Geodesic
One class of simultaneous pursuit games
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2012), pp. 46-55.

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

Let $A$ and $B$ be given convex closed bounded nonempty subsets in a Hilbert space $H$; let the first player choose points in the set $A$ and let the second one do those in the set $B$. We understand the payoff function as the mean value of the distance between these points. The goal of the first player is to minimize the mean value, while that of the second player is to maximize it. We study the structure of optimal mixed strategies and calculate the game value.
Keywords: simultaneous game, mixed strategy, payoff function, optimal mixed strategies, game value. 
@article{IVM_2012_5_a4,
     author = {N. Yu. Satimov and G. I. Ibragimov},
     title = {One class of simultaneous pursuit games},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {46--55},
     publisher = {mathdoc},
     number = {5},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2012_5_a4/}
}
TY  - JOUR
AU  - N. Yu. Satimov
AU  - G. I. Ibragimov
TI  - One class of simultaneous pursuit games
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2012
SP  - 46
EP  - 55
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2012_5_a4/
LA  - ru
ID  - IVM_2012_5_a4
ER  - 
%0 Journal Article
%A N. Yu. Satimov
%A G. I. Ibragimov
%T One class of simultaneous pursuit games
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2012
%P 46-55
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2012_5_a4/
%G ru
%F IVM_2012_5_a4
N. Yu. Satimov; G. I. Ibragimov. One class of simultaneous pursuit games. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2012), pp. 46-55. http://geodesic.mathdoc.fr/item/IVM_2012_5_a4/

[1] Vorobev N. N., Osnovy teorii igr. Beskoalitsionnye igry, Nauka, M., 1984 | MR

[2] Karlin S., Matematicheskie metody v teorii igr, ekonomike i programmirovanii, Mir, M., 1964 | Zbl

[3] Petrosyan L. A., Differentsialnye igry presledovaniya, Izd. LGU, L., 1977 | MR | Zbl

[4] Satimov N. Yu., Petrosyan L. A., Azamov A. A., “Struktura optimalnykh strategii v odnovremennykh igrakh presledovaniya”, Upravlyaemye sistemy, 13, Novosibirsk, 1974, 65–68 | Zbl

[5] Azamov A. A., “Postroenie optimalnykh strategii v odnoi beskonechnoi igre dvukh lits”, Izv. AN SSSR. Tekhn. kibernetika, 1978, no. 1, 27–29

[6] Satimov N. Yu., Ibragimov G. I., “Struktura optimalnykh strategii v odnovremennykh igrakh presledovaniya v gilbertovykh prostranstvakh”, Uzb. matem. zhurn., 1997, no. 4, 51–61 | MR

[7] Shiryaev A. N., Veroyatnost, Nauka, M., 1980 | MR | Zbl

[8] N. N. Vorobev (red.), Beskonechnye antagonicheskie igry, Sb. perevodov, Fizmatgiz, M., 1963

[9] Oben Zh.-P., Nelineinyi analiz i ego ekonomicheskie prilozheniya, Mir, M., 1988 | MR

[10] Pshenichnyi B. N., Neobkhodimoe uslovie ekstremuma, Nauka, M., 1982 | MR

[11] Felps R., Lektsii o teoremakh Shoke, Mir, M., 1968