A value for cooperative games with coalition and probabilistic graph structures

Jilei Shi, Lei Cai, Erfang Shan () and Wenrong Lyu
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Jilei Shi: Shanghai University
Lei Cai: Shanghai University
Erfang Shan: Shanghai University
Wenrong Lyu: Shanghai University

Journal of Combinatorial Optimization, 2022, vol. 43, issue 3, No 8, 646-671

Abstract: Abstract In this paper we generalize TU-games with coalition and graph structures to TU-games with coalition and probabilistic graph structures. We introduce the probabilistic graph-partition value and we show that the value is uniquely determined by the axioms of probabilistic graph efficiency, probabilistic balanced contributions and probabilistic collective balanced contributions and the axioms of probabilistic graph efficiency, probabilistic balanced contributions, probabilistic balanced per capita contributions and either probabilistic fairness for joining the grand coalition or probabilistic population solidarity within unions, respectively. Also, we apply this value to China’s railway network and compare it with other values.

Keywords: TU-game; Probabilistic graph; Coalition structure; Graph-partition value; 91A12; 91A43; 05C57; C71; D60 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10878-021-00805-2

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