Non-Renewable Resource Extraction Model with Uncertainties

Peichen Ye (), Anna Tur and Yilun Wu
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Peichen Ye: Faculty of Applied Mathematics and Control Processes, St. Petersburg State University, 199034 St. Petersburg, Russia
Anna Tur: Faculty of Applied Mathematics and Control Processes, St. Petersburg State University, 199034 St. Petersburg, Russia
Yilun Wu: Faculty of Applied Mathematics and Control Processes, St. Petersburg State University, 199034 St. Petersburg, Russia

Games, 2025, vol. 16, issue 5, 1-23

Abstract: This paper delves into a multi-player non-renewable resource extraction differential game model, where the duration of the game is a random variable with a composite distribution function. We first explore the conditions under which the cooperative solution also constitutes a Nash equilibrium, thereby extending the theoretical framework from a fixed duration to the more complex and realistic setting of random duration. Assuming that players are unaware of the switching moment of the distribution function, we derive optimal estimates in both time-dependent and state-dependent cases. The findings contribute to a deeper understanding of strategic decision-making in resource extraction under uncertainty and have implications for various fields where random durations and cooperative strategies are relevant.

Keywords: differential game; non-renewable resource extraction; random duration; uncertainty; minimax problem (search for similar items in EconPapers)
JEL-codes: C C7 C70 C71 C72 C73 (search for similar items in EconPapers)
Date: 2025
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