IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1710.00377.html
   My bibliography  Save this paper

A Note on the Multi-Agent Contracts in Continuous Time

Author

Listed:
  • Qi Luo
  • Romesh Saigal

Abstract

Dynamic contracts with multiple agents is a classical decentralized decision-making problem with asymmetric information. In this paper, we extend the single-agent dynamic incentive contract model in continuous-time to a multi-agent scheme in finite horizon and allow the terminal reward to be dependent on the history of actions and incentives. We first derive a set of sufficient conditions for the existence of optimal contracts in the most general setting and conditions under which they form a Nash equilibrium. Then we show that the principal's problem can be converted to solving Hamilton-Jacobi-Bellman (HJB) equation requiring a static Nash equilibrium. Finally, we provide a framework to solve this problem by solving partial differential equations (PDE) derived from backward stochastic differential equations (BSDE).

Suggested Citation

  • Qi Luo & Romesh Saigal, 2017. "A Note on the Multi-Agent Contracts in Continuous Time," Papers 1710.00377, arXiv.org, revised Oct 2017.
    • Handle: RePEc:arx:papers:1710.00377
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1710.00377
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. repec:cwl:cwldpp:1953rrr is not listed on IDEAS
    2. repec:cwl:cwldpp:1953rr is not listed on IDEAS
    3. Bergemann, Dirk & Strack, Philipp, 2015. "Dynamic revenue maximization: A continuous time approach," Journal of Economic Theory, Elsevier, vol. 159(PB), pages 819-853.
    4. Fudenberg, Drew & Holmstrom, Bengt & Milgrom, Paul, 1990. "Short-term contracts and long-term agency relationships," Journal of Economic Theory, Elsevier, vol. 51(1), pages 1-31, June.
    5. Stephen E. Spear & Sanjay Srivastava, 1987. "On Repeated Moral Hazard with Discounting," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(4), pages 599-617.
    6. Holmstrom, Bengt & Milgrom, Paul, 1987. "Aggregation and Linearity in the Provision of Intertemporal Incentives," Econometrica, Econometric Society, vol. 55(2), pages 303-328, March.
    7. Romuald Elie & Dylan Possamai, 2016. "Contracting theory with competitive interacting agents," Papers 1605.08099, arXiv.org.
    8. Oliver D. Hart & Jean Tirole, 1988. "Contract Renegotiation and Coasian Dynamics," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 55(4), pages 509-540.
    9. Williams, Noah, 2015. "A solvable continuous time dynamic principal–agent model," Journal of Economic Theory, Elsevier, vol. 159(PB), pages 989-1015.
    10. Rogerson, William P, 1985. "Repeated Moral Hazard," Econometrica, Econometric Society, vol. 53(1), pages 69-76, January.
    11. Yuliy Sannikov, 2008. "A Continuous-Time Version of the Principal-Agent Problem," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(3), pages 957-984.
    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. Luo, Qi & Saigal, Romesh & Chen, Zhibin & Yin, Yafeng, 2019. "Accelerating the adoption of automated vehicles by subsidies: A dynamic games approach," Transportation Research Part B: Methodological, Elsevier, vol. 129(C), pages 226-243.

    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. Guillermo Alonso Alvarez & Erhan Bayraktar & Ibrahim Ekren & Liwei Huang, 2024. "Sequential optimal contracting in continuous time," Papers 2411.04262, arXiv.org.
    2. Chang-Koo Chi & Kyoung Jin Choi, 2017. "The impact of firm size on dynamic incentives and investment," RAND Journal of Economics, RAND Corporation, vol. 48(1), pages 147-177, March.
    3. Giat, Yahel & Subramanian, Ajay, 2013. "Dynamic contracting under imperfect public information and asymmetric beliefs," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2833-2861.
    4. Florin c{S}abac, 2007. "Dynamic Agency with Renegotiation and Managerial Tenure," Management Science, INFORMS, vol. 53(5), pages 849-864, May.
    5. Abreu, Dilip & Milgrom, Paul & Pearce, David, 1991. "Information and Timing in Repeated Partnerships," Econometrica, Econometric Society, vol. 59(6), pages 1713-1733, November.
    6. Eduardo Abi Jaber & St'ephane Villeneuve, 2022. "Gaussian Agency problems with memory and Linear Contracts," Papers 2209.10878, arXiv.org.
    7. Zhiguo He & Bin Wei & Jianfeng Yu & Feng Gao, 2017. "Optimal Long-Term Contracting with Learning," The Review of Financial Studies, Society for Financial Studies, vol. 30(6), pages 2006-2065.
    8. Qi Luo & Romesh Saigal, 2020. "Dynamic Multiagent Incentive Contracts: Existence, Uniqueness, and Implementation," Mathematics, MDPI, vol. 9(1), pages 1-17, December.
    9. Garrett, Daniel F. & Pavan, Alessandro, 2015. "Dynamic managerial compensation: A variational approach," Journal of Economic Theory, Elsevier, vol. 159(PB), pages 775-818.
    10. Nadide Banu Olcay, 2016. "Dynamic incentive contracts with termination threats," Review of Economic Design, Springer;Society for Economic Design, vol. 20(4), pages 255-288, December.
    11. Sabac, Florin, 2008. "Dynamic incentives and retirement," Journal of Accounting and Economics, Elsevier, vol. 46(1), pages 172-200, September.
    12. George-Marios Angeletos & Alessandro Pavan, 2007. "Socially Optimal Coordination: Characterization and Policy Implications," Journal of the European Economic Association, MIT Press, vol. 5(2-3), pages 585-593, 04-05.
    13. Daniel Garrett & Alessandro Pavan, 2009. "Dynamic Managerial Compensation: a Mechanism Design Approach," Carlo Alberto Notebooks 127, Collegio Carlo Alberto.
    14. Anderson, Ronald W. & Bustamante, Maria Cecilia & Guibaud, Stéphane & Zervos, Mihail, 2018. "Agency, firm growth, and managerial turnover," LSE Research Online Documents on Economics 68784, London School of Economics and Political Science, LSE Library.
    15. LiCalzi, Marco & Pavan, Alessandro, 2005. "Tilting the supply schedule to enhance competition in uniform-price auctions," European Economic Review, Elsevier, vol. 49(1), pages 227-250, January.
    16. Eduardo Abi Jaber & Stéphane Villeneuve, 2022. "Gaussian Agency problems with memory and Linear Contracts," Working Papers hal-03783062, HAL.
    17. Francesc Dilmé & Daniel F. Garrett, 2023. "Relational Contracts: Public versus Private Savings," Econometrica, Econometric Society, vol. 91(3), pages 1025-1075, May.
    18. Bergemann, Dirk & Pavan, Alessandro, 2015. "Introduction to Symposium on Dynamic Contracts and Mechanism Design," Journal of Economic Theory, Elsevier, vol. 159(PB), pages 679-701.
    19. Karaivanov, Alexander K. & Martin, Fernando M., 2018. "Markov-perfect risk sharing, moral hazard and limited commitment," Journal of Economic Dynamics and Control, Elsevier, vol. 94(C), pages 1-23.
    20. Patrick Bolton & Neng Wang & Jinqiang Yang, 2019. "Optimal Contracting, Corporate Finance, and Valuation with Inalienable Human Capital," Journal of Finance, American Finance Association, vol. 74(3), pages 1363-1429, June.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:arx:papers:1710.00377. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.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.