A Differential Game Model for The Extraction of Nonrenewable Resources with Random Initial Times — The Cooperative and Competitive Cases

Ekaterina Viktorovna Gromova () and José Daniel López-Barrientos
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Ekaterina Viktorovna Gromova: Faculty of Applied Mathematics and Control Processes, St. Petersburg State University, Universitetskii Prospekt 35, Petergof, Saint Petersburg, 198504, Russia
José Daniel López-Barrientos: Facultad de Ciencias Actuariales, Universidad Anáhuac México Norte Av. Universidad Anáhuac, 46, Col. Lomas Anáhuac Huixquilucan, Edo. de México, México C. P. 52786

International Game Theory Review (IGTR), 2016, vol. 18, issue 02, 1-19

Abstract: In this work, we propose a model for the extraction of a nonrenewable resource in an economy where, initially, only one agent is enabled to perform extraction tasks. However, at certain nonpredictable (random) times, more companies receive the government’s approval for extracting the country’s resources. We provide a setup suitable for the use of standard dynamic programming results for both, the competitive and cooperative schemes; we develop the corresponding HJB equations, prove a verification theorem, and give an example. Our framework is inspired by the trends that oil industries are experiencing in countries like Mexico and Russia.

Keywords: Conditional distribution; random start; HJB equations; imputation distribution procedure (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (4)

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DOI: 10.1142/S0219198916400041

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