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On the Effect of the Absorption Coefficient in a Differential Game of Pollution Control

Author

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  • Ekaterina Marova

    (Faculty of Applied Mathematics and Control Processes, St. Petersburg State University, 198504 St. Petersburg, Russia)

  • Ekaterina Gromova

    (Faculty of Applied Mathematics and Control Processes, St. Petersburg State University, 198504 St. Petersburg, Russia)

  • Polina Barsuk

    (Faculty of Applied Mathematics and Control Processes, St. Petersburg State University, 198504 St. Petersburg, Russia)

  • Anastasia Shagushina

    (EPAM Systems, Inc., 22/2 Zastavskaya St., MegaPark, 196084 Saint Petersburg, Russia)

Abstract

We consider various approaches for a characteristic function construction on the example of an n players differential game of pollution control with a prescribed duration. We explore the effect of the presence of an absorption coefficient in the game on characteristic functions. As an illustration, we consider a game in which the parameters are calculated based on the real ecological situation of the Irkutsk region. For this game, we compute a number of characteristic functions and compare their properties.

Suggested Citation

  • Ekaterina Marova & Ekaterina Gromova & Polina Barsuk & Anastasia Shagushina, 2020. "On the Effect of the Absorption Coefficient in a Differential Game of Pollution Control," Mathematics, MDPI, vol. 8(6), pages 1-24, June.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:6:p:961-:d:370469
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    References listed on IDEAS

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    1. R.J. Aumann & S. Hart (ed.), 2002. "Handbook of Game Theory with Economic Applications," Handbook of Game Theory with Economic Applications, Elsevier, edition 1, volume 3, number 3.
    2. Dockner Engelbert J. & Van Long Ngo, 1993. "International Pollution Control: Cooperative versus Noncooperative Strategies," Journal of Environmental Economics and Management, Elsevier, vol. 25(1), pages 13-29, July.
    3. Jana Hajduková, 2006. "Coalition Formation Games: A Survey," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 8(04), pages 613-641.
    4. Gromova, Ekaterina V. & Marova, Ekaterina V., 2018. "On the Characteristi Function Construction Technique in Differential Games with Prescribed and Random Duration," Conference Papers 10475, Graduate School of Management, St. Petersburg State University.
    5. Petrosjan, Leon & Zaccour, Georges, 2003. "Time-consistent Shapley value allocation of pollution cost reduction," Journal of Economic Dynamics and Control, Elsevier, vol. 27(3), pages 381-398, January.
    6. Vladimir V. Mazalov & Anna N. Rettieva, 2010. "Fish Wars With Many Players," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 12(04), pages 385-405.
    7. Winter, Eyal, 2002. "The shapley value," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 53, pages 2025-2054, Elsevier.
    8. Dockner,Engelbert J. & Jorgensen,Steffen & Long,Ngo Van & Sorger,Gerhard, 2000. "Differential Games in Economics and Management Science," Cambridge Books, Cambridge University Press, number 9780521637329.
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