$\Pi$-strategy algorithm in discrete pursuit games

This paper is devoted to the study of one well-known problem of B.N. Pshenichnyi, namely the problem of simple group pursuit, when players make step-by-step movements. The paper considers two separate cases. In the first case, a discrete pursuit game is solved, when only one pursuer and one evader participate in the game. To solve this problem, an algorithm for applying the $\Pi$-strategy is given. According to the proposed method, the players first approach each other and eventually coincide exactly. In the second case, the proposed solution method is extended to the game of group pursuit. The obtained results are verified using animation models created in the Visual $C\#$ programming language using ScottPlot.WinForms technology.