IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2511.19838.html

Dynamic Reward Design

Author

Listed:
  • Yijun Liu

Abstract

We study a dynamic mechanism design problem with limited liability. A principal hires an agent to work over a finite horizon. The agent's costs are i.i.d. across periods and privately known, while his working status is publicly observable. The nonnegative-payment constraint distinguishes our problem from the dynamic screening literature. We identify conditions under which the optimal mechanism takes a simple form: a consecutive-working menu, in which the agent chooses when to start working and is then incentivized to work consecutively until the end. We explain why this consecutive structure is optimal despite i.i.d. costs and additively separable payoffs, shedding light on real-world reward schemes that require consecutive actions.

Suggested Citation

  • Yijun Liu, 2025. "Dynamic Reward Design," Papers 2511.19838, arXiv.org, revised Aug 2026.
    • Handle: RePEc:arx:papers:2511.19838
    as

    Download full text from publisher

    File URL: https://arxiv.org/pdf/2511.19838
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. PETER M. DeMARZO & YULIY SANNIKOV, 2006. "Optimal Security Design and Dynamic Capital Structure in a Continuous‐Time Agency Model," Journal of Finance, American Finance Association, vol. 61(6), pages 2681-2724, December.
    2. R. Vijay Krishna & Giuseppe Lopomo & Curtis R. Taylor, 2013. "Stairway to heaven or highway to hell: Liquidity, sweat equity, and the uncertain path to ownership," RAND Journal of Economics, RAND Corporation, vol. 44(1), pages 104-127, March.
    3. Bergemann, Dirk & Castro, Francisco & Weintraub, Gabriel Y., 2020. "The scope of sequential screening with ex post participation constraints," Journal of Economic Theory, Elsevier, vol. 188(C).
    4. Gian Luca Clementi & Hugo A. Hopenhayn, 2006. "A Theory of Financing Constraints and Firm Dynamics," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 121(1), pages 229-265.
    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. Itai Ashlagi & Constantinos Daskalakis & Nima Haghpanah, 2023. "Sequential Mechanisms with Ex Post Individual Rationality," Operations Research, INFORMS, vol. 71(1), pages 245-258, January.
    2. Dirk Bergemann & Juuso Välimäki, 2019. "Dynamic Mechanism Design: An Introduction," Journal of Economic Literature, American Economic Association, vol. 57(2), pages 235-274, June.
    3. Alex Bloedel & R. Vijay Krishna & Oksana Leukhina, 2018. "Insurance and Inequality with Persistent Private Information," Working Papers 2018-020, Federal Reserve Bank of St. Louis, revised 11 Aug 2024.
    4. Bergemann, Dirk & V�lim�ki, Juuso, 2017. "Dynamic Mechanism Design: An Introduction," CEPR Discussion Papers 12240, C.E.P.R. Discussion Papers.
    5. 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.
    6. Roberts, Michael R., 2015. "The role of dynamic renegotiation and asymmetric information in financial contracting," Journal of Financial Economics, Elsevier, vol. 116(1), pages 61-81.
    7. Oscar M. Valencia, 2014. "R&D Investment and Financial Frictions," Borradores de Economia 11840, Banco de la Republica.
    8. Rampini, Adriano A. & Viswanathan, S., 2013. "Collateral and capital structure," Journal of Financial Economics, Elsevier, vol. 109(2), pages 466-492.
    9. Rui Li & Dana Kiku & Hengjie Ai, 2014. "A Mechanism Design Model of Firm Dynamics: The Case of Limited Commitment," 2014 Meeting Papers 855, Society for Economic Dynamics.
    10. R. Vijay Krishna & Shiming Fu, 2016. "Dynamic Financial Contracting with Persistent Private Information," 2016 Meeting Papers 89, Society for Economic Dynamics.
    11. Chaigneau, Pierre & Edmans, Alex & Gottlieb, Daniel, 2018. "Does improved information improve incentives?," Journal of Financial Economics, Elsevier, vol. 130(2), pages 291-307.
    12. Aydin, Deniz & Kim, Olivia S., 2024. "Precautionary Debt Capacity," EconStor Preprints 281672, ZBW - Leibniz Information Centre for Economics.
    13. Ronald Anderson & Cecilia Bustamante & Stéphane Guibaud & Mihail Zervos, 2018. "Agency, Firm Growth, and Managerial Turnover," Post-Print hal-03391936, HAL.
    14. Guo, Yingni & Hörner, Johannes, 2020. "Dynamic Allocation without Money," TSE Working Papers 20-1133, Toulouse School of Economics (TSE).
    15. Feng Tian & Ekaterina Astashkina & Izak Duenyas, 2025. "Dynamic Contract Design in the Presence of Double Moral Hazard," Management Science, INFORMS, vol. 71(8), pages 6475-6494, August.
    16. Alessandro Dovis, 2013. "Efficient Sovereign Default," 2013 Meeting Papers 293, Society for Economic Dynamics.
    17. Di Corato, Luca & Moretto, Michele, 2026. "Dynamic Adverse Selection with Flow Limited Liability: A Closed-Form Approach to Price Regulation," FEEM Working Papers 396239, Fondazione Eni Enrico Mattei (FEEM).
    18. Golosov, M. & Tsyvinski, A. & Werquin, N., 2016. "Recursive Contracts and Endogenously Incomplete Markets," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 725-841, Elsevier.
    19. Jianjun Miao & Alejandro Rivera, 2016. "Robust Contracts in Continuous Time," Econometrica, Econometric Society, vol. 84, pages 1405-1440, July.
    20. Eduardo Abi Jaber & Stéphane Villeneuve, 2025. "Gaussian agency problems with memory and linear contracts," Finance and Stochastics, Springer, vol. 29(1), pages 143-176, January.

    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:2511.19838. 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: https://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.