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Time-Consistency of an Imputation in a Cooperative Hybrid Differential Game

Author

Listed:
  • Ekaterina Gromova

    (Faculty of Applied Mathematics and Control Processes, St. Petersburg State University, 199034 St. Petersburg, Russia)

  • Anastasiia Zaremba

    (Faculty of Applied Mathematics and Control Processes, St. Petersburg State University, 199034 St. Petersburg, Russia)

  • Shimai Su

    (Faculty of Applied Mathematics and Control Processes, St. Petersburg State University, 199034 St. Petersburg, Russia)

Abstract

This work is aimed at studying the problem of maintaining the sustainability of a cooperative solution in an n -person hybrid differential game. Specifically, we consider a differential game whose payoff function is discounted with a discounting function that changes its structure with time. We solve the problem of time-inconsistency of the cooperative solution using a so-called imputation distribution procedure, which was adjusted for this general class of differential games. The obtained results are illustrated with a specific example of a differential game with random duration and a hybrid cumulative distribution function (CDF). We completely solved the presented example to demonstrate the application of the developed scheme in detail. All results were obtained in analytical form and illustrated by numerical simulations.

Suggested Citation

  • Ekaterina Gromova & Anastasiia Zaremba & Shimai Su, 2021. "Time-Consistency of an Imputation in a Cooperative Hybrid Differential Game," Mathematics, MDPI, vol. 9(15), pages 1-14, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:15:p:1830-:d:607412
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    References listed on IDEAS

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    1. Bonneuil, N. & Boucekkine, R., 2016. "Optimal transition to renewable energy with threshold of irreversible pollution," European Journal of Operational Research, Elsevier, vol. 248(1), pages 257-262.
    2. de-Paz, Albert & Marín-Solano, Jesús & Navas, Jorge & Roch, Oriol, 2014. "Consumption, investment and life insurance strategies with heterogeneous discounting," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 66-75.
    3. Maxim Finkelstein, 2008. "Failure Rate Modelling for Reliability and Risk," Springer Series in Reliability Engineering, Springer, number 978-1-84800-986-8, December.
    4. de-Paz, Albert & Marín-Solano, Jesús & Navas, Jorge, 2013. "A consumption–investment problem with heterogeneous discounting," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 221-232.
    5. 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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