Geodesic
A multi-step generalization of the "attack-defense" model
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 2 (2017), pp. 89-100 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The article reviewed a multi-step generalization of the "attack-defense" model, which was defined and studied by Y.B. Germeyer. It is a modification of Gross's model. A similar model was proposed by V.A. Gorelik for the production of gasoline. The authors proposes a simplest multi-step expansion of the "attack-defense" model, consisting in the fact that the corresponding game is played repeatedly until one of the parties reaches a given level of loss (exhaustion) incompatible with the further continuation of the conflict. It is assumed that the conditions of the parties' awareness at each step remains the same and the reserves are not introduced during the conflict. It is shown that under these assumptions the multistep game model reduces to a discrete Osipov–Lanchester's model having a solution in the form of a linear function of two geometric progressions with piecewise constant coefficients and denominators of progressions.
Keywords: attack-defense game, guaranteed attack result, minimax defense strategy, guaranteed defense result, value of game, optimal mixed attack strategy, optimal pure defense strategy, simplest multi-step expansion of the game. 
@article{VTPMK_2017_2_a6,
     author = {A. G. Perevozchikov and V. Yu. Reshetov and A. I. Lesik},
     title = {A multi-step generalization of the "attack-defense" model},
     journal = {Vestnik Tverskogo gosudarstvennogo universiteta. Seri\^a Prikladna\^a matematika},
     pages = {89--100},
     year = {2017},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTPMK_2017_2_a6/}
}
TY  - JOUR
AU  - A. G. Perevozchikov
AU  - V. Yu. Reshetov
AU  - A. I. Lesik
TI  - A multi-step generalization of the "attack-defense" model
JO  - Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika
PY  - 2017
SP  - 89
EP  - 100
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/VTPMK_2017_2_a6/
LA  - ru
ID  - VTPMK_2017_2_a6
ER  - 
%0 Journal Article
%A A. G. Perevozchikov
%A V. Yu. Reshetov
%A A. I. Lesik
%T A multi-step generalization of the "attack-defense" model
%J Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika
%D 2017
%P 89-100
%N 2
%U http://geodesic.mathdoc.fr/item/VTPMK_2017_2_a6/
%G ru
%F VTPMK_2017_2_a6
A. G. Perevozchikov; V. Yu. Reshetov; A. I. Lesik. A multi-step generalization of the "attack-defense" model. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 2 (2017), pp. 89-100. http://geodesic.mathdoc.fr/item/VTPMK_2017_2_a6/

[1] Karlin S., Mathematical Methods in the Theory of Games, Programming and Economics, Mir Publ., Moscow, 1964 (in Russian)

[2] Germeyer Y. B., Introduction to the Theory of Operations Research, Nauka Publ., Moscow, 1971 (in Russian) | MR

[3] Gorelik V. A., Game Theory and Operations Research, Publishing house MINGP, Moscow, 1978 (in Russian)

[4] Vasin A. A., Morozov V. V., Game Theory and Models of Mathematical Economics, MAX Press, Moscow, 2005 (in Russian)

[5] Vasin A. A., Krasnoshchekov P. S., Morozov V. V., Operations Research, Publishing Center “Academy”, Moscow, 2008 (in Russian) | MR

[6] Molodtsov D. A., “Gross’s Model in the case of non-opposite interests”, Journal of Computational Mathematics and Mathematical Physics, 12:2 (1972), 309-320 (in Russian) | MR | Zbl

[7] Berzin E. A., Optimal Resource Allocation and Elements of System Synthesis, ed. E.V. Zolotov, Radio and Communication Publ., Moscow, 1974 (in Russian) | MR

[8] Berzin E. A., Optimal Resource Allocation and Game Theory, ed. E.V. Zolotov, Radio and Communication Publ., Moscow, 1983 (in Russian) | MR

[9] Danilchenko T. N., Masevich K. K., “Multistep game of two persons with a “cautious” second player and sequential transfer of information”, Journal of Computational Mathematics and Mathematical Physics, 19:5 (1974), 1323-1327 (in Russian)

[10] Krutov B. P., Dynamic Quasi-Informational Extensions of Games with an Expandable Coalition Structure, Computing Center of RAS Publ., Moscow, 1986 (in Russian)

[11] Perevozchikov A. G., Lesik I. A., “On a simplest model of the echeloned air defense system”, Vestnik TvGU. Seriya: Prikladnaya Matematika [Herald of Tver State University. Series: Applied Mathematics], 2013, no. 3 (30), 83-95 (in Russian)

[12] Perevozchikov A. G., Lesik I. A., Yanochkin I. Ye., “Model of the echeloned Air Defense queuing system”, Vestnik TvGU. Seriya: Prikladnaya Matematika [Herald of Tver State University. Series: Applied Mathematics], 2015, no. 4, 65-83 (in Russian)

[13] Reshetov V. Y., Perevozchikov A. G., Lesik I. A., “Model of overcoming the multilevel defense system by attack”, Applied Mathematics and Computer Science: Proceedings of the Faculty of Computational Mathematics and Cybernetics of Lomonosov Moscow State University, v. 49, ed. V.I. Dmitrieva, MAX Press, Moscow, 2015, 80-96 (in Russian)

[14] Hohzaki R., Tanaka V., “The effects of players recognition about the acquisition of his information by his opponent in an attrition game on a network”, Proceedings of 27th European conference on Operation Research, EURO2015 (12-15 July 2015, University of Strathclyde)

[15] Reshetov V. Y., Perevozchikov A. G., Lesik I. A., “Model of violation of layered defense system by attack with several constraints on the state”, Vestnik Moskovskogo Universiteta. Seriya 15. Vychislitel'naya Matematika i Kibernetika, 2017, no. 1, 26-32 (in Russian) | MR | Zbl

[16] Ogaryshev V. F., “Mixed strategies in a generalization of the Gross’s problem”, Journal of Computational Mathematics and Mathematical Physics \year 1973, 13:1, 59-70 (in Russian) | MR