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Component-wise proportional solutions for communication graph games

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  • Shan, Erfang
  • Zhang, Guang
  • Dong, Yanxia

Abstract

We introduce a class of solutions for graph games by considering the cooperation capacity which represented by bilateral agreements, i.e. degree of nodes in graphs. We replace the axiom of fairness for neighbors proposed by Béal et al. (2012a) by axioms of fairness for degree in order to characterize the component-wise proportional solutions. When a link of a graph is removed, fairness for neighbors states that a player incident to the link and any of his other neighbors should be affected similarly while fairness for degree states that a player incident to the link and all players connected to the player should be affected proportionally to their degree. We first characterize the component-wise proportional solution and the component-wise proportional surplus solution in terms of component efficiency, some kind of fairness for degree and equal treatment or fairness for two-player components. Secondly, we obtain a characterization of the two-step component-wise proportional surplus solution in terms of efficiency, fairness for degree with degree bi-surplus worth, fairness for two-player components and proportional distribution of the surplus.

Suggested Citation

  • Shan, Erfang & Zhang, Guang & Dong, Yanxia, 2016. "Component-wise proportional solutions for communication graph games," Mathematical Social Sciences, Elsevier, vol. 81(C), pages 22-28.
    • Handle: RePEc:eee:matsoc:v:81:y:2016:i:c:p:22-28
    DOI: 10.1016/j.mathsocsci.2016.03.004
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    References listed on IDEAS

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    5. van den Brink, René & Khmelnitskaya, Anna & van der Laan, Gerard, 2012. "An efficient and fair solution for communication graph games," Economics Letters, Elsevier, vol. 117(3), pages 786-789.
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    8. Borm, P.E.M. & Owen, G. & Tijs, S.H., 1992. "On the position value for communication situations," Other publications TiSEM 5a8473e4-1df7-42df-ad53-f, Tilburg University, School of Economics and Management.
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    Cited by:

    1. Daniel Li Li & Erfang Shan, 2017. "Cost sharing on prices for games on graphs," Journal of Combinatorial Optimization, Springer, vol. 34(3), pages 676-688, October.
    2. Shi, Jilei & Shan, Erfang, 2020. "Weighted component-wise solutions for graph games," Economics Letters, Elsevier, vol. 192(C).
    3. Erfang Shan & Guang Zhang & Xiaokang Shan, 2018. "The degree value for games with communication structure," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(3), pages 857-871, September.
    4. Li, Daniel Li & Shan, Erfang, 2023. "Tree solutions and standardness for cycle-free graph games," Economics Letters, Elsevier, vol. 222(C).

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