality; Fenchel transform; abstract convexity;
    All these keywords.

    JEL classification:

    • 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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