Geodesic
Stable cooperation in graph-restricted games
Contributions to game theory and management, Tome 7 (2014), pp. 271-281.

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In the paper we study stable coalition structures in the games with restrictions on players' cooperation and communication. Restriction on cooperation among players is given by a coalition structure, whereas restriction on their communication is described by a graph. Having both a coalition structure and a graph fixed, a payoff distribution can be calculated based on worth of each coalition of players. We use the concept of stability for a coalition structure similar to Nash stability, assuming that the graph structure is fixed. The results are illustrated with examples.
Keywords: cooperation, coalition structure, graph, characteristic function, stability, Shapley value, Myerson value, ES-value. 
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Elena Parilina; Artem Sedakov. Stable cooperation in graph-restricted games. Contributions to game theory and management, Tome 7 (2014), pp. 271-281. http://geodesic.mathdoc.fr/item/CGTM_2014_7_a24/

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

[2] Bogomolnaia A., Jackson M. O., “The Stability of Hedonic Coalition Structures”, Games and Economic Behavior, 38 (2002), 201–230 | DOI | MR | Zbl

[3] Casajus A., “Outside options, component efficiency, and stability”, Games and Economic Behavior, 65 (2009), 49–61 | DOI | MR | Zbl

[4] Caulier J.-F., Mauleon A., Vannetelbosch V., “Contractually stable networks”, International Journal of Game Theory, 42 (2013), 483–499 | DOI | MR | Zbl

[5] Driessen T. S. H., Funaki Y., “Coincidence of and Collinearity between Game Theoretic Solutions”, OR Spektrum, 13:1 (1991), 15–30 | DOI | MR | Zbl

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

[7] Hart S., Kurz M., “Endogenous Formation of Coalitions”, Econometrica, 51:4 (1983), 1047–1064 | DOI | MR | Zbl

[8] Hart S., Kurz M., “Stable coalition structures”, Coalitions and Collective Action, ed. Holler M. J., Physica-Verlag, Heidelberg, 1984, 235–258 | MR

[9] Khmelnitskaya A., “Graph-restricted games with coalition structures”, Contributions to Game Theory and Management, 6, 2010, 220–246 | MR | Zbl

[10] Myerson R., “Graphs and cooperation in games”, Mathematics of Operations Research, 2 (1977), 225–229 | DOI | MR | Zbl

[11] Owen G., “Values of games with a priori unions”, Essays in mathematical economics and game theory, eds. Henn R., Moeschlin O., Springer-Verlag, Berlin, 1977, 76–88 | DOI | MR

[12] Parilina E., Sedakov A., “Coalition structure stability in one model of bank cooperation”, Mathematical Game theory and Applications, 4:4 (2012), 45–62 (in Russian) | Zbl

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

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

[15] Tutic A., “The Aumann-Drèze Value, the Wiese Value, and Stability: A Note”, International Game Theory Review, 12:2 (2010), 189–195 | DOI | MR | Zbl

[16] Vázquez-Brage M., García-Jurado I., Carreras F., “The Owen value applied to games with graph-restricted communication”, Games and Economic Behavior, 12 (1996), 42–53 | DOI | MR