Geodesic
Existence of Stable Coalition Structures in Three-person Games
Contributions to game theory and management, Tome 6 (2013), pp. 407-422

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Cooperative games with coalition structures are considered and the principle of coalition structure stability with respect to 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. We also consider a specific model of cooperative cost-saving game among banks as an application. In the model, the characteristic function assigning the cost-saving game has a special form. For the model the software product is developed and illustrative examples are provided.
Keywords: coalition structure, stability, Shapley value, equal surplus division value. 
@article{CGTM_2013_6_a31,
     author = {Artem Sedakov and Elena Parilina and Yury Volobuev and Daria Klimuk},
     title = {Existence of {Stable} {Coalition} {Structures} in {Three-person} {Games}},
     journal = {Contributions to game theory and management},
     pages = {407--422},
     publisher = {mathdoc},
     volume = {6},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CGTM_2013_6_a31/}
}
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Artem Sedakov; Elena Parilina; Yury Volobuev; Daria Klimuk. Existence of Stable Coalition Structures in Three-person Games. Contributions to game theory and management, Tome 6 (2013), pp. 407-422. http://geodesic.mathdoc.fr/item/CGTM_2013_6_a31/