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Cooperative Differential Games with Dynamic Updating
IFAC-PapersOnLine. 2018. Vol. 51. No. 32. P. 413–417.
Petrosian O., Gromova E.
This work is devoted to study cooperative solutions in the games with Looking Forward Approach. LFA is used for constructing game theoretical models and defining solutions for conflict-controlled processes where information about the process updates dynamically. We suppose that during the game players lack certain information about the motion equation and payoff function. At each instant players possess only the truncated information about the game
structure. At a given instants information about the game updates, players receive new updated information and adapt. Described model cannot be formulized using classical differential game technics. The new resulting cooperative solution for LFA models is presented and studied
Kemgne M. W., Njionou B. B., Ignatov D. I. et al., International Journal of Approximate Reasoning 2025 Vol. 186 Article 109527
This paper introduces cooperative games with transferable utilities and fuzzy characteristic functions on concept lattices. While previous works have independently addressed games with fuzzy payoffs and games restricted to structured coalition systems such as lattices, our approach combines both perspectives. We consider cooperative settings where coalition formation is constrained by a concept lattice structure, and ...
Added: January 23, 2026
Afanasiev V., Куприянов А. О., Неусыпин К. А., Авиакосмическое приборостроение 2025 № 9 С. 37–45
The problem of a zero-sum differential stabilization game with a quadratic performance functional is considered. The navigation system of an aircraft, including a platform inertial navigation system with structural correction using a control algorithm, is investigated. Errors of the navigation system, subject to the influence of uncontrolled disturbances, are described by a nonlinear ordinary differential ...
Added: November 1, 2025
Afanasiev V., Гаража И. А., Труды Института системного анализа Российской академии наук 2025 Т. 75 № 3 С. 80–91
The problem of a zero-sum differential stabilization game with a quadratic performance functional is considered. The control plant, subject to uncontrollable disturbances, is described by a nonlinear ordinary differential
equation. It is known that the synthesis of optimal feedback controls leads to the need to solve a scalar Bellman-Isaacs partial differential equation at the system's operating speed. An algebraic ...
Added: September 29, 2025
Afanasiev V., М.: ЛЕНАНД, 2023.
Valery Nikolaevich Afanasyev
Differential Games in Control Problems of Uncertain Objects
This book examines uncertain control systems whose behavior is described by nonlinear differential inclusions with fuzzy initial conditions. The application of classical methods, based on the assumption that all system characteristics and disturbances are known, is either computationally difficult or impossible. This necessitates the development of ...
Added: September 24, 2025
Cham: Birkhäuser, 2024.
This book collects a selection of the articles presented at the virtual conference “Game Theory and Applications”, organized in St. Petersburg in the summer of 2022. The articles in this collection cover all the main applications of game theory, interpolating mathematical methods with economics, biology, sociology, mobile systems, and social networks. Scholars in the field ...
Added: May 21, 2025
Afanasiev V., Автоматика и телемеханика 2022 № 11 С. 103–120
We consider the problem of a zero-sum differential tracking game with a quadratic
performance functional in which the plant subjected to uncontrolled disturbances is described
by a nonlinear ordinary differential equation. The synthesis of optimal controls is known to
necessitate online solving a scalar Bellman–Isaacs partial differential equation that contains
information about the trajectory of the process to be ...
Added: June 19, 2023
N. M. Galieva, A. V. Korolev, Ougolnitsky G. A., Dynamic Games and Applications 2023 P. 1–34
The discrete- and continuous-time network models of opinions control and resource allocation in marketing are considered. Three cases of interaction of economic agents are studied: independent behavior, cooperation, and hierarchical control by the resource-owning Principal. The corresponding dynamic games are analytically solved. The agents’ payoffs in these cases are compared. Two concepts, “enough resources” and ...
Added: March 14, 2023
Korolev A. V., Ougolnitsky G. A., International Game Theory Review 2023 Vol. 25 No. 2 Article 2350004
In this paper, we build and investigate cooperative games with different characteristic
functions (von Neumann–Morgenstern, Petrosyan–Zaccour, Gromova–Petrosyan) on the
base of symmetrical Cournot oligopoly game-theoretic models in normal form. We find
Nash and Stackelberg equilibria and cooperative solutions for nonsymmetrical Cournot
oligopoly game-theoretic models in normal form. Also, we build and investigate coop27
erative three-player games with the same characteristic ...
Added: January 26, 2023
Afanasiev V., М.: Красанд/URSS, 2020.
This book has been prepared on the basis of lectures on control theory given by the author for a number of years to students of the Department of Applied Mathematics of the National Research University Higher School of Economics and the Faculty of Physics Moscow State University named after M. V. Lomonosov. The content of the ...
Added: August 27, 2022
Korolev A. V., , in: Frontiers of Dynamic Games: Game Theory and Management, St. Petersburg, 2020.: Cham: Birkhäuser, 2021. P. 167–187.
Added: April 5, 2022
Cham: Birkhäuser, 2021.
This book features contributions from the GTM 2020 International Meeting on Game Theory held virtually from St. Petersburg, Russia, including presentations by plenary speakers. The topics cover a wide range of game-theoretic models and include both theory and applications, including applications to management. ...
Added: April 5, 2022
Botkin N. D., Golubev A., Turova V. L., IFAC-PapersOnLine 2019 Vol. 52 No. 16 P. 706–711
The problem of aircraft take-off under windshear conditions is considered as a differential game. A simplified five-dimensional nonlinear model of aircraft dynamics, assuming the flight in a vertical plane, is used. The overloads, differences between the projections of the thrust and drag, respectively lift, forces are considered as control variables. The corresponding technically relevant control, ...
Added: November 18, 2021
Petrosyan L., Yeung D., Pankratova Y., , in: Mathematical Optimization Theory and Operations Research: Recent Trends: 20th International Conference, MOTOR 2021, Irkutsk, Russia, July 5–10, 2021, Revised Selected Papers.: Cham: Springer, 2021. P. 403–416.
A class of cooperative differential games on networks is considered. It is supposed that players have the possibility to cut connections with neighbors at each time instant of the game. This gives the possibility to compute the values of a characteristic function for each coalition as a joint payoff of players from this coalition without ...
Added: November 1, 2021
Korolev A. V., Математическая теория игр и ее приложения 2021 № 1 С. 102–129
In this paper, stochastic parameters are introduced into the network games model with production and knowledges externalities. This model was formulated by V. Matveenko and A. Korolev and generalized two-period Romer model. Agents' productivities have deterministic and Wiener components. The research represents the dynamics of a single agent and the dynamics in a triangle which ...
Added: May 15, 2021
Afanasiev V., Semion A., Проблемы управления 2021 № 1 С. 24–35
A differential game of several players is considered as follows. One player (attacker) penetrates some space, and several other players (pursuers) appear simultaneously to intercept the attacker. Upon detecting the pursuers, the attacker tries to evade them. The dynamics of each player are described by a time-invariant linear system of a general type with scalar ...
Added: April 6, 2021
Zaremba A., Gromova E., Tur A., Mathematics 2020 Vol. 8 No. 12 Article 2185
One class of differential games with random duration is considered. It is assumed that the duration of the game is a random variable with values from a given finite interval. The cumulative distribution function (CDF) of this random variable is assumed to be discontinuous with two jumps on the interval. It follows that the player’s ...
Added: January 31, 2021
Korolev A. V., , in: Frontiers of Dynamic Games Game Theory and Management, St. Petersburg, 2019.: Birkhauser/Springer, 2020. Ch. 6 P. 65–85.
In this paper we introduce stochastic parameters into the network game
model with production and knowledge externalities. This model was proposed
by V. Matveenko and A. Korolev as a generalization of the two-period Romer
model. Agents differ in their productivities which have deterministic and stochastic
(Wiener) components. We study the dynamics of a single agent and the dynamics
of a ...
Added: November 30, 2020
Birkhauser/Springer, 2020.
The content of this volume is mainly based on selected talks that were given at the
“International Meeting on Game Theory (ISDG12-GTM2019),” as joint meeting of
“12th International ISDG Workshop” and “13th International Conference on Game
Theory and Management,” held in St. Petersburg, Russia on July 03–05, 2019. The
meeting was organized by St. Petersburg State University and International ...
Added: November 30, 2020
Averboukh Y., SIAM Journal on Control and Optimization 2016 Vol. 54 No. 5 P. 2629–2649
The paper is concerned with a zero-sum continuous-time stochastic differential game with a dynamics controlled by a Markov process and a terminal payoff. The value function of the original game is estimated using the value function of a model game. The dynamics of the model game differs from the original one. The general result applied ...
Added: April 17, 2020
Averboukh Y., Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki 2017 Vol. 27 No. 3 P. 299–308
The paper is concerned with the randomized Nash equilibrium for a nonzero-sum deterministic differential game of two players. We assume that each player is informed about the control of the partner realized up to the current moment. Therefore, the game is formalized in the class of randomized non-anticipative strategies. The main result of the paper ...
Added: April 17, 2020