Game-theoretic models of battle action

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.