No 3 (11): 1.

Computer and Information Sciences

 2018

Scientific article
pdf-version

Anton E. Vladimirov
Student, Petrozavodsk State University
(Petrozavodsk, Belorusskaya 15, 433),
vladimirowant@yandex.ru
Daniil A. Egipti
Student, Petrozavodsk State University
(Petrozavodsk Sulajgorskaya 4/1 4),
san.delli253@gmail.com
Elizaveta M. Kurbankadieva
Student, Petrozavodsk State University
(Petrozavodsk Oktyabrsky prospect 63, 42),
kurbankadievalisa@yandex.ru

Game-theoretic model of patrolling on a linear graph

Scientific adviser:
Dorofeeva Julia Alexandrovna
Paper submitted on: 09/25/2018;
Accepted on: 12/12/2018;
 Abstract. The article deals with the problem of patrolling on a linear graph. The payment matrix of all possible variants of the game is constructed.
The winning strategies for attacking and patrolling are defined. The following regularities are revealed: how the patrolling strategies change, if you change the period of the game, the number of vertices of the graph (floors).
Keywords: Game Theory, payment matrix, graph, model, pure strategy

For citation: Vladimirov, A. E., Egipti, D. A., Kurbankadieva, E. M. Game-theoretic model of patrolling on a linear graph. StudArctic forum. 2018, 3 (11): 1.

References

1.V.V.Gusev,V.V.Mazalov,“Optimal'nye strategii v igre patrulirovaniya na grafe”, Vestn. S.-Peterburg. un-ta. Ser. 10. Prikl. matem. Inform. Proc. upr., 2015, № 2, 61–76

2. Zykov A.A. Osnovy teorii grafov. - M.:Nauka, 1987, 384 s.

3. Kobzar', A.I. Teoriya igr: Igrayut vse / A.I. Kobzar', V.N. Tikmenov, I.V. Tikmenova. - M.: Fizmatlit, 2015. - 272 c.

4.Mazalov V. V. Matematicheskaya teoriya igr i prilozheniya. — Sant-Peterburg - Moskva - Krasnodar: Lan', 2010. — 446 s.

5.Teoriya igr: Ucheb. posobie dlya un-tov:/L.A. Petrosyan, N.A. Zenkevich, E. A. Semina. - M.: Vyssh. shk., Knizhnyj dom «Universitet», 1998. - 304 s:

6. Kolesnik, G.V. Teoriya igr: Uchebnoe posobie / G.V. Kolesnik. - M.: KD Librokom, 2014. - 152 c.

7. Ore O. Teoriya grafov.— 2-e izd.— M.: Nauka, Glavnaya redakciya fiziko-matematicheskoj literatury, 1980, 336 s

8. Teoriya igr : uchebnik i praktikum dlya akademicheskogo bakalavriata / V. L. Shagin. — M. : Izdatel'stvo Yurajt, 2016. — 223 s. — Seriya : Avtorskij uchebnik.

9. F. Harari. Teoriya grafov. // Moskva, “Mir”, 1973. (Perevod s an- glijskogo. F.Harary, Graph theory, Addison-Wesley, 1969.)

Displays: 2792; Downloads: 396;