Unhomogeneous «attack-defense» game on the basis of the generalized equalization principle

The work generalizes Germeyer's «attack-defense» game in terms of accounting for heterogeneity of resources of the parties and is based on Krasnovshchekov's generalized principle of the equalization which leads in general case to convex problems on connected minimax that can be solved by the subgradient descent method. The classic Germeyer's «attack-defense» model is a modification of Gross's model. In Ogaryshev's work the game model which generalizes Gross's and Germeyer's models was studied. In Molodtsov's work Gross's model with the nonantagonistic interests of the parties was studied, in the works of Danilchenko, Masevich and Krutov dynamic extensions of the model were studied. In military models the points are usually interpreted as directions and characterize the spatial width distribution of defense's resources. However, in reality there is also a spatial distribution of defense's resources through depth, characterized by the number of defense levels in this direction. Further generalization of the «attack-defense» model can consist in taking into account the heterogeneity of parties' means through a corresponding change in the probability of impact at each level of defense, which in turn is the result of solving the corresponding target distribution problem. This leads, in general, to minimax problems with bound constraints to determine the guaranteed defense's result, an example of which is given by the game «attack-defense» with heterogeneous resources of the parties, based on the generalized equalization principle, posed and studied in this paper.