IDEAS home Printed from https://ideas.repec.org/a/the/publsh/3660.html
   My bibliography  Save this article

Optimal contracts with a risk-taking agent

Author

Listed:
  • Barron, Daniel

    (Kellogg School of Management, Northwestern University)

  • Georgiadis, George

    (Kellogg School of Management, Northwestern University)

  • Swinkels, Jeroen M.

    (Kellogg School of Management, Northwestern University)

Abstract

Consider an agent who can costlessly add mean-preserving noise to his output. To deter such risk-taking, the principal optimally offers a contract that makes the agent's utility concave in output. If the agent is risk-neutral and protected by limited liability, this concavity constraint binds and so linear contracts maximize profit. If the agent is risk averse, the concavity constraint might bind for some outputs but not others. We characterize the unique profit-maximizing contract and show how deterring risk-taking affects the insurance-incentive tradeoff. Our logic extends to costly risk-taking and to dynamic settings where the agent can shift output over time.

Suggested Citation

  • Barron, Daniel & Georgiadis, George & Swinkels, Jeroen M., 2020. "Optimal contracts with a risk-taking agent," Theoretical Economics, Econometric Society, vol. 15(2), May.
    • Handle: RePEc:the:publsh:3660
    as

    Download full text from publisher

    File URL: http://econtheory.org/ojs/index.php/te/article/viewFile/20200715/27024/783
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. repec:hal:journl:tel-01178107 is not listed on IDEAS
    2. Paul Oyer, 1998. "Fiscal Year Ends and Nonlinear Incentive Contracts: The Effect on Business Seasonality," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 113(1), pages 149-185.
    3. Emir Kamenica & Matthew Gentzkow, 2011. "Bayesian Persuasion," American Economic Review, American Economic Association, vol. 101(6), pages 2590-2615, October.
    4. Joaquín Poblete & Daniel Spulber, 2012. "The form of incentive contracts: agency with moral hazard, risk neutrality, and limited liability," RAND Journal of Economics, RAND Corporation, vol. 43(2), pages 215-234, June.
    5. Igor Makarov & Guillaume Plantin, 2015. "Rewarding Trading Skills without Inducing Gambling," Journal of Finance, American Finance Association, vol. 70(3), pages 925-962, June.
    6. Debraj Ray & Arthur Robson, 2012. "Status, Intertemporal Choice, and Risk‐Taking," Econometrica, Econometric Society, vol. 80(4), pages 1505-1531, July.
    7. Richard A. Lambert, 1986. "Executive Effort and Selection of Risky Projects," RAND Journal of Economics, The RAND Corporation, vol. 17(1), pages 77-88, Spring.
    8. Innes, Robert D., 1990. "Limited liability and incentive contracting with ex-ante action choices," Journal of Economic Theory, Elsevier, vol. 52(1), pages 45-67, October.
    9. Malcomson James M, 2009. "Principal and Expert Agent," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 9(1), pages 1-36, May.
    10. Rui de Figueiredo & Evan Rawley & Orie Shelef, 2014. "Bad Bets: Excessive Risk Taking, Convex Incentives, and Performance," Discussion Papers 13-002, Stanford Institute for Economic Policy Research.
    11. Elie Matta & Paul W. Beamish, 2008. "The accentuated CEO career horizon problem: evidence from international acquisitions," Post-Print hal-00486653, HAL.
    12. Chevalier, Judith & Ellison, Glenn, 1997. "Risk Taking by Mutual Funds as a Response to Incentives," Journal of Political Economy, University of Chicago Press, vol. 105(6), pages 1167-1200, December.
    13. Hazhir Rahmandad & Rebecca Henderson & Nelson P. Repenning, 2018. "Making the Numbers? “Short Termism” and the Puzzle of Only Occasional Disaster," Management Science, INFORMS, vol. 64(3), pages 1328-1347, March.
    14. James A. Mirrlees, 1976. "The Optimal Structure of Incentives and Authority Within an Organization," Bell Journal of Economics, The RAND Corporation, vol. 7(1), pages 105-131, Spring.
    15. Luis Garicano & Luis Rayo, 2016. "Why Organizations Fail: Models and Cases," Journal of Economic Literature, American Economic Association, vol. 54(1), pages 137-192, March.
    16. Hellwig, Martin F., 2009. "A reconsideration of the Jensen-Meckling model of outside finance," Journal of Financial Intermediation, Elsevier, vol. 18(4), pages 495-525, October.
    17. Galina Vereshchagina & Hugo A. Hopenhayn, 2009. "Risk Taking by Entrepreneurs," American Economic Review, American Economic Association, vol. 99(5), pages 1808-1830, December.
    18. Florian Ederer & Richard Holden & Margaret Meyer, 2018. "Gaming and strategic opacity in incentive provision," RAND Journal of Economics, RAND Corporation, vol. 49(4), pages 819-854, December.
    19. Holmstrom, Bengt & Milgrom, Paul, 1987. "Aggregation and Linearity in the Provision of Intertemporal Incentives," Econometrica, Econometric Society, vol. 55(2), pages 303-328, March.
    20. Palomino, Frederic & Prat, Andrea, 2003. "Risk Taking and Optimal Contracts for Money Managers," RAND Journal of Economics, The RAND Corporation, vol. 34(1), pages 113-137, Spring.
    21. Brav, Alon & Graham, John R. & Harvey, Campbell R. & Michaely, Roni, 2005. "Payout policy in the 21st century," Journal of Financial Economics, Elsevier, vol. 77(3), pages 483-527, September.
    22. Bengt Holmstrom & Joan Ricart i Costa, 1986. "Managerial Incentives and Capital Management," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 101(4), pages 835-860.
    23. Elie Matta & Paul W. Beamish, 2008. "The accentuated CEO career horizon problem: evidence from international acquisitions," Strategic Management Journal, Wiley Blackwell, vol. 29(7), pages 683-700, July.
    24. Jewitt, Ian, 1988. "Justifying the First-Order Approach to Principal-Agent Problems," Econometrica, Econometric Society, vol. 56(5), pages 1177-1190, September.
    25. Jensen, Michael C. & Meckling, William H., 1976. "Theory of the firm: Managerial behavior, agency costs and ownership structure," Journal of Financial Economics, Elsevier, vol. 3(4), pages 305-360, October.
    26. Ian Larkin, 2014. "The Cost of High-Powered Incentives: Employee Gaming in Enterprise Software Sales," Journal of Labor Economics, University of Chicago Press, vol. 32(2), pages 199-227.
    27. Robson, Arthur J, 1992. "Status, the Distribution of Wealth, Private and Social Attitudes to Risk," Econometrica, Econometric Society, vol. 60(4), pages 837-857, July.
    28. 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.
    29. Marina Halac & Andrea Prat, 2016. "Managerial Attention and Worker Performance," American Economic Review, American Economic Association, vol. 106(10), pages 3104-3132, October.
    30. Sylvain Chassang, 2013. "Calibrated Incentive Contracts," Econometrica, Econometric Society, vol. 81(5), pages 1935-1971, September.
    31. Igor Makarov & Guillaume Plantin, 2015. "Rewarding Trading Skills Without Inducing Gambling," SciencePo Working papers hal-01178107, HAL.
    32. Peter Diamond, 1998. "Managerial Incentives: On the Near Linearity of Optimal Compensation," Journal of Political Economy, University of Chicago Press, vol. 106(5), pages 931-957, October.
    33. Moroni, Sofia & Swinkels, Jeroen, 2014. "Existence and non-existence in the moral hazard problem," Journal of Economic Theory, Elsevier, vol. 150(C), pages 668-682.
    34. Igor Makarov & Guillaume Plantin, 2015. "Rewarding Trading Skills Without Inducing Gambling," SciencePo Working papers Main hal-01178107, HAL.
    35. Oliver Hart & Bengt Holmstrom, 1986. "The Theory of Contracts," Working papers 418, Massachusetts Institute of Technology (MIT), Department of Economics.
    36. Gabriel Carroll, 2015. "Robustness and Linear Contracts," American Economic Review, American Economic Association, vol. 105(2), pages 536-563, February.
    37. Brown, Keith C & Harlow, W V & Starks, Laura T, 1996. "Of Tournaments and Temptations: An Analysis of Managerial Incentives in the Mutual Fund Industry," Journal of Finance, American Finance Association, vol. 51(1), pages 85-110, March.
    38. repec:hal:spmain:info:hdl:2441/2lk3hracjf8vip44o7neiujmv7 is not listed on IDEAS
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Boleslavsky, Raphael & Taylor, Curtis R., 2024. "Make it 'til you fake it," Journal of Economic Theory, Elsevier, vol. 217(C).
    2. Qu, Yingge & Kumar, V. & Zhao, Yi, 2023. "A dynamic model of the contract length and early termination: The roles of technology evolution and pricing strategy," Journal of Business Research, Elsevier, vol. 167(C).
    3. Weinschenk, Philipp, 2024. "Incentives and performance under two-dimensional moral hazard," Journal of Economic Behavior & Organization, Elsevier, vol. 225(C), pages 107-115.
    4. Onjewu, Adah-Kole Emmanuel & Walton, Nigel & Koliousis, Ioannis, 2023. "Blockchain agency theory," Technological Forecasting and Social Change, Elsevier, vol. 191(C).
    5. Keenan, Donald C. & Snow, Arthur, 2024. "Full downside risk aversion," Mathematical Social Sciences, Elsevier, vol. 131(C), pages 93-101.

    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. Georgiadis, George & Szentes, Balázs, 2020. "Optimal monitoring design," LSE Research Online Documents on Economics 104062, London School of Economics and Political Science, LSE Library.
    2. Balmaceda, Felipe & Balseiro, Santiago R. & Correa, José R. & Stier-Moses, Nicolás E., 2016. "Bounds on the welfare loss from moral hazard with limited liability," Games and Economic Behavior, Elsevier, vol. 95(C), pages 137-155.
    3. Palomino, Frederic & Prat, Andrea, 2003. "Risk Taking and Optimal Contracts for Money Managers," RAND Journal of Economics, The RAND Corporation, vol. 34(1), pages 113-137, Spring.
    4. Eduard Marinov, 2016. "The 2016 Nobel Prize in Economics," Economic Thought journal, Bulgarian Academy of Sciences - Economic Research Institute, issue 6, pages 97-149.
    5. Aubrey Clark & Giovanni Reggiani, 2021. "Contracts for acquiring information," Papers 2103.03911, arXiv.org.
    6. Inés Macho-Stadler & David Pérez-Castrillo, 2018. "Moral hazard: Base models and two extensions," Chapters, in: Luis C. Corchón & Marco A. Marini (ed.), Handbook of Game Theory and Industrial Organization, Volume I, chapter 16, pages 453-485, Edward Elgar Publishing.
    7. George Georgiadis & Balazs Szentes, 2020. "Optimal Monitoring Design," Econometrica, Econometric Society, vol. 88(5), pages 2075-2107, September.
    8. Committee, Nobel Prize, 2016. "Oliver Hart and Bengt Holmström: Contract Theory," Nobel Prize in Economics documents 2016-1, Nobel Prize Committee.
    9. repec:eee:labchp:v:3:y:1999:i:pb:p:2373-2437 is not listed on IDEAS
    10. Ron Kaniel & Péter Kondor, 2013. "The Delegated Lucas Tree," The Review of Financial Studies, Society for Financial Studies, vol. 26(4), pages 929-984.
    11. Oindrila Dey & Swapnendu Banerjee, 2022. "Incentives, Status and Thereafter: A Critical Survey," South Asian Journal of Macroeconomics and Public Finance, , vol. 11(1), pages 95-115, June.
    12. Malcomson James M, 2009. "Principal and Expert Agent," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 9(1), pages 1-36, May.
    13. Bengt Holmström, 2017. "Pay for Performance and Beyond," American Economic Review, American Economic Association, vol. 107(7), pages 1753-1777, July.
    14. James M. Malcomson, 2011. "Do Managers with Limited Liability Take More Risky Decisions? An Information Acquisition Model," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 20(1), pages 83-120, March.
    15. Felipe Balmaceda, 2020. "Contracting with moral hazard, adverse selection and risk neutrality: when does one size fit all?," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(2), pages 601-637, June.
    16. Rui de Figueiredo & Evan Rawley & Orie Shelef, 2014. "Bad Bets: Excessive Risk Taking, Convex Incentives, and Performance," Discussion Papers 13-002, Stanford Institute for Economic Policy Research.
    17. Citci, Sadettin Haluk & Inci, Eren, 2016. "The masquerade ball of the CEOs and the mask of excessive risk," Economic Modelling, Elsevier, vol. 58(C), pages 383-393.
    18. Nicolas Quérou & Antoine Soubeyran & Raphael Soubeyran, 2020. "Contracting under unverifiable monetary costs," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 29(4), pages 892-909, October.
    19. He, Zhiguo & Xiong, Wei, 2013. "Delegated asset management, investment mandates, and capital immobility," Journal of Financial Economics, Elsevier, vol. 107(2), pages 239-258.
    20. Alexei Tchistyi, 2012. "Risking Other People's Money: Gambling, Limited Liability, and Optimal Incentives," 2012 Meeting Papers 1091, Society for Economic Dynamics.
    21. Mario Tirelli, 2021. "On the optimal investment finance of small businesses," Small Business Economics, Springer, vol. 56(4), pages 1639-1665, April.

    More about this item

    Keywords

    Risk-taking; contract theory; gaming;
    All these keywords.

    JEL classification:

    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics
    • M5 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Personnel Economics
    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law

    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:the:publsh:3660. 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: Martin J. Osborne (email available below). General contact details of provider: http://econtheory.org .

    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.