TY - JOUR
T1 - Cooperative games with coalition structures
AU - Aumann, R. J.
AU - Dreze, J. H.
PY - 1974/12
Y1 - 1974/12
N2 - Many game-theoretic solution notions have been defined or can be defined not only with reference to the all-player coalition, but also with reference to an arbitrary coalition structure. In this paper, theorems are established that connect a given solution notion, defined for a coalition structure ℬ with the same solution notion applied to appropriately defined games on each of the coalitions in ℬ. This is done for the kernel, nucleolus, bargaining set, value, core, and the von Neumann-Morgenstern solution. It turns out that there is a single function that plays the central role in five out of the six solution notions in question, though each of these five notions is entirely different. This is an unusual instance of a game theoretic phenomenon that does not depend on a particular solution notion but holds across a wide class of such notions.
AB - Many game-theoretic solution notions have been defined or can be defined not only with reference to the all-player coalition, but also with reference to an arbitrary coalition structure. In this paper, theorems are established that connect a given solution notion, defined for a coalition structure ℬ with the same solution notion applied to appropriately defined games on each of the coalitions in ℬ. This is done for the kernel, nucleolus, bargaining set, value, core, and the von Neumann-Morgenstern solution. It turns out that there is a single function that plays the central role in five out of the six solution notions in question, though each of these five notions is entirely different. This is an unusual instance of a game theoretic phenomenon that does not depend on a particular solution notion but holds across a wide class of such notions.
UR - http://www.scopus.com/inward/record.url?scp=0039119995&partnerID=8YFLogxK
U2 - 10.1007/BF01766876
DO - 10.1007/BF01766876
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AN - SCOPUS:0039119995
SN - 0020-7276
VL - 3
SP - 217
EP - 237
JO - International Journal of Game Theory
JF - International Journal of Game Theory
IS - 4
ER -