IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i12p2185-d458745.html
   My bibliography  Save this article

A Differential Game with Random Time Horizon and Discontinuous Distribution

Author

Listed:
  • Anastasiia Zaremba

    (Faculty of Applied Mathematics and Control Processes, St. Petersburg State University, 199034 St Petersburg, Russia)

  • Ekaterina Gromova

    (Department of Mathematics, St. Petersburg School of Physics, Mathematics, and Computer Science, National Research University Higher School of Economics (HSE), Soyuza Pechatnikov ul. 16, 190008 St. Petersburg, Russia
    Krasovskii Institute of Mathematics and Mechanics (IMM UB RAS), 620108 Yekaterinburg, Russia)

  • Anna Tur

    (Faculty of Applied Mathematics and Control Processes, St. Petersburg State University, 199034 St Petersburg, Russia)

Abstract

One class of differential games with random duration is considered. It is assumed that the duration of the game is a random variable with values from a given finite interval. The cumulative distribution function (CDF) of this random variable is assumed to be discontinuous with two jumps on the interval. It follows that the player’s payoff takes the form of the sum of integrals with different but adjoint time intervals. In addition, the first interval corresponds to the zero probability of the game to be finished, which results in terminal payoff on this interval. The method of construction optimal solution for the cooperative scenario of such games is proposed. The results are illustrated by the example of differential game of investment in the public stock of knowledge.

Suggested Citation

  • Anastasiia Zaremba & Ekaterina Gromova & Anna Tur, 2020. "A Differential Game with Random Time Horizon and Discontinuous Distribution," Mathematics, MDPI, vol. 8(12), pages 1-21, December.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:12:p:2185-:d:458745
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/12/2185/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/12/2185/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Bonneuil, N. & Boucekkine, R., 2016. "Optimal transition to renewable energy with threshold of irreversible pollution," European Journal of Operational Research, Elsevier, vol. 248(1), pages 257-262.
    2. Feichtinger, Gustav & Jorgensen, Steffen, 1983. "Differential game models in management science," European Journal of Operational Research, Elsevier, vol. 14(2), pages 137-155, October.
    3. Menahem E. Yaari, 1965. "Uncertain Lifetime, Life Insurance, and the Theory of the Consumer," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 32(2), pages 137-150.
    4. Steffen Jørgensen & Georges Zaccour, 2007. "Developments in differential game theory and numerical methods: economic and management applications," Computational Management Science, Springer, vol. 4(2), pages 159-181, April.
    5. Dockner,Engelbert J. & Jorgensen,Steffen & Long,Ngo Van & Sorger,Gerhard, 2000. "Differential Games in Economics and Management Science," Cambridge Books, Cambridge University Press, number 9780521637329.
    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. Tatyana Balas & Anna Tur, 2023. "The Hamilton–Jacobi–Bellman Equation for Differential Games with Composite Distribution of Random Time Horizon," Mathematics, MDPI, vol. 11(2), pages 1-13, January.

    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. Ekaterina Gromova & Anastasiia Zaremba & Nahid Masoudi, 2022. "Reclamation of a Resource Extraction Site Model with Random Components," Mathematics, MDPI, vol. 10(24), pages 1-15, December.
    2. S. Kostyunin & A. Palestini & E. Shevkoplyas, 2014. "On a Nonrenewable Resource Extraction Game Played by Asymmetric Firms," Journal of Optimization Theory and Applications, Springer, vol. 163(2), pages 660-673, November.
    3. José Daniel López-Barrientos & Ekaterina Viktorovna Gromova & Ekaterina Sergeevna Miroshnichenko, 2020. "Resource Exploitation in a Stochastic Horizon under Two Parametric Interpretations," Mathematics, MDPI, vol. 8(7), pages 1-29, July.
    4. Chan, Chi Kin & Zhou, Yan & Wong, Kar Hung, 2018. "A dynamic equilibrium model of the oligopolistic closed-loop supply chain network under uncertain and time-dependent demands," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 118(C), pages 325-354.
    5. H. Dawid & M. Kopel & P. Kort, 2010. "Dynamic strategic interaction between an innovating and a non-innovating incumbent," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 18(4), pages 453-463, December.
    6. Ekaterina Gromova & Anastasiya Malakhova & Arsen Palestini, 2018. "Payoff Distribution in a Multi-Company Extraction Game with Uncertain Duration," Mathematics, MDPI, vol. 6(9), pages 1-17, September.
    7. Eric Innocenti & Corinne Idda & Dominique Prunetti & Pierre-Régis Gonsolin, 2022. "Agent-based modelling of a small-scale fishery in Corsica," Post-Print hal-03886619, HAL.
    8. Ekaterina Gromova & Anastasiia Zaremba & Shimai Su, 2021. "Time-Consistency of an Imputation in a Cooperative Hybrid Differential Game," Mathematics, MDPI, vol. 9(15), pages 1-14, August.
    9. Tatyana Balas & Anna Tur, 2023. "The Hamilton–Jacobi–Bellman Equation for Differential Games with Composite Distribution of Random Time Horizon," Mathematics, MDPI, vol. 11(2), pages 1-13, January.
    10. Dmitry Gromov & Ekaterina Gromova, 2017. "On a Class of Hybrid Differential Games," Dynamic Games and Applications, Springer, vol. 7(2), pages 266-288, June.
    11. Martín-Herrán, Guiomar & Sigué, Simon Pierre & Zaccour, Georges, 2011. "Strategic interactions in traditional franchise systems: Are franchisors always better off?," European Journal of Operational Research, Elsevier, vol. 213(3), pages 526-537, September.
    12. Kogan, Konstantin & Tapiero, Charles, 2011. "Inter-temporal inventory competition and the effects of capacity constraints," International Journal of Production Economics, Elsevier, vol. 131(2), pages 682-688, June.
    13. Mengyuan Zhou, 2022. "Does the Source of Inheritance Matter in Bequest Attitudes? Evidence from Japan," Journal of Family and Economic Issues, Springer, vol. 43(4), pages 867-887, December.
    14. Markku Ollikainen, 1998. "Sustainable Forestry: Timber Bequests, Future Generations and Optimal Tax Policy," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 12(3), pages 255-273, October.
    15. An Chen & Thai Nguyen & Thorsten Sehner, 2022. "Unit-Linked Tontine: Utility-Based Design, Pricing and Performance," Risks, MDPI, vol. 10(4), pages 1-27, April.
    16. Jiang Cheng & Lu Yu, 2019. "Life and health insurance consumption in China: demographic and environmental risks," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 44(1), pages 67-101, January.
    17. Anikó Bíró, 2013. "Subjective mortality hazard shocks and the adjustment of consumption expenditures," Journal of Population Economics, Springer;European Society for Population Economics, vol. 26(4), pages 1379-1408, October.
    18. Masahiko Hattori & Yasuhito Tanaka, 2019. "General analysis of dynamic oligopoly with sticky price," Economics Bulletin, AccessEcon, vol. 39(4), pages 2990-2998.
    19. Frédéric Gannon & Vincent Touzé, 2006. "Insurance and Optimal Growth," Post-Print halshs-00085181, HAL.
    20. Robert Gazzale & Julian Jamison & Alexander Karlan & Dean Karlan, 2013. "Ambiguous Solicitation: Ambiguous Prescription," Economic Inquiry, Western Economic Association International, vol. 51(1), pages 1002-1011, January.

    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:gam:jmathe:v:8:y:2020:i:12:p:2185-:d:458745. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.