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Computing the Shapley Value of Threshold Cardinality Matching Games

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Book cover Game Theory and Applications (China GTA 2016, China-Dutch GTA 2016)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 758))

Abstract

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.

The work is partially supported by National Natural Science Foundation of China (NSFC) (No. 11271341 and 11501316).

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Authors and Affiliations

  1. School of Mathematical Sciences, Ocean University of China, Qingdao, China

    Lei Zhao, Xin Chen & Qizhi Fang

Authors
  1. Lei Zhao
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  2. Xin Chen
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  3. Qizhi Fang
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Corresponding author

Correspondence to Xin Chen .

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Editors and Affiliations

  1. Fuzhou University, Fuzhou, Fujian, China

    Deng-Feng Li

  2. Chinese Academy of Sciences, Beijing, China

    Xiao-Guang Yang

  3. University of Twente, Enschede, The Netherlands

    Marc Uetz

  4. Northwestern Polytechnical University, Xi'an, China

    Gen-Jiu Xu

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Zhao, L., Chen, X., Fang, Q. (2017). Computing the Shapley Value of Threshold Cardinality Matching Games. In: Li, DF., Yang, XG., Uetz, M., Xu, GJ. (eds) Game Theory and Applications. China GTA China-Dutch GTA 2016 2016. Communications in Computer and Information Science, vol 758. Springer, Singapore. https://doi.org/10.1007/978-981-10-6753-2_13

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  • DOI: https://doi.org/10.1007/978-981-10-6753-2_13

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  • Print ISBN: 978-981-10-6752-5

  • Online ISBN: 978-981-10-6753-2

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