IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v140y2023icp33-49.html
   My bibliography  Save this article

An analytically solvable principal-agent model

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899825623000337
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.geb.2023.03.002?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Daniel L. McFadden & Mogens Fosgerau, 2012. "A theory of the perturbed consumer with general budgets," NBER Working Papers 17953, National Bureau of Economic Research, Inc.
    2. Andrew Caplin & Mark Dean & John Leahy, 2019. "Rational Inattention, Optimal Consideration Sets, and Stochastic Choice," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(3), pages 1061-1094.
    3. Filip Matêjka & Alisdair McKay, 2015. "Rational Inattention to Discrete Choices: A New Foundation for the Multinomial Logit Model," American Economic Review, American Economic Association, vol. 105(1), pages 272-298, January.
    4. Nestor Gandelman & Ruben Hernandez-Murillo, 2015. "Risk Aversion at the Country Level," Review, Federal Reserve Bank of St. Louis, vol. 97(1), pages 53-66.
    5. Grossman, Sanford J & Hart, Oliver D, 1983. "An Analysis of the Principal-Agent Problem," Econometrica, Econometric Society, vol. 51(1), pages 7-45, January.
    6. Drew Fudenberg & Ryota Iijima & Tomasz Strzalecki, 2015. "Stochastic Choice and Revealed Perturbed Utility," Econometrica, Econometric Society, vol. 83, pages 2371-2409, November.
    7. HOLMSTROM, Bengt, 1979. "Moral hazard and observability," LIDAM Reprints CORE 379, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Shun‐ichi Amari, 2021. "Information Geometry," International Statistical Review, International Statistical Institute, vol. 89(2), pages 250-273, August.
    9. Garrett, Daniel F. & Georgiadis, George & Smolin, Alex & Szentes, Balázs, 2023. "Optimal technology design," Journal of Economic Theory, Elsevier, vol. 209(C).
    10. Mattsson, Lars-Göran & Weibull, Jörgen W. & Lindberg, Per Olov, 2014. "Extreme values, invariance and choice probabilities," Transportation Research Part B: Methodological, Elsevier, vol. 59(C), pages 81-95.
    11. Andrew Caplin & Mark Dean & John Leahy, 2022. "Rationally Inattentive Behavior: Characterizing and Generalizing Shannon Entropy," Journal of Political Economy, University of Chicago Press, vol. 130(6), pages 1676-1715.
    12. Sims, Christopher A., 2003. "Implications of rational inattention," Journal of Monetary Economics, Elsevier, vol. 50(3), pages 665-690, April.
    13. Jewitt, Ian & Kadan, Ohad & Swinkels, Jeroen M., 2008. "Moral hazard with bounded payments," Journal of Economic Theory, Elsevier, vol. 143(1), pages 59-82, November.
    14. Mattsson, Lars-Goran & Weibull, Jorgen W., 2002. "Probabilistic choice and procedurally bounded rationality," Games and Economic Behavior, Elsevier, vol. 41(1), pages 61-78, October.
    15. Roy Allen & John Rehbeck, 2019. "Identification With Additively Separable Heterogeneity," Econometrica, Econometric Society, vol. 87(3), pages 1021-1054, May.
    16. Bengt Holmstrom, 1979. "Moral Hazard and Observability," Bell Journal of Economics, The RAND Corporation, vol. 10(1), pages 74-91, Spring.
    17. Tinessa, Fiore, 2021. "Closed-form random utility models with mixture distributions of random utilities: Exploring finite mixtures of qGEV models," Transportation Research Part B: Methodological, Elsevier, vol. 146(C), pages 262-288.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Flynn, Joel P. & Sastry, Karthik A., 2023. "Strategic mistakes," Journal of Economic Theory, Elsevier, vol. 212(C).
    2. Mogens Fosgerau & Emerson Melo & André de Palma & Matthew Shum, 2020. "Discrete Choice And Rational Inattention: A General Equivalence Result," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 61(4), pages 1569-1589, November.
    3. Roy Allen & John Rehbeck, 2021. "A Generalization of Quantal Response Equilibrium via Perturbed Utility," Games, MDPI, vol. 12(1), pages 1-16, March.
    4. Mensch, Jeffrey, 2021. "Rational inattention and the monotone likelihood ratio property," Journal of Economic Theory, Elsevier, vol. 196(C).
    5. Lindbeck, Assar & Weibull, Jörgen, 2020. "Delegation of investment decisions, and optimal remuneration of agents," European Economic Review, Elsevier, vol. 129(C).
    6. Bartosz Maćkowiak & Filip Matějka & Mirko Wiederholt, 2023. "Rational Inattention: A Review," Journal of Economic Literature, American Economic Association, vol. 61(1), pages 226-273, March.
    7. Hugo Hopenhayn & Arantxa Jarque, 2010. "Unobservable Persistent Productivity and Long Term Contracts," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 13(2), pages 333-349, April.
    8. Chade, Hector & Swinkels, Jeroen, 2020. "The moral hazard problem with high stakes," Journal of Economic Theory, Elsevier, vol. 187(C).
    9. Garrett, Daniel F. & Georgiadis, George & Smolin, Alex & Szentes, Balázs, 2023. "Optimal technology design," Journal of Economic Theory, Elsevier, vol. 209(C).
    10. Mogens Fosgerau & Dennis Kristensen, 2021. "Identification of a class of index models: A topological approach," The Econometrics Journal, Royal Economic Society, vol. 24(1), pages 121-133.
    11. Fabian Herweg & Daniel Muller & Philipp Weinschenk, 2010. "Binary Payment Schemes: Moral Hazard and Loss Aversion," American Economic Review, American Economic Association, vol. 100(5), pages 2451-2477, December.
    12. Florian Hoffmann & Roman Inderst & Marcus Opp, 2021. "Only Time Will Tell: A Theory of Deferred Compensation [Motivating Innovation in Newly Public Firms]," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 88(3), pages 1253-1278.
    13. Mogens Fosgerau & Julien Monardo & André de Palma, 2019. "The Inverse Product Differentiation Logit Model," Working Papers hal-02183411, HAL.
    14. Florian Hoffmann & Roman Inderst & Marcus Opp, 2022. "The Economics of Deferral and Clawback Requirements," Journal of Finance, American Finance Association, vol. 77(4), pages 2423-2470, August.
    15. Hector Chade, 2017. "Disentangling Moral Hazard and Adverse Selection," 2017 Meeting Papers 1537, Society for Economic Dynamics.
    16. Monte, Daniel & Linhares, Luis Henrique, 2023. "Stealth Startups, Clauses, and Add-ons: A Model of Strategic Obfuscation," MPRA Paper 115926, University Library of Munich, Germany.
    17. Matysková, Ludmila & Montes, Alfonso, 2023. "Bayesian persuasion with costly information acquisition," Journal of Economic Theory, Elsevier, vol. 211(C).
    18. Eric S. Chou & Chien-Lung Chen, 2015. "Can Agents Be Better Off with Pay Caps?," Scandinavian Journal of Economics, Wiley Blackwell, vol. 117(4), pages 1069-1090, October.
    19. Yoram Halevy & David Walker-Jones & Lanny Zrill, 2023. "Difficult Decisions," Working Papers tecipa-753, University of Toronto, Department of Economics.
    20. Martin Bustos, 2024. "Identification with Posterior-Separable Information Costs," Papers 2402.09789, arXiv.org.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:gamebe:v:140:y:2023:i:c:p:33-49. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622836 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.