Expansion of the «attack–defense» model

A probabilistic model of combat based on the principles of warfare and the definition of combat is considered. The parameter of combat superiority takes into account the moral and technological characteristics. Its estimation by the maximum likelihood method is proposed. The «attack-defense» model is formulated, taking into account the two-tier formation of troops (implementation of the next and subsequent tasks). The solution of three problems connected with search is found: 1) distribution of means between the points of defense; 2) quantity (share) of the means allocated in the second echelon (reserve); 3) the rate of movement of units in battle and their losses. The first problem is solved using the Y.B. Germeyer's generalized principle of equalization. Within the second problem reducing the game to an antagonistic matrix type allowed us to find optimal solutions for the distribution of forces of the parties between the echelons. It is shown that the decision of the game has a meaningful interpretation from the military science point of view (positional and mobile defense). To solve the third problem, military statistics data were used. The applicability of the presented models during command-staff and experimental exercises is shown on concrete examples.