Cooperative games with restricted formation of coalitions

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• 作者：Gleb Koshevoy^a ; ^{koshevoy@cemi.rssi.ru} ; Takamasa Suzuki^b ; ^{tsuzuki@inf.kyushu-u.ac.jp} ; Dolf Talman^c ; ^{talman@tilburguniversity.edu}
• 关键词：Set system ; Rooted tree ; Core ; Convexity ; Marginal vector ; Shapley value
• 刊名：Discrete Applied Mathematics
• 出版年：2017
• 出版时间：19 February 2017
• 年：2017
• 卷：218
• 期：Complete
• 页码：1-13
• 全文大小：443 K
• 卷排序：218

文摘

In the study of cooperative games, restricted cooperation between players is typically modeled by a set system of feasible coalitions of the players. In this paper, we go one step further and allow for a distinction among players within a feasible coalition, between those who are able to form the coalition and those who are not. This defines a contracting map, a choice function. We introduce the notion of quasi-building system and require that such a choice function gives rise to a quasi-building system. Many known set systems and structures studied in the literature are covered by quasi-building systems. For transferable utility games having a quasi-building system as cooperation structure we take as a solution the average of the marginal vectors that correspond to the set of rooted trees that are compatible with the quasi-building system. Properties of this solution, called the AMV-value, are studied. Relations with other solutions in the literature are also studied. To establish that the AMV-value is an element of the core, we introduce appropriate convexity-type conditions for the game with respect to the underlying quasi-building system. In case of universal cooperation, the AMV-value coincides with the Shapley value.