Contracts with Private Cost per Unit-of-Effort

Tal Alon, Paul Dutting, Inbal Talgam-Cohen

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

16 Scopus citations

Abstract

Economic theory distinguishes between principal-agent settings in which the agent has a private type and settings in which the agent takes a hidden action. Many practical problems, however, involve aspects of both. For example, brand X may seek to hire an influencer Y to create sponsored content to be posted on social media platform Z. This problem has a hidden action component (the brand may not be able or willing to observe the amount of effort exerted by the influencer), but also a private type component (influencers may have different costs per unit-of-effort). This effort and cost per unit-of-effort perspective naturally leads to a principal-agent problem with hidden action and single-dimensional private type, which generalizes both the classic principal-agent hidden action model of contract theory a la Grossmann and Hart [1986] and the (procurement version) of single-dimensional mechanism design a la Myerson [1983]. A natural goal in this model is to design an incentive-compatible contract, which consist of an allocation rule that maps types to actions, and a payment rule that maps types to payments for the stochastic outcomes of the chosen action. Our main contribution is an LP-duality based characterization of implementable allocation rules for this model, which applies to both discrete and continuous types. This characterization shares important features of Myerson's celebrated characterization result, but also departs from it in significant ways. We present several applications, including a polynomial-time algorithm for finding the optimal contract with a constant number of actions. This in sharp contrast to recent work on hidden action problems with multi-dimensional private information, which has shown that the problem of computing an optimal contract for constant numbers of actions is APX-hard.

Original languageEnglish
Title of host publicationEC 2021 - Proceedings of the 22nd ACM Conference on Economics and Computation
PublisherAssociation for Computing Machinery, Inc
Pages52-69
Number of pages18
ISBN (Electronic)9781450385541
DOIs
StatePublished - 18 Jul 2021
Externally publishedYes
Event22nd ACM Conference on Economics and Computation, EC 2021 - Virtual, Online, Hungary
Duration: 18 Jul 202123 Jul 2021

Publication series

NameEC 2021 - Proceedings of the 22nd ACM Conference on Economics and Computation

Conference

Conference22nd ACM Conference on Economics and Computation, EC 2021
Country/TerritoryHungary
CityVirtual, Online
Period18/07/2123/07/21

Funding

FundersFunder number
Taub Family Foundation
Israel Science Foundation336/18

    Keywords

    • Myerson's theory
    • adverse selection
    • duality characterization
    • moral hazard
    • single-parameter

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