A Reduced Harsanyi Power Solution for Cooperative Games with a Weight Vector

  • Xianghui Li
  • Hao Sun
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 758)


The Harsanyi power solution for cooperative games allocates dividends generated by coalitions proportionally to each player’s power index. Normally, cooperative games tacitly treat all players symmetric. However, the fact is that different players may be asymmetric and contribute to different efforts, bargaining powers, or stability in the process of cooperation. A weight vector is used to reflect players’ asymmetry. In view of these weights are possible to be less than 1, that is, not all players are absolutely important, a loss of dividends of coalitions can happen. We define and characterize a reduced Harsanyi power solution for cooperative games with a weight vector, which is relevant to a loss function of dividends. Moreover, when the loss function takes particular forms, the reduced Harsanyi power solution has a linear relationship with the Harsanyi power solution.


Harsanyi dividend Loss function Reduced Harsanyi power solution 



The research has been supported by the National Natural Science Foundation of China (Grant Nos. 71571143, 71601156, 71671140 and 71271171).


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Copyright information

© Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  1. 1.Department of Applied MathematicsNorthwestern Polytechnical UniversityXi’anPeople’s Republic of China

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