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Path cooperative games

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Abstract

Cooperative games provide an appropriate framework for fair and stable profit distribution in multiagent systems. In this paper, we study the algorithmic issues on path cooperative games that arise from the situations where some commodity flows through a network. In these games, a coalition of edges or vertices is successful if they establish a path from the source to the sink in the network, and lose otherwise. Based on dual theory of linear programming and the relationship with flow games, we provide the characterizations on the core, CS-core, least-core and nucleolus of path cooperative games, which implies all of these solution concepts are polynomial-time solvable for path cooperative games.

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Notes

  1. In this paper, we use \(\mathbb {R}_{+}\) to represent the set of nonnegative real numbers.

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Authors and Affiliations

  1. School of Mathematical Sciences, Ocean University of China, Qingdao, 266100, China

    Qizhi Fang

  2. Department of Computer Science, Stony Brook University, Stony Brook, NY, 11794, USA

    Bo Li

  3. CAS Key Lab of Network Data Science and Technology, Institute of Computing Technology, University of Chinese Academy of Sciences, Beijing, 10010, China

    Xiaohan Shan & Xiaoming Sun

Authors
  1. Qizhi Fang
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  2. Bo Li
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  3. Xiaohan Shan
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  4. Xiaoming Sun
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Corresponding author

Correspondence to Xiaohan Shan.

Additional information

An extended abstract of this paper appears at the The 21st Annual International Computing and Combinatorics Conference (COCOON’15) Fang et al. (2015). The first author is supported by the National Natural Science Foundation of China (NSFC) (No. 11271341). The fourth author is supported in part by the National Natural Science Foundation of China Grant 61433014, 61502449, 61602440, the 973 Program of China Grants No. 2016YFB1000201. Finally, we would like to acknowledge our editors and a superb set of anonymous referees for their excellent suggestions.

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Fang, Q., Li, B., Shan, X. et al. Path cooperative games. J Comb Optim 36, 211–229 (2018). https://doi.org/10.1007/s10878-018-0296-4

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