Implementation of weighted values in hierarchical and horizontal cooperation structures |
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| Institution: | 1. Korea University, Republic of Korea;2. University of Exeter, United Kingdom;1. School of Management, Qufu Normal University, Rizhao 276826, China;2. School of Management, Shanghai University, Shanghai 200444, China;3. Department of Mathematics, Shanghai University, Shanghai 200444, China;1. College of Business, Korea Advanced Institute of Science and Technology, 291 Daehak-ro, Yuseong-gu, Daejeon 34141, Republic of Korea;2. Department of Economics, Yale University, 28 Hillhouse Avenue, New Haven CT 06511, USA |
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| Abstract: | This paper studies a non-cooperative mechanism implementing a cooperative solution for a situation in which members of a society are subdivided into groups and/or coalitions and there is asymmetry among the individuals of the society. To describe hierarchical and horizontal cooperation structure simultaneously, we present unified classes of games, the games with social structure, and define a weighted value for these games. We show that our mechanism works in any zero-monotonic environment and implements the Shapley value, the weighted Shapley value, the Owen’s coalitional value, and the weighted coalitional value, in some special cases. |
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