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On the Estimation of the Initial Stock in the Problem of Resource Extraction

Author

Listed:
  • Anna Tur

    (Faculty of Applied Mathematics and Control Processes, St Petersburg State University, University Emb. 7/9, 199034 St. Petersburg, Russia)

  • Ekaterina Gromova

    (Faculty of Applied Mathematics and Control Processes, St Petersburg State University, University Emb. 7/9, 199034 St. Petersburg, Russia)

  • Dmitry Gromov

    (Faculty of Applied Mathematics and Control Processes, St Petersburg State University, University Emb. 7/9, 199034 St. Petersburg, Russia)

Abstract

We consider a differential game of non-renewable resource extraction, in which the players do not know the precise value of the resource stock and, thus, have to make an estimate. We define the value of information about the initial stock and give recommendations for the choice of the estimate depending on the parameters of the problem. Further, we consider the situation where the players only know the bounds for the stock of the resource and solve the problem of computing the optimal estimate, such that it minimizes the players’ losses in the worst-case scenario. The analysis allows us to give a simple rule for the choice of the optimal estimate of the resource stock.

Suggested Citation

  • Anna Tur & Ekaterina Gromova & Dmitry Gromov, 2021. "On the Estimation of the Initial Stock in the Problem of Resource Extraction," Mathematics, MDPI, vol. 9(23), pages 1-10, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:23:p:3099-:d:692441
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    References listed on IDEAS

    as
    1. Hart, Rob, 2016. "Non-renewable resources in the long run," Journal of Economic Dynamics and Control, Elsevier, vol. 71(C), pages 1-20.
    2. Jeffrey M. Keisler & Zachary A. Collier & Eric Chu & Nina Sinatra & Igor Linkov, 2014. "Value of information analysis: the state of application," Environment Systems and Decisions, Springer, vol. 34(1), pages 3-23, March.
    3. Fumie Yokota & Kimberly M. Thompson, 2004. "Value of Information Analysis in Environmental Health Risk Management Decisions: Past, Present, and Future," Risk Analysis, John Wiley & Sons, vol. 24(3), pages 635-650, June.
    4. 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.
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    Cited by:

    1. Shimai Su & Anna Tur, 2022. "Estimation of Initial Stock in Pollution Control Problem," Mathematics, MDPI, vol. 10(19), pages 1-11, September.

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