IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v173y2024ics030441492400067x.html
   My bibliography  Save this article

A controller-stopper-game with hidden controller type

Author

Listed:
  • Bodnariu, Andi
  • Lindensjö, Kristoffer

Abstract

We consider a continuous time stochastic dynamic game between a stopper (the owner of an asset) and a controller (the manager) who is either effective or non-effective. An effective manager can exert high or low effort which corresponds to a high or a low positive drift for the accumulated income of the owner with random noise in terms of Brownian motion. The manager earns a salary until the owner stops the game. A non-effective manager cannot act but receives a salary. We find a threshold (Nash) equilibrium using stochastic filtering methods in a weak formulation.

Suggested Citation

  • Bodnariu, Andi & Lindensjö, Kristoffer, 2024. "A controller-stopper-game with hidden controller type," Stochastic Processes and their Applications, Elsevier, vol. 173(C).
    • Handle: RePEc:eee:spapps:v:173:y:2024:i:c:s030441492400067x
    DOI: 10.1016/j.spa.2024.104361
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S030441492400067X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2024.104361?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. repec:dau:papers:123456789/6927 is not listed on IDEAS
    2. 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.
    3. Fabien Gensbittel & Catherine Rainer, 2018. "A Two-Player Zero-sum Game Where Only One Player Observes a Brownian Motion," Dynamic Games and Applications, Springer, vol. 8(2), pages 280-314, June.
    4. Fabien Gensbittel & Christine Grün, 2019. "Zero-Sum Stopping Games with Asymmetric Information," Mathematics of Operations Research, INFORMS, vol. 44(1), pages 277-302, February.
    5. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, December.
    6. De Angelis, Tiziano & Ekström, Erik, 2020. "Playing with ghosts in a Dynkin game," Stochastic Processes and their Applications, Elsevier, vol. 130(10), pages 6133-6156.
    7. Erhan Bayraktar & Yu-Jui Huang, 2010. "On the Multi-Dimensional Controller and Stopper Games," Papers 1009.0932, arXiv.org, revised Jan 2013.
    8. Marcel Nutz & Jianfeng Zhang, 2012. "Optimal stopping under adverse nonlinear expectation and related games," Papers 1212.2140, arXiv.org, revised Sep 2015.
    9. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796.
    10. Hernández-Hernández, Daniel & Yamazaki, Kazutoshi, 2015. "Games of singular control and stopping driven by spectrally one-sided Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 125(1), pages 1-38.
    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. , H. & ,, 2016. "Approximate efficiency in repeated games with side-payments and correlated signals," Theoretical Economics, Econometric Society, vol. 11(1), January.
    2. Renault, Jérôme & Solan, Eilon & Vieille, Nicolas, 2013. "Dynamic sender–receiver games," Journal of Economic Theory, Elsevier, vol. 148(2), pages 502-534.
    3. Salomon, Antoine & Forges, Françoise, 2015. "Bayesian repeated games and reputation," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 70-104.
    4. H. Dharma Kwon & Jan Palczewski, 2022. "Exit game with private information," Papers 2210.01610, arXiv.org, revised Oct 2023.
    5. ,, 2015. "Unraveling in a repeated moral hazard model with multiple agents," Theoretical Economics, Econometric Society, vol. 10(1), January.
    6. Pierre Cardaliaguet & Catherine Rainer & Dinah Rosenberg & Nicolas Vieille, 2016. "Markov Games with Frequent Actions and Incomplete Information—The Limit Case," Mathematics of Operations Research, INFORMS, vol. 41(1), pages 49-71, February.
    7. Tsakas, Elias & Tsakas, Nikolas, 2021. "Noisy persuasion," Games and Economic Behavior, Elsevier, vol. 130(C), pages 44-61.
    8. Juntao Chen & Quanyan Zhu & Tamer Başar, 2021. "Dynamic Contract Design for Systemic Cyber Risk Management of Interdependent Enterprise Networks," Dynamic Games and Applications, Springer, vol. 11(2), pages 294-325, June.
    9. Bayraktar, Erhan & Yao, Song, 2015. "Doubly reflected BSDEs with integrable parameters and related Dynkin games," Stochastic Processes and their Applications, Elsevier, vol. 125(12), pages 4489-4542.
    10. Gradwohl, Ronen & Smorodinsky, Rann, 2017. "Perception games and privacy," Games and Economic Behavior, Elsevier, vol. 104(C), pages 293-308.
    11. Bayraktar, Erhan & Yao, Song, 2017. "Optimal stopping with random maturity under nonlinear expectations," Stochastic Processes and their Applications, Elsevier, vol. 127(8), pages 2586-2629.
    12. Angoshtari, Bahman & Bayraktar, Erhan & Young, Virginia R., 2016. "Minimizing the probability of lifetime drawdown under constant consumption," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 210-223.
    13. Kolotilin, Anton & Li, Hongyi, 2021. "Relational communication," Theoretical Economics, Econometric Society, vol. 16(4), November.
    14. Alexander M. G. Cox & Sigrid Kallblad & Martin Larsson & Sara Svaluto-Ferro, 2021. "Controlled Measure-Valued Martingales: a Viscosity Solution Approach," Papers 2109.00064, arXiv.org, revised Aug 2023.
    15. Banas, Lubomir & Ferrari, Giorgio & Randrianasolo, Tsiry Avisoa, 2020. "Numerical Appromixation of the Value of a Stochastic Differential Game with Asymmetric Information," Center for Mathematical Economics Working Papers 630, Center for Mathematical Economics, Bielefeld University.
    16. Luciano Campi & Davide Santis, 2020. "Nonzero-Sum Stochastic Differential Games Between an Impulse Controller and a Stopper," Journal of Optimization Theory and Applications, Springer, vol. 186(2), pages 688-724, August.
    17. Laclau, M., 2014. "Communication in repeated network games with imperfect monitoring," Games and Economic Behavior, Elsevier, vol. 87(C), pages 136-160.
    18. Fabien Gensbittel, 2019. "Continuous-Time Markov Games with Asymmetric Information," Dynamic Games and Applications, Springer, vol. 9(3), pages 671-699, September.
    19. Laclau, Marie & Tomala, Tristan, 2017. "Repeated games with public deterministic monitoring," Journal of Economic Theory, Elsevier, vol. 169(C), pages 400-424.
    20. Yuichi Yamamoto, 2013. "Individual Learning and Cooperation in Noisy Repeated Games," PIER Working Paper Archive 13-038, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.

    More about this item

    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:spapps:v:173:y:2024:i:c:s030441492400067x. 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/wps/find/journaldescription.cws_home/505572/description#description .

    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.