Numerical construction of the information set and sufficient conditions for k-detection in the simple search game on the plane
Matematičeskie zametki SVFU, Tome 24 (2017) no. 2, pp. 13-29 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The antagonistic differential simple search game on the plane is considered. The searcher is moving along straight lines. Using the auxiliary game with a detail of pursuers the estimates for the detection probability are determined. The information sets are built in the example with two and three pursuers.
Keywords: differential search game, mixed strategies.
Mots-clés : information set
@article{SVFU_2017_24_2_a1,
     author = {S. V. Mestnikov and N. V. Petrov},
     title = {Numerical construction of the information set and sufficient conditions for k-detection in the simple search game on the plane},
     journal = {Matemati\v{c}eskie zametki SVFU},
     pages = {13--29},
     year = {2017},
     volume = {24},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVFU_2017_24_2_a1/}
}
TY  - JOUR
AU  - S. V. Mestnikov
AU  - N. V. Petrov
TI  - Numerical construction of the information set and sufficient conditions for k-detection in the simple search game on the plane
JO  - Matematičeskie zametki SVFU
PY  - 2017
SP  - 13
EP  - 29
VL  - 24
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SVFU_2017_24_2_a1/
LA  - ru
ID  - SVFU_2017_24_2_a1
ER  - 
%0 Journal Article
%A S. V. Mestnikov
%A N. V. Petrov
%T Numerical construction of the information set and sufficient conditions for k-detection in the simple search game on the plane
%J Matematičeskie zametki SVFU
%D 2017
%P 13-29
%V 24
%N 2
%U http://geodesic.mathdoc.fr/item/SVFU_2017_24_2_a1/
%G ru
%F SVFU_2017_24_2_a1
S. V. Mestnikov; N. V. Petrov. Numerical construction of the information set and sufficient conditions for k-detection in the simple search game on the plane. Matematičeskie zametki SVFU, Tome 24 (2017) no. 2, pp. 13-29. http://geodesic.mathdoc.fr/item/SVFU_2017_24_2_a1/

[1] Petrosyan L. A. and Zenkevich N. A., Optimal Search under Conditions of Conflict. Textbook, Leningr. Univ., Leningrad, 1986 | MR

[2] Petrosyan L. A. and Garnaev A. Yu., Search Games. Textbook, Izdat. St. Petersb. Univ., St. Petersburg, 1992 | MR

[3] Zenkevich N. A. and Mestnikov S. V., “Dynamic search for a moving object in conditions of a conflict”, Control of dynamical systems, 14 (1991), 68–76

[4] Mestnikov S. V., “Approximation of the domain of uncertainty in differential search games”, Differ. Equations, 28:6 (1992), 967–972 | MR

[5] Mestnikov S. V., “Estimates for the detection probability and uncertainty domain in a differen tial search game”, Mat. Zamet. YaGU, 1:2 (1994), 99–104

[6] Mestnikov S. V., “Information sets and mixed strategies in a differential search game”, Mat. Zamet. YaGU, 3:1 (1996), 87–94

[7] Mestnikov S. V., “Approximation of The Information Sets in Differential Search game with Detail of Pursuers”, Dynamic Games Appl., Proc. Tenth Intern. Sympos. (St. Petersburg, Russia), 2002, 630–631

[8] Mestnikov S. V., “Approximation of the information set of a differential search game with detail of searchers”, Mat. Zamet. YaGU, 9:1 (2002), 58–71 | MR

[9] Mestnikov S. V., Everstova G. V., “Approximation of the information set in a differential search game with a team of evaders”, Contributions to Game Theory and Management, 3 (2010), 280-288 | MR

[10] Mestnikov S. V., Petrov N. V., Everstova G. V., “Numerical cobstruction of the information sets in the simple search game with a team of pursuers and estimates for a detection probability”, Collected abstracts of papers presented on the Eighth International Conference Game Theory and Management (GTM2014), Graduate School of Management, SPbU, 2014, 207-208

[11] Hohzaki R., “Search games: Literature and survey”, J. Operat. Res. Soc. Japan, 59:1 (2016), 1–34 | DOI | MR