Safety of links with respect to the Myerson value for communication situations

Daniel Li Li () and Erfang Shan ()
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Daniel Li Li: Shanghai Business School
Erfang Shan: Shanghai University

Operational Research, 2022, vol. 22, issue 3, No 16, 2131 pages

Abstract: Abstract Let $$\mu (N,v,L)$$ μ ( N , v , L ) be the Myerson value for graph games (N, v, L). We call a link ij of a graph L safe if $$\mu _k(N,v,L)\ge \mu _k(N,v,L\setminus \{ij\})$$ μ k ( N , v , L ) ≥ μ k ( N , v , L \ { i j } ) for any $$k\in N$$ k ∈ N , which means that none of players benefits from breaking the link ij. A link $$ij\in L$$ i j ∈ L is called a bridge if N splits into more components after ij is deleted. We show that if (N, v) is convex, then any bridge is safe. Furthermore, if (N, v) is strictly convex, then a link is safe if and only if it is a bridge.

Keywords: Cooperative game; Myerson value; Stability; Safety; 91A12; 91A43; 05C57 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s12351-020-00602-5

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