Geodesic
Generalized `Lion Man’ Game of R. Rado
Contributions to game theory and management, Tome 2 (2009), pp. 8-20 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In the present work we study the game of degree for generalized "Lion and Man" game where "Lion" L moves on the plane while "Man" M must move along the given curve $\Gamma $ . The case when $\Gamma $ is circumference the problem was formulated by R. Rado and can be considered as the first example of dynamic games. By elementary but refined arguments R. Rado (Littlewood, 1957, Rado, 1973) proved that $L$ can capture $M$ if speeds of both points are equal. Further interesting results on "Lion $\$ Man" game concerning the case when both points moved inside a circle, was obtained by J. O. Flynn (1973, 1974).
Keywords: differential game, pursuit, strategy, "Lion and Man".
Mots-clés : evasion 
@article{CGTM_2009_2_a1,
     author = {Abdulla A. Azamov and Atamurot Sh. Kuchkarov},
     title = {Generalized {`Lion} & {Man{\textquoteright}} {Game} of {R.~Rado}},
     journal = {Contributions to game theory and management},
     pages = {8--20},
     year = {2009},
     volume = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CGTM_2009_2_a1/}
}
TY  - JOUR
AU  - Abdulla A. Azamov
AU  - Atamurot Sh. Kuchkarov
TI  - Generalized `Lion & Man’ Game of R. Rado
JO  - Contributions to game theory and management
PY  - 2009
SP  - 8
EP  - 20
VL  - 2
UR  - http://geodesic.mathdoc.fr/item/CGTM_2009_2_a1/
LA  - en
ID  - CGTM_2009_2_a1
ER  - 
%0 Journal Article
%A Abdulla A. Azamov
%A Atamurot Sh. Kuchkarov
%T Generalized `Lion & Man’ Game of R. Rado
%J Contributions to game theory and management
%D 2009
%P 8-20
%V 2
%U http://geodesic.mathdoc.fr/item/CGTM_2009_2_a1/
%G en
%F CGTM_2009_2_a1
Abdulla A. Azamov; Atamurot Sh. Kuchkarov. Generalized `Lion & Man’ Game of R. Rado. Contributions to game theory and management, Tome 2 (2009), pp. 8-20. http://geodesic.mathdoc.fr/item/CGTM_2009_2_a1/

[1] Littlewood F. I., A Mathematician's Miscellany, Methuen Co., London, 1957

[2] Rado R., “How the leon tames was saved”, Math. Spectrum, 6:1 (1973), 14–18

[3] Flynn J. O., “Lion and Man: the boundari constraint”, SIAM J. Control Optim., 11:3 (1973), 397–411 | MR | Zbl

[4] Flynn J. O., “Pursuit in the circle: lion versus man”, Different. Games and Cont. Theory, 1974, 99–124 | Zbl

[5] Lewin J., “The Lion and Man Problem Revisited”, JOTA, 49:3 (1986), 411–430 | DOI | MR | Zbl

[6] Friedman A., Differential games, Wiley, New York, 1971 | MR | Zbl

[7] Krasovskiy N. N., Subbotin A. I., Game-theoretical control problems, Springer-Verlag, 1988 | MR

[8] Petrosyan L. A., Differential games of pursuit, Leningrad University Press, Leningrad, 1977 (in Russian) | MR

[9] Pontryagin L. S., “Linear differential dames of evasion”, Dokladi Akademii Nauk SSSR, 191:2 (1970), 283–285 (in Russian) | MR | Zbl

[10] Kuchkarov A. Sh., “Solusion of Simple pursuit-Evasion Problem when Evader Moves on Given Curve”, IGTR, 2008 (to appear) http://www.worldscinet.com/iqtr/edioterial/paper

[11] Azamov A. A., “On a Problem of Escape Along a Prescribed Curve”, J. App. Math. and Mash., 46:4 (1986), 553–555 | MR

[12] Azamov A. A., Samatov B. T., $\pi$-strategy, Press of the Nashional University of Uzbekistan, Tashkent, 2000