The vectors of Shapley, Owen, and the Aumann--Dreze in the game patrolling with coalition structure
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 8 (2016) no. 4, pp. 30-42.

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

We consider a simple model of cooperative version for a patrolling game with coalition structure. It is shown that the Shapley value coincides with the Owen and the Aumann–Dreze vector for odd number of the patrolling.
Keywords: patrolling game, cooperative approach, Shapley value, Owen value, Aumann–Dreze value.
Mots-clés : coalition structure
@article{MGTA_2016_8_4_a2,
     author = {Vasilij V. Gusev},
     title = {The vectors of {Shapley,} {Owen,} and the {Aumann--Dreze} in the game patrolling with coalition structure},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
     pages = {30--42},
     publisher = {mathdoc},
     volume = {8},
     number = {4},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MGTA_2016_8_4_a2/}
}
TY  - JOUR
AU  - Vasilij V. Gusev
TI  - The vectors of Shapley, Owen, and the Aumann--Dreze in the game patrolling with coalition structure
JO  - Matematičeskaâ teoriâ igr i eë priloženiâ
PY  - 2016
SP  - 30
EP  - 42
VL  - 8
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MGTA_2016_8_4_a2/
LA  - ru
ID  - MGTA_2016_8_4_a2
ER  - 
%0 Journal Article
%A Vasilij V. Gusev
%T The vectors of Shapley, Owen, and the Aumann--Dreze in the game patrolling with coalition structure
%J Matematičeskaâ teoriâ igr i eë priloženiâ
%D 2016
%P 30-42
%V 8
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MGTA_2016_8_4_a2/
%G ru
%F MGTA_2016_8_4_a2
Vasilij V. Gusev. The vectors of Shapley, Owen, and the Aumann--Dreze in the game patrolling with coalition structure. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 8 (2016) no. 4, pp. 30-42. http://geodesic.mathdoc.fr/item/MGTA_2016_8_4_a2/

[1] Gusev V. V., “Situatsiya ravnovesiya v igre patrulirovaniya na grafe”, Trudy Karelskogo nauchnogo tsentra RAN, 2015, no. 10, 28–33

[2] Gusev V. V., Mazalov V. V., “Optimalnye strategii v igre patrulirovaniya na grafe”, Vestn. S.-Peterburg. un-ta. Ser. 10. Prikl. matem. Inform. Prots. upr., 2015, no. 2, 61–76

[3] Mazalov V. V., Matematicheskaya teoriya igr i prilozheniya, Ucheb. posobie, Izd-vo «Lan», SPb., 2010

[4] Parilina E. M., Sedakov A. A., “Ustoichivost koalitsionnykh struktur odnoi modeli bankovskoi kooperatsii”, Matematicheskaya Teoriya Igr i ee Prilozheniya, 4:4 (2012), 45–62

[5] Alpern S., Fokkink R., Simanjuntak M., “Optimal search and ambush for a hider who can escape the search region”, European Journal of Operational Research, 251:3 (2016), 707–714 | DOI | MR | Zbl

[6] Bachrach Y., Markakis E., Resnick E., Procaccia A. D., Rosenschein J. S., Saberi A., “Approximating power indices: theoretical and empirical analysis”, Autonomous Agents and Multi-Agent Systems, 20 (2010), 105–122 | DOI

[7] Belau J., “A Note on the Owen Value for Glove Games”, International Game Theory Review, 17:4 (2015), 1550014-1–1550014-8 | DOI | MR

[8] Garnaev A., Search Games and Other Applications of Game Theory, Springer, Heidelberg–New York, 2000 | MR | Zbl

[9] Juan J., “Vidal-Puga and Gustavo Bergantinos An implementation of the Owen value”, Games and Economic Behavior, 44:2 (2003), 412–427 | DOI | MR | Zbl

[10] Hamiache G., “A new axiomatization of the Owen value for games with coalition structures”, Mathematical Social Sciences, 37 (1999), 281–305 | DOI | MR | Zbl

[11] Khmelnitskaya A. B., Yanovskaya E. B., “Owen coalitional value without additivity axiom”, Mathematical Methods of Operations Research, 66:2 (2007), 255–261 | DOI | MR | Zbl