Game-theoretic models of battle action

Vladislav V. Shumov ; Vsevolod O. Korepanov

Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 13 (2021) no. 2, pp. 80-117.

Résumé

The main types of combined arms combat operations are offensive and defense. Using the function of victory in battle, which is an extension of the function of conflict by G. Tullock, the following game-theoretic problems have been solved. First, the extended Gross-Germeier "attack-defense" model, which is a special case of a more general "offensive-defense" model, and describing the solution by the parties of the nearest tactical tasks, is investigated. Secondly, it has been proved that in the problem of breaking through points of defense (the closest tactical task), the criteria “breaking through the weakest point” and “breaking through at least one point” are equivalent. Thirdly, in the model of resource distribution of attackers and defenders between tactical tasks (echelons), the use of two criteria: 1) the product of the probabilities of solving the nearest and subsequent tactical tasks, 2) the minimum value of the named probabilities, – gives two fundamentally different solutions. Fourthly, the results of decisions were checked for compliance with the principles of military art and the practice of battles, battles and operations.

Détail

Keywords: probabilistic model, combined arms battle, offensive, defense, resource distribution between points and tactical tasks, decision making in conditions of uncertainty.

Bibliographie

[1] Vasin A. A., Krasnoschekov P. S., Morozov V. V., Issledovanie operatsii, uchebnoe posobie, Izdatelskii tsentr Akademiya, M., 2008

[2] Vasin A. A., Morozov V. V., Teoriya igr i modeli matematicheskoi ekonomiki, uchebnoe posobie, Maks-Press, M., 2005

[3] D. Rogozin (red.), Voina i mir v terminakh i opredeleniyakh: voenno-politicheskii slovar, PoRog, M., 2004

[4] Vorobev I. N., Taktika – iskusstvo boya, uchebnik, Obschevoiskovaya akademiya VS Rossii, M., 2002

[5] Germeier Yu. B., Vvedenie v teoriyu issledovaniya operatsii, Gl. red. fiz.-mat. lit. izd-va «Nauka», M., 1971 | MR

[6] Glants D. M., Sovetskoe voennoe chudo 1941-1943. Vozrozhdenie Krasnoi Armii, Yauza, Eksmo, M., 2008

[7] Golovin N. N., Nauka o voine. O sotsiologicheskom izuchenii voiny, Izdatelstvo gazety «Signal», Parizh, 1938

[8] Dorokhov V. N., Ischuk V. A., “Boevye potentsialy podrazdelenii kak integralnyi kriterii otsenki boevykh vozmozhnostei voinskikh formirovanii i boevoi effektivnosti vooruzheniya, voennoi i spetsialnoi tekhniki”, Izvestiya rossiiskoi akademii raketnykh i artilleriiskikh nauk, 2017, no. 4 (99), 27–36

[9] Ionin G., “Teoriya obschevoiskovogo boya trebuet pereosmysleniya, razvitiya i sovershenstvovaniya”, Voenno-promyshlennyi kurer, 2005, no. 21 (88), 4

[10] Karlin S., Matematicheskie metody v teorii igr, programmirovanii i ekonomike, Mir, M., 1964

[11] Morozov V. V., Shalbuzov K. D., “Igrovaya model raspredeleniya resursov pri zaschite ob'ekta”, Matematicheskaya teoriya igr i ee prilozheniya, 5:4 (2013), 66–83 | Zbl

[12] Novikov D. A., “Ierarkhicheskie modeli voennykh deistvii”, Upravlenie bolshimi sistemami, 2012, no. 37, 25–62

[13] Ogaryshev V. F., “Smeshannye strategii v odnom obobschenii zadachi Grossa”, Zhurnal vychislitelnoi matematiki i matematicheskoi fiziki, 13:1 (1973), 59 | MR

[14] Osipov M. P., “Vliyanie chislennosti srazhayuschikhsya storon na ikh poteri”, Voennyi sbornik, 1915, no. 6, 59–74; No 7, 25–36; No 8, 31–40; No 9, 25–37

[15] Perevozchikov A. G., Reshetov V. Yu., Shapovalov T. G., “Mnogourovnevoe obobschenie modeli «napadenie-oborona»”, Vestnik TvGU. Seriya: Prikladnaya matematika, 2017, no. 1, 57–69

[16] Reshetov V. Yu., Perevozchikov A. G., Lesik I. A., “Model preodoleniya mnogourovnevoi sistemy zaschity napadeniem”, Prikladnaya matematika i informatika, 2015, no. 49, 80–96

[17] “Rech G. K. Zhukova na voenno-nauchnoi konferentsii, dekabr 1945 g.”, Voennaya mysl, 1985, Spetsialnyi vypusk (fevral), 3, 17–33

[18] Tsygichko V. I., Stoili F., “Metod boevykh potentsialov: istoriya i nastoyaschee”, Voennaya mysl, 1997, no. 4, 23–28

[19] Shumov V. V., “Uchet psikhologicheskikh faktorov v modelyakh boya (konflikta)”, Kompyuternye issledovaniya i modelirovanie, 8:6 (2016), 951–964

[20] Shumov V. V., “Issledovanie funktsii pobedy v boyu (srazhenii, operatsii)”, Problemy upravleniya, 2020, no. 6, 19–30

[21] Shumov V. V., Korepanov V. O., “Matematicheskie modeli boevykh i voennykh deistvii”, Kompyuternye issledovaniya i modelirovanie, 12:1 (2020), 217–242

[22] Borel E., “La theorie du jeu les equations integrales a noyau symetrique”, Comptes Rendus de l'Academie, 173 (1921), 1304–1308 | Zbl

[23] Brown G., Carlyle M., Salmeron J., Wood K., “Defending Critical Infrastructure”, Interfaces, 36:6 (2006), 530–544 | DOI

[24] Clausewitz K., Vom Krieg, 1832/34

[25] Dasgupta P. et al., “The existence of equilibrium in discontinuous economic games, I: Theory”, Review of Economic Studies, 53:1 (1986), 1–26 | DOI | MR | Zbl

[26] Hirshleifer J., “The Macrotechnology of Conflict”, Journal of Conflict Resolution, 44:6 (2000), 773–792 | DOI

[27] Jia H., Skaperdas S., Vaidya S., “Contest functions: Theoretical foundations and issues in estimation”, International Journal of Industrial Organization, 2013, no. 31, 211–222 | DOI

[28] Kar D. et al., “Trends and Applications in Stackelberg Security Games”, Handbook of Dynamic Game Theory, eds. Basar T., Zaccour G., Springer, Cham, 2016, 1–47 | MR

[29] Poropudas J., Virtanen K., “Game-theoretic validation and analysis of air combat simulation models”, IEEE Transactions on Systems, Man, and Cybernetics – Part A: Systems and Humans, 40:5 (2010), 1057–1070 | DOI | MR