Geodesic
Two Approaches for Solving a Group Pursuit Game
Contributions to game theory and management, Tome 6 (2013), pp. 362-376.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we study a game of group pursuit in which players move on a plane with bounded velocities. The game is supposed to be a nonzero-sum simple pursuit game between a pursuer and $m$ evaders acting independently of each other. The case of complete information is considered. Here we assume that the evaders are discriminated. Two different approaches to formalize this pursuit problem are considered: noncooperative and cooperative. In a noncooperative case we construct a Nash equilibrium, and in a cooperative case we construct the core. We proved that the core is not empty for any initial positions of the players.
Keywords: group pursuit game, Nash equilibrium, realizability area, TU-game, core. 
@article{CGTM_2013_6_a27,
     author = {Yaroslavna B. Pankratova and Svetlana I. Tarashnina},
     title = {Two {Approaches} for {Solving} a {Group} {Pursuit} {Game}},
     journal = {Contributions to game theory and management},
     pages = {362--376},
     publisher = {mathdoc},
     volume = {6},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CGTM_2013_6_a27/}
}
TY  - JOUR
AU  - Yaroslavna B. Pankratova
AU  - Svetlana I. Tarashnina
TI  - Two Approaches for Solving a Group Pursuit Game
JO  - Contributions to game theory and management
PY  - 2013
SP  - 362
EP  - 376
VL  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CGTM_2013_6_a27/
LA  - en
ID  - CGTM_2013_6_a27
ER  - 
%0 Journal Article
%A Yaroslavna B. Pankratova
%A Svetlana I. Tarashnina
%T Two Approaches for Solving a Group Pursuit Game
%J Contributions to game theory and management
%D 2013
%P 362-376
%V 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CGTM_2013_6_a27/
%G en
%F CGTM_2013_6_a27
Yaroslavna B. Pankratova; Svetlana I. Tarashnina. Two Approaches for Solving a Group Pursuit Game. Contributions to game theory and management, Tome 6 (2013), pp. 362-376. http://geodesic.mathdoc.fr/item/CGTM_2013_6_a27/

[1] Bondareva O., “Some applications of methods of linear programming to coorerative games theory”, Problems of Cybernatics, 10 (1963), 119–140 (in Russian) | MR

[2] Isaaks R., Differential Games: a mathematical theory with applications to warfare and pursuit, Control and Optimization, Wiley, New York, 1965 | MR

[3] Pankratova Y., “Some cases of cooperation in differential pursuit games”, Collected papers presented on the International Conference Game Theory and Management, Contributions to Game Theory and Management, eds. L. A. Petrosjan, N. A. Zenkevich, Graduated School of Management, SPbGU, St. Petersburg, 2007, 361–380

[4] Pankratova Ya. B., “A Solution of a cooperative differential group pursuit game”, Diskretnyi Analiz i Issledovanie Operatsii, 17:2 (2010), 57–78 (in Russian) | MR | Zbl

[5] Pankratova Ya., Tarashnina S., “How many people can be controlled in a group pursuit game”, Theory and Decision, 56 (2004), 165–181 | DOI | MR | Zbl

[6] Petrosjan L. A., Shirjaev V. D., “Simultaneous pursuit of several evaders by one pursuer”, Vestnik Leningrad Univ. Math., 13 (1981)

[7] Petrosjan L., Tomskii G., Geometry of Simple Pursuit, Nauka, Novosibirsk, 1983 (in Russian)

[8] Scarf H. E., “The core of an $n$-person game”, Econometrica, 35 (1967), 50–69 | DOI | MR | Zbl

[9] Shapley L., “On balanced sets and cores”, Naval Research Logistic Quarterly, 14 (1967), 453–460 | DOI

[10] Tarashnina S., “Nash equilibria in a differential pursuit game with one pursuer and $m$ evaders”, Game Theory and Applications, III, Nova Science Publ., N. Y., 1998, 115–123 | MR

[11] Tarashnina S., “Time-consistent solution of a cooperative group pursuit game”, International Game Theory Review, 4 (2002), 301–317 | DOI | MR | Zbl