TY - JOUR
T1 - The collective value
T2 - A new solution for games with coalition structures
AU - Kamijo, Yoshio
N1 - Funding Information:
This research is supported by the Japanese Ministry of Education, Culture, Sports, Science and Technology under the Waseda 21st COE-GLOPE project.
PY - 2013/10
Y1 - 2013/10
N2 - In this study, we provide a new solution for cooperative games with coalition structures. The collective value of a player is defined as the sum of the equal division of the pure surplus obtained by his coalition from the coalitional bargaining and of his Shapley value for the internal coalition. The weighted Shapley value applied to a game played by coalitions with coalition-size weights is assigned to each coalition, reflecting the size asymmetries among coalitions. We show that the collective value matches exogenous interpretations of coalition structures and provide an axiomatic foundation of this value. A noncooperative mechanism that implements the collective value is also presented.
AB - In this study, we provide a new solution for cooperative games with coalition structures. The collective value of a player is defined as the sum of the equal division of the pure surplus obtained by his coalition from the coalitional bargaining and of his Shapley value for the internal coalition. The weighted Shapley value applied to a game played by coalitions with coalition-size weights is assigned to each coalition, reflecting the size asymmetries among coalitions. We show that the collective value matches exogenous interpretations of coalition structures and provide an axiomatic foundation of this value. A noncooperative mechanism that implements the collective value is also presented.
KW - Axiomatization
KW - Coalition structure
KW - Coalition-size weights
KW - Implementation
KW - Two-step Shapley value
KW - Weighted Shapley value
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U2 - 10.1007/s11750-011-0191-y
DO - 10.1007/s11750-011-0191-y
M3 - Article
AN - SCOPUS:84885907193
VL - 21
SP - 572
EP - 589
JO - TOP
JF - TOP
SN - 1134-5764
IS - 3
ER -