Differential Game Model of Resource Extraction with Continuous and Dynamic Updating

doi:10.1007/s40305-023-00484-2

Journal of the Operations Research Society of China ›› 2024, Vol. 12 ›› Issue (1): 51-75.doi: 10.1007/s40305-023-00484-2

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Differential Game Model of Resource Extraction with Continuous and Dynamic Updating

Ovanes Petrosian^1,2,3, Tihomirov Denis⁴, Jiang-Jing Zhou³, Hong-Wei Gao⁵

1. School of Mathematics, Harbin Institute of Technology, Harbin, 150001, Heilongjiang, China;
2. School of Automation, Qingdao University, Qingdao, 266071, Shandong, China;
3. Faculty of Applied Mathematics and Control Processes, Saint-Petersburg State University, Saint Petersburg, Russia;
4. National Research University "High School of Economics", Saint-Petersburg, Russia;
5. School of Mathematics and Statistics, Qingdao University, Qingdao, 266071, Shandong, China

Received:2022-04-07 Revised:2023-03-25 Online:2024-03-30 Published:2024-03-13
Contact: Ovanes Petrosian, Tihomirov Denis, Jiang-Jing Zhou, Hong-Wei Gao E-mail:petrosian.ovanes@yandex.ru;dstikhomirov@hse.edu.ru;st092028@student.spbu.ru;gaohongwei@qdu.edu.cn
Supported by:
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).

Abstract

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.

Key words: Differential games, Dynamic updating, Continuous updating, Optimal control, Feedback Nash equilibrium

CLC Number:

Ovanes Petrosian, Tihomirov Denis, Jiang-Jing Zhou, Hong-Wei Gao. Differential Game Model of Resource Extraction with Continuous and Dynamic Updating[J]. Journal of the Operations Research Society of China, 2024, 12(1): 51-75.

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Differential Game Model of Resource Extraction with Continuous and Dynamic Updating

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