The $\Pi$-strategy: Analogies and Applications

The notion of the strategy of parallel pursuit (briefly $\Pi$-strategy) was introduced and used to solve the quality problem in “the game with a survival zone” by L. A. Petrosyan. Further it was found other applications of $\Pi$-strategy. In the present work $\Pi$-strategy will be constructed in the cases when 1) a control function of Pursuer should be chosen from the space $L_2$ and that for Evader should be chosen from $L_\infty$; 2) control functions both of players should be chosen from the space $L_2$; 3) a control function of Pursuer should be chosen from intersection of spaces $L_2$ and $L_\infty$ while that for Evader should belong to $L_\infty$.