Geodesic
The $\Pi$-strategy: Analogies and Applications
Contributions to game theory and management, Tome 4 (2011), pp. 33-46

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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 $L_\infty$.
Keywords: differential game, Pursuer, Evader, strategy, parallel pursuit, domain of attainability, survival zone. 
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     author = {A. A. Azamov and B. T. Samatov},
     title = {The $\Pi$-strategy: {Analogies} and {Applications}},
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     url = {http://geodesic.mathdoc.fr/item/CGTM_2011_4_a3/}
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A. A. Azamov; B. T. Samatov. The $\Pi$-strategy: Analogies and Applications. Contributions to game theory and management, Tome 4 (2011), pp. 33-46. http://geodesic.mathdoc.fr/item/CGTM_2011_4_a3/