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Weighted component-wise solutions for graph games

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  • Shi, Jilei
  • Shan, Erfang

Abstract

This paper generalizes the component-wise egalitarian solutions (Béal et al., 2012) and component-wise proportional solutions (Shan et al., 2016) on graph games in order to take into account the bargaining powers of players on the allocation of the worth or the centralities of players on the graphs. The bargaining powers or centralities of players are represented by measure functions depending on individuals or the structures of graphs. We define the weighed component-wise solutions such that the payoffs of the players are proportional to their weights. By providing more concise axioms than the previous ones in Béal et al. (2012); Shan et al. (2016), we characterize the weighed component-wise solutions.

Suggested Citation

  • Shi, Jilei & Shan, Erfang, 2020. "Weighted component-wise solutions for graph games," Economics Letters, Elsevier, vol. 192(C).
    • Handle: RePEc:eee:ecolet:v:192:y:2020:i:c:s0165176520301646
    DOI: 10.1016/j.econlet.2020.109233
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    References listed on IDEAS

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    1. 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.
    2. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2012. "Fairness and fairness for neighbors: The difference between the Myerson value and component-wise egalitarian solutions," Economics Letters, Elsevier, vol. 117(1), pages 263-267.
    3. 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.
    4. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    5. René Brink & Gerard Laan & Vitaly Pruzhansky, 2011. "Harsanyi power solutions for graph-restricted games," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(1), pages 87-110, February.
    6. Yoshio Kamijo, 2009. "A Two-Step Shapley Value For Cooperative Games With Coalition Structures," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 11(02), pages 207-214.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    TU-game; Graph game; Myerson value; Proportional solutions; Egalitarian solutions;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D60 - Microeconomics - - Welfare Economics - - - General

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