Abstract
The algorithm for constructing solutions for a class of hierarchical dynamic two-person games in the Stackelberg formulation is stated. The algorithm performance is illustrated by the example of software implementation fulfilled for the nonlinear dynamic Stackelberg game that admits, however, the solution by the indicated algorithm with a little modification. The obtained results are compared with the analytic solution.
Similar content being viewed by others
References
Krasovskii, N.N. and Subbotin, A.I., Pozitsionnye differentsial’nye igry, Moscow: Nauka, 1974. Translated into English under the title Positional Differential Games, Berlin: Springer-Verlag, 1988.
Krasovskii, N.N., Upravlenie dinamicheskoi sistemoi (Control of Dynamic Systems), Moscow: Nauka, 1985.
Kleimenov, A.F., Neantagonisticheskie pozistionnye differentsial’nye igry (Nonantagonistic Positional Differential Games), Yekaterinburg: Nauka, 1993.
Osipov, S.I., Numerical Construction of Solutions to One Class of Hierarchical Linear Differential Games in the PLane, in Ustoichivost’i nelineinye kolebaniya (Stability and Nonlinear Oscillations), Sverdlovsk: Ural. Gos. Univ., 1991.
Osipov, S.I., Algorithm for Constructing the Algebraic Sum of Nonconvex Simply Connected and Convex Polygons, in Problemy teoreticheskoi i prikladnoi matematiki (Problems of Theoretical and Applied Mathematics), Sverdlovsk: Inst. Mat. Mekh., 1989.
Vakhrushev, V.A., Taras’ev, A.M., and Ushakov, V.N., Algorithm for Constructing the Intersection and Union of Sets in the Plane, in Upravlenie s garantirovannym resul’tatom (Control with the Guaranteed Result), Sverdlovsk: Inst. Mat. Mekh., 1987.
Isakova, E.A., Logunova, G.V., and Patsko, V.S., Construction of Stable Bridges in the Linear Differentail Game with the Fixed Termination Moment, in Algoritmy i programmy resheniya lineinykh differentsial’nykh igr (materialy po matematicheskomu obespecheniyu EVM) (Algorithms and Programs for Solving Linear Differential Games (Reports on Software)), Sverdlovsk: Inst. Mat. Mekh., 1984.
Kleimenov, A. and Osipov S., Computation of Stackelberg Trajectories in a Class of Two-Person Linear Differential Games with Terminal Players’ Payoffs and Polygonal Constraining for Control, CAO 2003 Workshop, IFAC Proc., Oxford: Elsevier, 2003.
Vaisblat, P.M. and Kleimenov, A.F., Solution to One Hierarchical Differential Two-Person Game, in Upravlenie s garantirovannym resul’tatom (Control with the Guaranteed Result), Sverdlovsk: Inst. Mat. Mekh., 1987, pp. 15–27.
Brooks, F., The Mythical Man-Month: Essays on Software Engineering, Reading: Addison-Wesley, 1975. Translated under the title Mificheskii cheloveko-mesyats, ili kak sozdayutsya programmnye sistemy, Moscow: Simvol-Plyus, 2006.
Author information
Authors and Affiliations
Additional information
Original Russian Text © S.I. Osipov, 2007, published in Avtomatika i Telemekhanika, 2007, No. 11, pp. 195–207.
Rights and permissions
About this article
Cite this article
Osipov, S.I. Realization of the algorithm for constructing solutions for a class of hierarchical Stackelberg games. Autom Remote Control 68, 2071–2082 (2007). https://doi.org/10.1134/S0005117907110148
Received:
Issue Date:
DOI: https://doi.org/10.1134/S0005117907110148