A multi-step generalization of the "attack-defense" model

The article reviewed a multi-step generalization of the "attack-defense" model, which was defined and studied by Y.B. Germeyer. It is a modification of Gross's model. A similar model was proposed by V.A. Gorelik for the production of gasoline. The authors proposes a simplest multi-step expansion of the "attack-defense" model, consisting in the fact that the corresponding game is played repeatedly until one of the parties reaches a given level of loss (exhaustion) incompatible with the further continuation of the conflict. It is assumed that the conditions of the parties' awareness at each step remains the same and the reserves are not introduced during the conflict. It is shown that under these assumptions the multistep game model reduces to a discrete Osipov–Lanchester's model having a solution in the form of a linear function of two geometric progressions with piecewise constant coefficients and denominators of progressions.