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Duality in Contracting


  • Peter Bardsley


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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    References listed on IDEAS

    1. Vohra,Rakesh V., 2011. "Mechanism Design," Cambridge Books, Cambridge University Press, number 9780521179461.
    2. Vohra,Rakesh V., 2011. "Mechanism Design," Cambridge Books, Cambridge University Press, number 9781107004368.
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    More about this item


    mechanism design; contract theory; duality; Fenchel transform; abstract convexity;

    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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