Computing the Shapley Value of Threshold Cardinality Matching Games

  • Lei Zhao
  • Xin Chen
  • Qizhi Fang
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 758)


The Shapley value is one of the most important solutions on the scheme of distributing the profits among agents in cooperative games. In this paper, we discuss the computational and complexity issues on the Shapley value in a particular multi-agent domain, a threshold cardinality matching game (TCMG). We show that the Shapley value can be calculated in polynomial time when graphs are restricted to some special graphs, such as linear graphs and the graphs having clique or coclique modules decomposition. For general graphs, we prove that calculating the Shapley value is #P-complete when the threshold is a constant.


Shapley value Threshold matching game #P-complete Efficient algorithm 


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Copyright information

© Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  1. 1.School of Mathematical SciencesOcean University of ChinaQingdaoChina

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