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A mean value for games with communication structures

Author

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  • Gérard Hamiache

Abstract

The mean value is a new extension of the Shapley value for games with communication structure representable by a simple graph; only pairwise meetings can occur, although some of them might not be permitted. The new value is characterized by a set of axioms of which the one with the most far-reaching effect is an associated consistency property already used in various contexts. The mean value of an n-player unanimity game is the arithmetic average of the mean values of (n−1)-player unanimity games with connected support, which means games in which the deleted players are not articulation point of the considered graph. Copyright Springer-Verlag 2004

Suggested Citation

  • Gérard Hamiache, 2004. "A mean value for games with communication structures," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(4), pages 533-544, August.
    • Handle: RePEc:spr:jogath:v:32:y:2004:i:4:p:533-544
    DOI: 10.1007/s001820400175
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    Citations

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    Cited by:

    1. Gérard Hamiache & Florian Navarro, 2020. "Associated consistency, value and graphs," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(1), pages 227-249, March.
    2. Florian Navarro, 2022. "Associated consistency and the Aumann-Drèze value," Post-Print hal-03678064, HAL.
    3. Gérard Hamiache, 2011. "Graph monotonic values," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 37(2), pages 287-307, July.
    4. Navarro, Florian, 2020. "The center value: A sharing rule for cooperative games on acyclic graphs," Mathematical Social Sciences, Elsevier, vol. 105(C), pages 1-13.
    5. Florian Navarro, 2022. "Associated consistency and the Aumann-Drèze value," Working Papers hal-03678064, HAL.

    More about this item

    Keywords

    Shapley value; communication structure; associated game; consistency; graph;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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