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An analytically solvable principal-agent model

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  • Mattsson, Lars-Göran
  • Weibull, Jörgen W.

Abstract

We analyze a principal-agent model with moral hazard where the principal is risk neutral while the agent is risk averse or risk neutral. The agent is free to choose any probability distribution over outcomes, where some distributions require more effort than others. The agent's effort-cost function is of “Legendre type” and satisfies an axiom of invariance under mergers of outcomes that are equally paid by the principal. We analyze a family of such effort-cost functions. For a canonical subclass of these, and arbitrary outcome spaces, the principal's contract problem allows for closed-form solutions. Optimal contracts then combine debt with a monotonic sharing rule for the surplus above a threshold chosen by the principal. When the agent is risk neutral, the contract boils down to a pure debt contract. For agents with unit degree of relative risk aversion, the surplus is divided in fixed shares.

Suggested Citation

  • Mattsson, Lars-Göran & Weibull, Jörgen W., 2023. "An analytically solvable principal-agent model," Games and Economic Behavior, Elsevier, vol. 140(C), pages 33-49.
    • Handle: RePEc:eee:gamebe:v:140:y:2023:i:c:p:33-49
    DOI: 10.1016/j.geb.2023.03.002
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    References listed on IDEAS

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    More about this item

    Keywords

    Principal-agent; Moral hazard; Hidden action; Optimal contract; Debt contract; Legendre; f-divergence; Kullback-Leibler;
    All these keywords.

    JEL classification:

    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law
    • G30 - Financial Economics - - Corporate Finance and Governance - - - General
    • J33 - Labor and Demographic Economics - - Wages, Compensation, and Labor Costs - - - Compensation Packages; Payment Methods
    • L14 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Transactional Relationships; Contracts and Reputation
    • M12 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Administration - - - Personnel Management; Executives; Executive Compensation
    • M52 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Personnel Economics - - - Compensation and Compensation Methods and Their Effects

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