A Differential Game-Based Approach to Extraction of Exhaustible Resource with Random Terminal Instants

Authors

  • Sergey Kostyunin Saint Petersburg State University
  • Arsen Palestini Sapienza University of Rome
  • Ekaterina Shevkoplyas Saint Petersburg Sate University

Abstract

We investigate a noncooperative differential game in which two firms compete in extracting a unique nonrenewable resource over time. The respective times of extraction are random and after the first firm finishes extraction, the remaining one continues and gets the final reward for winning. An example is introduced where the optimal feedback strategy, i.e. the optimal extraction rate, is calculated in a closed form.

Keywords:

Differential game, exhaustible resources, random terminal time, Hamilton-Jacobi-Bellman equation

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References

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Kostyunin, S. and E.V. Shevkoplyas (2011). A Class of Differential Games with Random Terminal Time, mimeo.

Marin-Solano, J. and E. Shevkoplyas (2011). Non-constant discounting in differential games with random time horizon. Automatica, vol.48, 50, 2011. DOI: 10.1016/j.automatica.2011.09.010

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Petrosjan, L.A and E.V. Shevkoplyas (2003). Cooperative Solutions for Games with Random Duration. Game Theory and Applications, Vol. IX. Nova Science Publishers, 125–139.

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Published

2023-01-25

How to Cite

Kostyunin, S., Palestini, A., & Shevkoplyas, E. (2023). A Differential Game-Based Approach to Extraction of Exhaustible Resource with Random Terminal Instants. Contributions to Game Theory and Management, 5, 147–155. Retrieved from https://gametheory.spbu.ru/article/view/14319

Issue

Vol. 5 (2012)

Section

Articles

License

Articles of "Contributions to Game Theory and Management" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.