The ``attack-defense'' game with restrictions on the intake capacity of points

A. G. Perevozchikov ; V. Yu. Reshetov ; A. I. Lesik

Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 3 (2020), pp. 78-92

Résumé

The work generalizes the Germeier’s "attack-defense" game in terms of accounting for the intake capacity of points and is based on his generalized equalization principle, which leads to convex minimax problems that can be solved by subgradient descent in the case of homogeneity of the parties' resources. The classical Germeier’s "attack-defense" model is a modification of the Gross’ model. The game model that generalizes Gross’ model and Germeier’s model was studied by Ogaryshev. Molodtsov studied the Gross’s model with nonantagonistic interests of the parties; Danilchenko, Masevich and Krutova studied the dynamic extensions of the model. In the military models the points are usually interpreted as directions and characterize the spatial distribution of defense resources by width. However, there are also actual restrictions on the intake capacity of points. This leads, in the case of homogeneous resources, to minimax problems for determining the best guaranteed defense result (BGDR). An accurate upper estimate for the best guaranteed defense result was obtained, which shows the potential defense capabilities taking into account the intake capacity of points.

Détail

Keywords: Gross’ model, Germeier’s model, generalized equalization principle, restrictions on the intake capacity of points, best guaranteed defense result, minimax defense strategy, mixed attack strategy.