Geodesic
Graph-Restricted Games with Coalition Structures
Contributions to game theory and management, Tome 3 (2010), pp. 220-246

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We consider a new model of a TU game endowed with both coalition and two-level cooperation structures that applies to various network situations. The approach to the value is close to that of both Myerson (1977) and Aumann and Drèze (1974): it is based on ideas of component efficiency and of one or another deletion link property, and it treats an a priori union as a self-contained unit; moreover, our approach incorporates also the idea of the Owen's quotient game property (1977). The axiomatically introduced values possess an explicit formula representation and in many cases can be quite simply computed. The results obtained are applied to the problem of sharing an international river among multiple users without international firms.
Keywords: TU game, coalition structure, cooperation structure, Myerson value, Owen value, Aumann–Drèze value, component efficiency, deletion link property. 
@article{CGTM_2010_3_a17,
     author = {Anna B. Khmelnitskaya},
     title = {Graph-Restricted {Games} with {Coalition} {Structures}},
     journal = {Contributions to game theory and management},
     pages = {220--246},
     publisher = {mathdoc},
     volume = {3},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CGTM_2010_3_a17/}
}
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Anna B. Khmelnitskaya. Graph-Restricted Games with Coalition Structures. Contributions to game theory and management, Tome 3 (2010), pp. 220-246. http://geodesic.mathdoc.fr/item/CGTM_2010_3_a17/