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Games with Graph Restricted Communication and Levels Structure of Cooperation

Author

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  • Oriol Tejada

    (ETH-Zurich)

  • Mikel Álvarez-Mozos

    (Universitat de Barcelona)

Abstract

We analyze surplus allocation problems where cooperation between agents is restricted both by a communication graph and by a sequence of embedded partitions of the agent set. For this type of problem, we define and characterize two new values extending the Shapley value and the Banzhaf value respectively. Our results enable the axiomatic comparison between the two values and provide some basic insights for the analysis of fair resource allocation in nowadays fully integrated societies.

Suggested Citation

  • Oriol Tejada & Mikel Álvarez-Mozos, 2017. "Games with Graph Restricted Communication and Levels Structure of Cooperation," UB School of Economics Working Papers 2017/363, University of Barcelona School of Economics.
    • Handle: RePEc:ewp:wpaper:363web
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    File URL: http://hdl.handle.net/2445/114072
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    References listed on IDEAS

    as
    1. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    2. Feltkamp, Vincent, 1995. "Alternative Axiomatic Characterizations of the Shapley and Banzhaf Values," International Journal of Game Theory, Springer;Game Theory Society, vol. 24(2), pages 179-186.
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    4. Vazquez-Brage, Margarita & Garcia-Jurado, Ignacio & Carreras, Francesc, 1996. "The Owen Value Applied to Games with Graph-Restricted Communication," Games and Economic Behavior, Elsevier, vol. 12(1), pages 42-53, January.
    5. José Alonso-Meijide & M. Fiestras-Janeiro, 2002. "Modification of the Banzhaf Value for Games with a Coalition Structure," Annals of Operations Research, Springer, vol. 109(1), pages 213-227, January.
    6. Carolyn L. Evans, 2003. "The Economic Significance of National Border Effects," American Economic Review, American Economic Association, vol. 93(4), pages 1291-1312, September.
    7. Lehrer, E, 1988. "An Axiomatization of the Banzhaf Value," International Journal of Game Theory, Springer;Game Theory Society, vol. 17(2), pages 89-99.
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    9. Winter, Eyal, 1989. "A Value for Cooperative Games with Levels Structure of Cooperation," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(2), pages 227-240.
    10. Alonso-Meijide, J.M. & Álvarez-Mozos, M. & Fiestras-Janeiro, M.G., 2009. "Values of games with graph restricted communication and a priori unions," Mathematical Social Sciences, Elsevier, vol. 58(2), pages 202-213, September.
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    More about this item

    Keywords

    Coalitional games; Restricted cooperation; Graph restricted communication; Levels structure; Shapley value; Banzhaf value.;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

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