A Differential Game Model for the Extraction of Non Renewable Resources with Random Initial Times

Authors

  • Ekaterina V. Gromova Saint Petersburg State University
  • José Daniel López-Barrientos Facultad de Ciencias Actuariales

Abstract

In this work we propose a model for the extraction of a non renewable resource in an economy where, initially, only one agent is enabled to perform extraction tasks. However, at certain non predictable (random) times, more companies receive the government's approval for extracting the country's resources. We provide a set up suitable for the use of standard dynamic programming results; 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

Downloads

Download data is not yet available.

References

Bardi, M. (2012). Explicit solutions of some linear-quadratic mean field games. Networks and heterogeneous media. American Institute of Mathematical Sciences, 7, 1–19.

Fleming, W., Soner, H. M. (2005). Controlled Markov Processes and Viscosity Solutions. Springer. 2nd edition.

Gromov, D.; Gromova, E. V. (2014). Differential games with random duration: a hybrid systems formulation, Contributions to Game Theory and Management, 7, 104–119.

Kostyunin, S.; Shevkoplyas, E. (2011). On simplification of integral payoff in differential games with random duration, Vestnik S. Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 4, 47–56.

Kostyunin, S.; Palestini, A.; Shevkoplyas, E. (2012). A Differential Game-Based Approach to Extraction of Exhaustible Resource with Random Terminal Instants, Contributions to Game Theory and Management, 5, 147–155.

Downloads

Published

2022-05-24

How to Cite

Gromova, E. V. ., & López-Barrientos, J. D. . (2022). A Differential Game Model for the Extraction of Non Renewable Resources with Random Initial Times. Contributions to Game Theory and Management, 8. Retrieved from https://gametheory.spbu.ru/article/view/13449

Issue

Vol. 8 (2015)

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.