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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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/

[1] Alekseev V. M., Tikhomirov V. M., Fomin S. V., Optimal Control, Nauka, M., 1979, 432 pp. (in Russian) | MR

[2] Azamov A. A., “About the quality problem for the games of simple pursuit with the restriction”, Serdika. Bulgarian math. spisanie, 12 (1986), 38–43 (in Russian) | MR | Zbl

[3] Azamov A. A., Samatov B. T., $\Pi$-strategy, UzNU, Tashkent, 2000, 36 pp.

[4] Blagodatskiy V. I., Differential Inclusions Theory, v. I, MSU, Moscow, 1979, 89 pp. (in Russian)

[5] Chikrii A. A., Conflict-controlled processes, Kluwer Academ. Publ., Boston–London–Dordrecht, 1997, 424 pp. | MR | Zbl

[6] Friedman A., Differential Games, Wiley, New York, 1971, 350 pp. | MR | Zbl

[7] Grigorenco N. L., Diff. games pursuit with some objects, MSU, M., 1990, 198 pp. (in Russian)

[8] Hajek O., Pursuit Games, Mathematics in Science and Engineering, 120, AkademPress, New York, 1975, 266 pp. | DOI | MR

[9] Isaacs R., Differential Games, J. Wiley, New York–London–Sydney, 1965, 384 pp. | MR | Zbl

[10] Ibragimov G. I., “Collective pursuit with integral constrains on the controls of players”, Siberian Advances in Mathematics, 14:2 (2004), 13–26 | MR

[11] Krasovskiy N. N., Control of a Dynamical System, Nauka, M., 1985, 520 pp. (in Russian) | MR

[12] Petrosyan L. A., “About some of the family differential games at a survival in the space $\mathbb R^n$”, Dokl. Akad. Nauk SSSR, 161:1 (1965), 52–54 (in Russian) | MR | Zbl

[13] Petrosyan L. A., The Differential Games of pursuit, LSU, Leningrad, 1977, 224 pp. (in Russian) | MR

[14] Petrosyan L. A., Rikhsiev B. B., Pursuit on the plane, Nauka, M., 1991, 96 pp. (in Russian)

[15] Petrosyan L. A., Mazalov V. V., Game Theory and Applications, v. I, Nova Sci. Publ., New York, 1996, 211 pp. ; v. II, 219 pp. | MR

[16] Petrosyan L. A., “Pursuit Games with “a Survival Zone””, Vestnic Leningard State Univ., 13 (1967), 76–85 (in Russian) | Zbl

[17] Petrosyan L. A., Dutkevich V. G., “Games with “a Survival Zone”, Occation $l$-catch”, Vestnic Leningard State Univ., 13:3 (1969), 31–38 (in Russian)

[18] Pontryagin L. S., “Linear Differential Pursuit Games”, Math. USSR-Sb, 112:3, 307–330 | MR | Zbl

[19] Pshenichnyi B. N., “The simple pursuit with some objects”, Cybernetics, 3 (1976), 145–146

[20] Rikhsiev B. B., The differential games with simple motions, Fan, Tashkent, 1989, 232 pp. (in Russian) | MR | Zbl

[21] Ushakov V. N., “Extremal strategies in Theory Differential Games with integral constraints”, Journal of Applied Mathematics and Mechanics, 36:1 (1972), 15–22 | DOI | MR

[22] Satimov N. Yu., Methods of solving of pursuit problem in differential games, NUUz, Tashkent, 2003, 245 pp. (in Russian)

[23] Samatov B. T., “The construction of the $\Pi$-strategy for the game on simple pursuit with integral constraints”, The boudary value problems for non-classical mathematical-physical eguations, Fan, Tashkent, 1986, 402–412 (in Russian) | MR

[24] Samatov B. T., The some problems Linear Differential Games with integral constraints, The pertaining to kandidat dissertation, Tashkent, 1990, 127 pp. (in Russian)

[25] Samatov B. T., “The Differential Game with “A Survival Zone” with Different Classes of Admissiable Control Functions”, Game Theory and Applications, 13, Nova Science Publ, 2008, 143–150 | MR