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Differential Game Model of Resource Extraction with Continuous and Dynamic Updating

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Abstract

This paper is devoted to a new class of differential games with continuous and dynamic updating. The direct application of resource extraction in a case of dynamic and continuous updating is considered. It is proved that the optimal control (cooperative strategies) and feedback Nash equilibrium strategies uniformly converge to the corresponding strategies in the game model with continuous updating as the number of updating instants converges to infinity. Similar results are presented for an optimal trajectory (cooperative trajectory), equilibrium trajectory and corresponding payoffs.

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Authors and Affiliations

  1. School of Mathematics, Harbin Institute of Technology, Harbin, 150001, Heilongjiang, China

    Ovanes Petrosian

  2. School of Automation, Qingdao University, Qingdao, 266071, Shandong, China

    Ovanes Petrosian

  3. Faculty of Applied Mathematics and Control Processes, Saint-Petersburg State University, Saint Petersburg, Russia

    Ovanes Petrosian & Jiang-**g Zhou

  4. National Research University “High School of Economics”, Saint-Petersburg, Russia

    Tihomirov Denis

  5. School of Mathematics and Statistics, Qingdao University, Qingdao, 266071, Shandong, China

    Hong-Wei Gao

Authors
  1. Ovanes Petrosian
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  2. Tihomirov Denis
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  3. Jiang-**g Zhou
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  4. Hong-Wei Gao
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The authors contributed equally to the work.

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Correspondence to Hong-Wei Gao.

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The authors declare no conflict of interest.

Additional information

The work is supported by Postdoctoral International Exchange Program of China, and corresponding author’ work is also supported by the National Natural Science Foundation of China (No. 72171126).

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Petrosian, O., Denis, T., Zhou, JJ. et al. Differential Game Model of Resource Extraction with Continuous and Dynamic Updating. J. Oper. Res. Soc. China 12, 51–75 (2024). https://doi.org/10.1007/s40305-023-00484-2

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  • DOI: https://doi.org/10.1007/s40305-023-00484-2

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