Abstract
The classical Germeier’s attack–defense game is generalized for the case of defense in depth (multilayered defense) that has a network structure. The generalization is based on the work by Hohzaki and Tanaka. In distinction from this work, the defense in each possible direction of motion between the network nodes given by directed arcs may have multiple layers, which leads in the general case to convex minimax problems that can be solved using the subgradient descent method. In particular, the proposed model generalizes the classical attack–defense model for the multilayered defense without the simplifying assumption that the effectiveness of defense is independent of the defense layer.
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REFERENCES
A. G. Perevozchikov, I. A. Lesik, and T. G. Shapovalov, “A multi-level generalization of the attack–defense model,” Vestn. Tver. Gos. Univ., Ser. Prikl. Mat., No. 1, 39–51 (2017).
V. Yu. Reshetov, A. G. Perevozchikov, and I. A. Lesik, “A model of overcoming multilayered air defense by means of attack,” in Applied Mathematics and Informatics: Proceedings of the Faculty of Computational Mathematics and Cybernetics, Moscow State University, Ed. by V. I. Dmitriev (MAKS, Moscow, 2015), No. 49, pp. 80–96.
I. A. Lesik, A. G. Perevozchikov, and V. Yu. Reshetov, “Multi-level defense system models: Overcoming by means of attacks with several phase constraints,” Moscow Univ. Comput. Math. Cybernet. 41, 25–31 (2017).
A. G. Perevozchikov, V. Yu. Reshetov, and I. E. Yanochkin, “An attack–defense model with inhomogeneous resources of the opponents,” Comput. Math. Math. Phys. 58, 38–47 (2018).
Yu. B. Germeier, Introduction to the Theory of Operations Research (Nauka, Moscow, 1971) [in Russian].
S. Karlin, Mathematical Methods and Theory in Games, Programming and Economics (Addison-Wesley, Reading, 1959; Moscow, Mir, 1964).
V. F. Ogaryshev, “Mixed strategies in a generalization of the Gross problem,” Zh. Vychisl. Mat. Mat. Fiz. 13 (1), 59–70 (1973).
D. A. Molodtsov, “The Gross model in the case of nonopposite interests,” Zh. Vychisl. Mat. Mat. Fiz. 12 (2), 309–320 (1972).
T. N. Danil’chenko and K. K. Masevich, “A multistep two-person game in the case of a cautious second player and sequential information transmission,” Zh. Vychisl. Mat. Mat. Fiz. 19, 1323–1327 (1974).
B. P. Krutov, Dynamic quasi-information extensions of games with the extendable coalition structure (Vych. Tsentr. Ross. Akad. Nauk, Moscow, 1986) [in Russian].
R. Hohzaki and V. Tanaka, “The effects of players recognition about the acquisition of his information by his opponent in an attrition game on a network,” Abstract of 27th European Conference on Operation Research (EURO2015), 2015, University of Strathclyde.
V. S. Tanaev, Yu. N. Sotskov, and V. A. Strusevich, Scheduling Theory: Multistage Systems (Nauka, Moscow, 1989) [in Russian].
A. A. Vasin and V. V. Morozov, Game Theory and Models of Mathematical Economics (MAKS, Moscow, 2005) [in Russian].
A. G. Sukharev, A. V. Timokhov, and V. V. Fedorov, A Course of Optimization Methods (Nauka, Moscow, 1986) [in Russian].
B. T. Polyak, Introduction to Optimization (Optimization Software, New York, 1987; Nauka, Moscow, 1983).
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Translated by A. Klimontovich
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Perevozchikov, A.G., Reshetov, V.Y. & Yanochkin, I.E. Multilayered Attack–Defense Model on Networks. Comput. Math. and Math. Phys. 59, 1389–1397 (2019). https://doi.org/10.1134/S0965542519080128
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DOI: https://doi.org/10.1134/S0965542519080128