Geodesic
Efficient Myerson value for union stable structures
Contributions to game theory and management, Tome 7 (2014), pp. 17-23.

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

In this work, an axiomatization of a new value for union stable structures, efficient Myerson value, is shown by average equity, redundant fairness, superfluous component property and other three properties. And the independence of the axioms is illustrated. Besides, the difference of three values, efficient Myerson value, the two-step Shapley value and collective value, is shown.
Keywords: Union stable structure; average equity; redundant fairness. 
@article{CGTM_2014_7_a2,
     author = {Hua Dong and Hao Sun and Genjiu Xu},
     title = {Efficient {Myerson} value for union stable structures},
     journal = {Contributions to game theory and management},
     pages = {17--23},
     publisher = {mathdoc},
     volume = {7},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CGTM_2014_7_a2/}
}
TY  - JOUR
AU  - Hua Dong
AU  - Hao Sun
AU  - Genjiu Xu
TI  - Efficient Myerson value for union stable structures
JO  - Contributions to game theory and management
PY  - 2014
SP  - 17
EP  - 23
VL  - 7
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CGTM_2014_7_a2/
LA  - en
ID  - CGTM_2014_7_a2
ER  - 
%0 Journal Article
%A Hua Dong
%A Hao Sun
%A Genjiu Xu
%T Efficient Myerson value for union stable structures
%J Contributions to game theory and management
%D 2014
%P 17-23
%V 7
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CGTM_2014_7_a2/
%G en
%F CGTM_2014_7_a2
Hua Dong; Hao Sun; Genjiu Xu. Efficient Myerson value for union stable structures. Contributions to game theory and management, Tome 7 (2014), pp. 17-23. http://geodesic.mathdoc.fr/item/CGTM_2014_7_a2/

[1] Algaba E., Bilbao J. M., Borm P., Lopez J. J., “The position value for union stable systems”, Mathematical Methods of Operations Research, 52 (2000), 221–236 | DOI | MR | Zbl

[2] Algaba E., Bilbao J. M., Borm P., Lopez J. J., “The Myerson value for union stable structures”, Mathematical Methods of Operations Research, 54 (2001), 359–371 | DOI | MR | Zbl

[3] Driessen T. S. H., “Associated consistency and values for TU games”, International Journal of Game Theory, 39 (2010), 467–482 | DOI | MR | Zbl

[4] Gilles R. P, Owen G., Brink R., “Games with permission structures: the conjunctive approach”, International Journal of Game Theory, 20 (1992), 277–293 | DOI | MR | Zbl

[5] Hamiache G., “Associated consistency and Shapley value”, International Journal of Game Theory, 30 (2001), 279–289 | DOI | MR | Zbl

[6] Hamiache G., “A matrix approach to Shapley value”, International Game Theory Review, 12 (2010), 1–13 | DOI | MR

[7] Hamiache G., “A matrix approach to TU games with coalition and communication structures”, Social Choice and Welfare, 38 (2012), 85–100 | DOI | MR | Zbl

[8] Myerson R. B., “Graphs and cooperation in games”, Mathematics of operations research, 2 (1977), 225–229 | DOI | MR | Zbl

[9] Shapley L. S., “A value for n-person games”, Contributions to the Theory of Games, eds. Tucker A. W., Kuhn H. W., Princeton University Press, 1953 | MR

[10] Xu G., Driessen T., Sun H., “Matrix analysis for associated consistency in cooperative game theory”, Linear Algebra and its Applications, 428 (2008), 1571–1586 | DOI | MR | Zbl

[11] van den Brink R., Khmelnitskaya A., Van der Laan G., “An efficient and fair solution for communication graph games”, Economics Letters, 117 (2012), 786–789 | DOI | MR | Zbl

[12] Kamijo Y., “The collective value: a new solution for games with coalition structures”, TOP, 2011, 1–18 | MR