C-ядро в дифференциальных играх на сетях с коммуникационными ограничениями

Анна Викторовна Тур

doi:10.21638/11701/spbu10.2023.406

Авторы

Анна Викторовна Тур Санкт-Петербургский государственный университет, 199034, Санкт-Петербург, Российская Федерация

DOI:

https://doi.org/10.21638/11701/spbu10.2023.406

Аннотация

Рассматривается класс дифференциальных игр на сетях. Предполагается, что игроки отождествляются с вершинами сети, а их взаимодействие осуществляется вдоль путей этой сети. Для построения кооперативных решений используется характеристическая функция специального вида, учитывающая сетевую структуру игры. В качестве кооперативного принципа оптимальности исследуется С-ядро. Приводится пример.

Ключевые слова:

дифференциальная игра, игра на сети, кооперативная игра, С-ядро, вектор Шепли

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Библиографические ссылки

Литература

Petrosyan L., Yeung D. Shapley value for differential network games: Theory and application // Journal of Dynamics and Games. 2021. Vol. 8. N 2. P. 151–166.

Tur A. V., Petrosyan L. A. Cooperative optimality principals in differential games on networks // Automation and Remote Control. 2021. Vol. 82. N 6. P. 1095–1106.

Petrosyan L., Yeung D. Construction of dynamically stable solutions in differential network games // Stability, Control and Differential Games / еds A. Tarasyev, V. Maksimov, T. Filippova. Lecture Notes in Control and Information Sciences — Proceedings. 2020. Cham: Springer, 2020. P. 51–61. https://doi.org/10.1007/978-3-030-42831-0_5

Tur A., Petrosyan L. The core of cooperative differential games on networks // Mathematical Optimization Theory and Operations Research. MOTOR 2022 / eds P. Pardalos, M. Khachay, V. Mazalov. Lecture Notes in Computer Sciences, 2022. Cham: Springer, 2022. Vol. 13367. P. 295–314. https://doi.org/10.1007/978-3-031-09607-5_21

Petrosyan L. A., Yeung D., Pankratova Y. B. Cooperative differential games with partner sets on networks // Труды Института математики и механики Урал. отд. РАН. 2021. Т. 27. № 3. С. 286–295.

Tur A., Petrosyan L. Communication restriction-based characteristic function in differential games on networks // Mathematical Optimization Theory and Operations Research. MOTOR 2023 / eds M. Khachay, Y. Kochetov, A. Eremeev, O. Khamisov, V. Mazalov, P. Pardalos. Lecture Notes in Computer Science, 2023. Vol. 13930. P. 314–324.

Von Neumann J., Morgenstern O. Theory of games and economic behavior. Princeton: Princeton University Press, 1944. 625 p.

Petrosjan L., Zaccour G. Time-consistent Shapley value allocation of pollution cost reduction // Journal of Economic Dynamics and Control. 2003. Vol. 27. N 3. P. 381–398.

Parilina E., Petrosyan L. On a simplified method of defining characteristic function in stochastic games // Mathematics. 2020. Vol. 8. Art. N 1135.

Gromova E., Petrosyan L. On an approach to constructing a characteristic function in cooperative differential games // Automation and Remote Control. 2017. Vol. 78. P. 98–118.

Shapley L. S. Cores of convex games // International Journal of Game Theory. 1971. Vol. 1. P. 11–26.

Shapley L. S. A value for n-person games // Contributions to the theory of games II / eds H. Kuhn, A. Tucker. Princeton: Princeton University Press, 1953. P. 307–317. https://doi.org/10.1515/9781400881970-018

References

Petrosyan L., Yeung D. Shapley value for differential network games: Theory and application. Journal of Dynamics and Games, 2021, vol. 8, no. 2, pp. 151–166.

Tur A. V., Petrosyan L. A. Cooperative optimality principals in differential games on networks. Automation Remote Control, 2021, vol. 82, no. 6, pp. 1095–1106.

Petrosyan L., Yeung D. Construction of dynamically stable solutions in differential network games. Stability, Control and Differential Games. Eds A. Tarasyev, V. Maksimov, T. Filippova. Lecture Notes in Control and Information Sciences — Proceedings. Cham, Springer Publ., 2020, pp. 51–61. https://doi.org/10.1007/978-3-030-42831-0_5

Tur A., Petrosyan L. The core of cooperative differential games on networks. Mathematical Optimization Theory and Operations Research. MOTOR 2022. Eds P. Pardalos, M. Khachay, V. Mazalov. Lecture Notes in Computer Science. Cham, Springer Publ., 2022, vol. 13367, pp. 295–314. https://doi.org/10.1007/978-3-031-09607-5_21

Petrosyan L. A., Yeung D., Pankratova Y. B. Cooperative differential games with partner sets on networks. Trudy Instituta Matematiki i Mekhaniki UrO RAN [ Transactions of Institute Mathematics and Mechanics of the Ural Department Russian Academy of Sciences], 2021, vol. 27, no. 3, pp. 286–295.

Tur A., Petrosyan L. Communication restriction-based characteristic function in differential games on networks. Mathematical Optimization Theory and Operations Research. MOTOR 2023. Eds M. Khachay, Y. Kochetov, A. Eremeev, O. Khamisov, V. Mazalov, P. Pardalos. Lecture Notes in Computer Science, 2023, vol. 13930, pp. 314–324. https://doi.org/10.1007/978-3-031-35305-5_22

Von Neumann J., Morgenstern O. Theory of games and economic behavior. Princeton, Princeton University Press, 1944, 625 p.

Petrosjan L., Zaccour G. Time-consistent Shapley value allocation of pollution cost reduction. Journal of Economic Dynamics and Control, 2003, vol. 27, no. 3, pp. 381–398.

Parilina E., Petrosyan L. On a simplified method of defining characteristic function in stochastic games. Mathematics, 2020, vol. 8, art. no. 1135.

Gromova E., Petrosyan L. On an approach to constructing a characteristic function in cooperative differential games. Automation and Remote Control, 2017, vol. 78, pp. 98–118.

Shapley L. S. Cores of convex games. International Journal of Game Theory, 1971, vol. 1, pp. 11–26.

Shapley L. S. A value for n-person games. Contributions to the Theory of Games II. Eds H. Kuhn, A. Tucker. Princeton, Princeton University Press, 1953, pp. 307–317. https://doi.org/10.1515/9781400881970-018