The core in differential games on networks with communication restrictions
DOI:
https://doi.org/10.21638/11701/spbu10.2023.406Abstract
In this paper we consider a class of differential games on networks. It is assumed that the players are identified with the nodes of the network and their interaction takes place along the paths of this network. A characteristic function of a special kind is used, which takes into account the network structure of the game. The C-core is studied as a cooperative optimality principle. An illustrative example is considered.
Keywords:
differential game, network game, cooperative game, core, the Shapley value
Downloads
References
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
Downloads
Published
How to Cite
Issue
Section
License
Articles of "Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes" 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.
