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An application of the representations of symmetric groups to characterizing solutions of games in partition function form

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  • Joss Sánchez-Pérez
Abstract
A different perspective from the more “traditional” approaches to studying solutions of games in partition function form has been presented. We provide a decomposition of the space of such games under the action of the symmetric group, for the cases with three and four players. In particular, we identify all the irreducible subspaces that are relevant to the study of linear symmetric solutions. We then use such a decomposition to derive a characterization of the class of linear and symmetric solutions, as well as of the class of linear, symmetric and efficient solutions.

Suggested Citation

  • Joss Sánchez-Pérez, 2014. "An application of the representations of symmetric groups to characterizing solutions of games in partition function form," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 24(2), pages 97-122.
    • Handle: RePEc:wut:journl:v:2:y:2014:p:97-122:id:1088
    DOI: 10.5277/ord140205
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    References listed on IDEAS

    as
    1. Yuan Ju, 2007. "The Consensus Value For Games In Partition Function Form," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 9(03), pages 437-452.
    2. M. J. Albizuri & J. Arin & J. Rubio, 2005. "An Axiom System For A Value For Games In Partition Function Form," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 7(01), pages 63-72.
    3. Geoffroy de Clippel & Roberto Serrano, 2008. "Marginal Contributions and Externalities in the Value," Econometrica, Econometric Society, vol. 76(6), pages 1413-1436, November.
    4. Kim Hang Pham Do & Henk Norde, 2007. "The Shapley Value For Partition Function Form Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 9(02), pages 353-360.
    5. R. M. Thrall & W. F. Lucas, 1963. "N‐person games in partition function form," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 10(1), pages 281-298, March.
    6. Macho-Stadler, Ines & Perez-Castrillo, David & Wettstein, David, 2007. "Sharing the surplus: An extension of the Shapley value for environments with externalities," Journal of Economic Theory, Elsevier, vol. 135(1), pages 339-356, July.
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    Cited by:

    1. Sanchez-Perez, Joss, 2015. "A decomposition for the space of games with externalities," MPRA Paper 67932, University Library of Munich, Germany.

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