Geodesic
Existence of stable coalition structures in four-person games
Contributions to game theory and management, Tome 11 (2018), pp. 224-248.

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

Cooperative games with coalition structures are considered and the principle of coalition structure stability with respect to some cooperative solution concepts is determined. This principle is close to the concept of Nash equilibrium. The existence of a stable coalition structure with respect to the Shapley value and the equal surplus division value for the cases of two- and three-person games is proved. In this paper, the problem of existence of a stable coalition structure with respect to the Shapley value and the equal surplus division value for the case of four-person games with special characteristic function is examined.
Keywords: coalition structure, stability, the Shapley value, the ES-value, four-player cooperative games. 
@article{CGTM_2018_11_a12,
     author = {Fengyan Sun and Elena Parilina},
     title = {Existence of stable coalition structures in four-person games},
     journal = {Contributions to game theory and management},
     pages = {224--248},
     publisher = {mathdoc},
     volume = {11},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CGTM_2018_11_a12/}
}
TY  - JOUR
AU  - Fengyan Sun
AU  - Elena Parilina
TI  - Existence of stable coalition structures in four-person games
JO  - Contributions to game theory and management
PY  - 2018
SP  - 224
EP  - 248
VL  - 11
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CGTM_2018_11_a12/
LA  - en
ID  - CGTM_2018_11_a12
ER  - 
%0 Journal Article
%A Fengyan Sun
%A Elena Parilina
%T Existence of stable coalition structures in four-person games
%J Contributions to game theory and management
%D 2018
%P 224-248
%V 11
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CGTM_2018_11_a12/
%G en
%F CGTM_2018_11_a12
Fengyan Sun; Elena Parilina. Existence of stable coalition structures in four-person games. Contributions to game theory and management, Tome 11 (2018), pp. 224-248. http://geodesic.mathdoc.fr/item/CGTM_2018_11_a12/

[1] Aumann R. J., Dreze J. H., “Cooperative Games with Coalition Structures”, International Journal of Game Theory, 3 (1974), 217–237 | DOI | MR | Zbl

[2] Carraro C., “The Structure of International Environmental Agreements”, International Environmental Agreements on Climate Change, ed. C. Carraro, Kluwer Academic Publishers, Dordrecht, 1997, 9–26

[3] Driessen T., Funaki Y., “Coincidence of and collinearity between game theoretic solutions”, OR Spectrum, 13:1 (1991), 15–30 | DOI | MR | Zbl

[4] Haeringer G., “Stable Coalition Structures with Fixed Decision Scheme”, Economics with Heterogeneous Interacting Agents, Lecture Notes in Economics and Mathematical Systems, 503, 2001, 217–230 | DOI | MR | Zbl

[5] Hart S., Kurz M., “Endogenous formation of coalitions”, Econometrica, 52 (1983), 1047–1064 | DOI | MR

[6] Parilina E., Sedakov A., “Stable Bank Cooperation for Cost Reduction Problem”, The Czech Economic Review, 8:1 (2014), 7–25 | MR

[7] Parilina E., Sedakov A., “Stable Cooperation in Graph-Restricted Games”, Contributions to Game Theory and Management, 7 (2014), 271–281 | MR

[8] Sedakov A., Parilina E., Volobuev Yu., Klimuk D., “Existence of Stable Coalition Structures in Three-person Games”, Contributions to Game Theory and Management, 6 (2013), 407–422 | MR

[9] Shapley L. S., “A value for n-person games”, Contributions to the Theory of Games, v. II, eds. Kuhn H. W., Tucker A. W., 1953, 307–317 | MR | Zbl