A note on cooperative differential games with pairwise interactions
DOI:
https://doi.org/10.21638/11701/spbu10.2024.108Abstract
In this paper, a differential game with pairwise interaction in a network is proposed. For explicitly, the vertices are players, and the edges are connections between them. Meanwhile, we consider the cooperative case. One special characteristic function is introduced and its convexity is proved. The core is used as a cooperative optimality principle. The characteristic function allows the construction of a time-consistent (dynamically stable) solutions, such as the Shapley value and the core. Finally, the results are illustrated by an example.
Keywords:
cooperative games, differential network games, pairwise interactions, characteristic function, the Shapley value, time-consistency
Downloads
References
References
Dyer M., Mohanaraj V. Pairwise-interaction games. International Colloquium on Automata, Languages, and Programming. Berlin, Heidelberg, Springer, 2011, pp. 159–170.
Cheng S. F., Reeves D. M., Vorobeychik Y., Wellman M. P. Notes on equilibria in symmetric games. Proceedings of the 6th International Workshop on game theoretic and decision theoretic agents, GTDT, Research Collection School of Computing and Information Systems, 2004, pp. 71–78.
Bulgakova M. A. Reshenija setevyh igr s poparnym vzaimodejstviem [Solutions of network games with pairwise interactions]. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2019, vol. 15, iss. 1, pp. 147–156. https://doi.org/10.21638/11702/spbu10.2019.112 (In Russian)
Bulgakova M. A., Petrosyan L. A. Kooperativnye setevye igry s poparnym vzaimodejstviem [Cooperative network games with pairwise interactions]. Mathematical Game Theory and its Applications, 2015, vol. 7, iss. 4, pp. 7–18. (In Russian)
Petrosyan L. A., Bulgakova M. A., Sedakov A. A. Time-consistent solutions for two-stage network games with pairwise interactions. Mobile Networks and Applications, 2021, vol. 26, iss. 2, pp. 491–500. https://doi.org/10/1007/s1136-018-1127-7
Bulgakova M. A., Petrosyan L. A. Ob odnoj mnogoshagovoj neantagonisticheskoj igre na seti [About one multi-stage non-cooperative game on the network]. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2019, vol. 15, iss. 4, pp. 603–615. https://doi.org/10.21638/11701/spbu10.2019.415 (In Russian)
Bulgakova M. A., Petrosyan L. A. About strongly time-consistency of core in the network game with pairwise interactions. International Conference Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference), IEEE, 2016, pp. 1–4.
Bulgakova M. A., Petrosyan L. A. Multistage games with pairwise interactions on complete graph. Automation and Remote Control, 2020, vol. 81, iss. 8, pp. 1539–1550.
Petrosyan L. A., Sedakov A. A. One-way flow two-stage network games. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Process, 2014, vol. 10, iss. 4, pp. 72–81.
Mazalov V., Chirkova J. V. Networking games: network forming games and games on networks. London, Academic Press, 2019, 322 p.
Sun P., Parilina E. M. Two stage network games modeling the Belt and Road Initiative. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2022, vol. 18, iss. 1, pp. 87–98. https://doi.org/10.21638/11701/spbu10.2022.107
Wie B. W. A differential game model of Nash equilibrium on a congested traffic network. Networks, 1993, vol. 23, iss. 6, pp. 557–565.
Petrosyan L. A., Yeung D. W. K., Pankratova Y. B. Dynamic cooperative games on networks. International Conference on Mathematical Optimization Theory and Operations Research. Cham, Springer Publ., 2021, pp. 403–416. https://doi.org/10.1007-3-030-86433-0-28
Tur A. V., Petrosyan L. A. Cooperative optimality principles in differential games on networks. Autom. Remote Control, 2021, vol. 82, pp. 1095–1106. https://doi.org/10.1134/S0005117921060096
Tur A. V., Petrosyan L. A. The core of cooperative differential games on networks. International Conference on Mathematical Optimization Theory and Operations Research. Cham, Springer, 2022, pp. 295–314. https://doi.org/10.1007/978-3-031-09607-5-21
Petrosyan L. A. Ustojchivost' reshenij v differencial'nyh igrah so mnogimi uchastnikami [Stability of solutions of differential games with participants]. Vestnik of Leningrad State University, 1977, vol. 19, pp. 46–52. (In Russian)
Petrosyan L. A., Danilov N. A. Ustojchivye reshenija v neantagonisticheskih differencial'nyh igrah s transferabel'nymi vyishryshami [Time consistent solutions of zero-sum differential games with transferable payoffs]. Vestnik of Leningrad State University, 1979, vol. 1, pp. 46–52. (In Russian)
Petrosyan L. A., Yeung D. W. K., Pankratova Y. B. Characteristic functions in cooperative differential games on network. Journal of Dynamics and Games, 2024, vol. 11, iss. 2, pp. 115–130. https://doi.org/10.3934/jdg.2023017
Gromova E. V. The Shapley value as a sustainable cooperative solution in differential games of three players. Recent Advances in Game Theory and Applications. Cham, Birkh"auser, 2016, pp. 67–89. https://doi.org/10.1007/978-3-319-43838-27
Petrosyan L. A., Zaccour G. Time-consistent Shapley value allocation of pollution cost reduction. Journal of Economic Dynamics and Control, 2003, vol. 27, iss. 3, pp. 381–398. https://doi.org/10.1016/S0165-1889(01)00053-7
Petrosyan L. A., Yeung D. W. K. The Shapley value for differential network games: Theory and application. Journal of Dynamics and Games, 2020, vol. 8, iss. 2, pp. 151–166. https://doi.org/10.3934/jdg.2020021
Breton M., Zaccour G., Zahaf M. A differential game of joint implementation of environmental projects. Automatica, 2005, vol. 41, iss. 10, pp. 1737–1749.
Gromova E., Tur A., Barsuk P. A pollution control problem for the aluminum production in eastern Siberia: Differential game approach. Stability and Control Processes, SCP 2020. Lecture Notes in Control and Information Sciences — Proceedings. Eds N. Smirnov, A. Golovkina. Cham, Springer, 2020, pp. 399–407. https://doi.org/10.1007/978-3-030-87966-2-44
Su S., Parilina E. M. Can partial cooperation between developed and developing countries be stable? Operations Research Letters, 2023, vol. 51, iss. 3, pp. 370–377. https://doi.org/10.1016/j.orl.2023.05.003
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.
