A Game-Theoretic Model of Pollution Control with Asymmetric Time Horizons

Authors

  • Ekaterina V. Gromova Saint Petersburg State University
  • Anna V. Tur Saint Petersburg State University
  • Lidiya I. Balandina Bauman Moscow State Technical University

Abstract

In the contribution a problem of pollution control is studied within the game-theoretic framework (Kostyunin et al., 2013; Gromova and Plekhanova, 2015; Shevkoplyas and Kostyunin, 2011). Each player is assumed to have certain equipment whose functioning is related to pollution control. The i-th player’s equipment may undergo an abrupt failure at time Ti.. The game lasts until any of the players’ equipment breaks down. Thus, the game duration is defined as T= min( T1,...Tn) , where Ti  is the time instant at which the i-th player stops the game. We assume that the time instant of the i-th equipment failure is described bytheWeibull distribution. According to Weibull distribution form parameter, we consider different scenarios of equipment exploitation, where each of player can be in “an infant”, “an adult” or “an aged” stage. The cooperative 2-player game with different scenarios is studied.

Keywords:

differential game, cooperative game, pollution control, random duration, Weibull distribution

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References

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Kostyunin, S. Yu., Palestini, A., Shevkoplyas, E. V. (2013). On a exhaustible resource extraction differential game with random terminal instants. Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., no. 3, 73–82.

Gromova, E., Plekhanova, K. (2015). A differential game of pollution control with participation of developed and developing countries. Contributions to Game Theory and Management, 8, 64–83.

Kostyunin, S. and E. Shevkoplyas (2011). On simplification of integral payoff in the differential games with random duration. Vestnik St. Petersburg University. Ser. 10, Issue 4, 47–56.

Shevkoplyas, E., Kostyunin, S. (2011). Modeling of Environmental Projects under Condition of a Random Time Horizon. Contributions to Game Theory and Management, 4, 447–459.

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Yeung, D. W. K., Petrosjan, L. A. (2006). Cooperative Stochastic Differential Games. New-York, Heidelberg, London: Springer, 242 P.

Weibull, W. (1951). A statistical distribution function of wide applicability. J. Appl. Mech.-Trans. ASME 18 (3), 293–297.

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Published

2022-05-01

How to Cite

Gromova, E. V. ., Tur, A. V. ., & Balandina, L. I. . (2022). A Game-Theoretic Model of Pollution Control with Asymmetric Time Horizons. Contributions to Game Theory and Management, 9. Retrieved from https://gametheory.spbu.ru/article/view/13352

Issue

Vol. 9 (2016)

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.

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