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A decomposition for the space of games with externalities

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  • Sanchez-Perez, Joss

Abstract

The main goal of this paper is to present a different perspective than the more `traditional' approaches to study solutions for games with externalities. We provide a direct sum decomposition for the vector space of these games and use the basic representation theory of the symmetric group to study linear symmetric solutions. In our analysis we identify all irreducible subspaces that are relevant to the study of linear symmetric solutions and we then use such decomposition to derive some applications involving characterizations of classes of solutions.

Suggested Citation

  • Sanchez-Perez, Joss, 2015. "A decomposition for the space of games with externalities," MPRA Paper 67932, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:67932
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    File URL: https://mpra.ub.uni-muenchen.de/67932/1/MPRA_paper_67932.pdf
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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. 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.
    3. Kleinberg, Norman L. & Weiss, Jeffrey H., 1986. "Weak values, the core, and new axioms for the Shapley value," Mathematical Social Sciences, Elsevier, vol. 12(1), pages 21-30, August.
    4. Cheng-Cheng Hu & Yi-You Yang, 2010. "An axiomatic characterization of a value for games in partition function form," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 1(4), pages 475-487, September.
    5. 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.
    6. 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.
    7. L. Hernández-Lamoneda & R. Juárez & F. Sánchez-Sánchez, 2007. "Dissection of solutions in cooperative game theory using representation techniques," International Journal of Game Theory, Springer;Game Theory Society, vol. 35(3), pages 395-426, February.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Games with externalities; value; representation theory; symmetric group.;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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