Characterization of a value for games under restricted cooperation
研究了部分联盟收益未知的受限合作博弈，基于Harsanyi红利方法定义了一个值（可视为Shapley值的推广），并用载体、对称伙伴和可加性三个公理刻画该值，最后应用于分析1980年加泰罗尼亚议会的权力分布。
Abstract The object of this paper is to study restricted cooperative games, that is, cooperative games for which the worth of some coalitions is unknown. We consider a value for these restricted cooperative games whose definition is based on the Harsanyi’s dividends approach, and can therefore be seen as an extension of the Shapley value. We provide a characterization of this value with three axioms: Carrier, Symmetric-partnership and Additivity, which are similar to those proposed by Shapley (in: Kuhn and Tucker (eds) Contributions to the theory of games, Princeton University Press, Princeton, 1953). In addition, we characterize this value on the subclass of restricted cooperative simple games. Finally, we apply this value for restricted cooperative games to analyze the power distribution of the Catalonian Parliament in 1980 and compare the results with those of the coalitional value in Carreras and Owen (Math Soc Sci 15:87–92, 1988).