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

Author

Listed:
  • Daniel Li Li

    (Shanghai Business School
    Shanghai University)

  • Erfang Shan

    (Shanghai University)

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.

Suggested Citation

  • Daniel Li Li & Erfang Shan, 2022. "Safety of links with respect to the Myerson value for communication situations," Operational Research, Springer, vol. 22(3), pages 2121-2131, July.
    • Handle: RePEc:spr:operea:v:22:y:2022:i:3:d:10.1007_s12351-020-00602-5
    DOI: 10.1007/s12351-020-00602-5
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    References listed on IDEAS

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