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The Shapley Value For Partition Function Form Games



    (Department of Applied and International Economics, Massey University, Private Bag 11 222, Palmerston North, New Zealand)


    () (Department of Econometrics and Operations Research, and CentER, Tilburg University, P. O. Box 90513, 5000 LE Tilburg, The Netherlands)


Different axiomatizations of the Shapley value for TU games can be found in the literature. The Shapley value has been generalized in several ways to the class of games in partition function form. In this paper we discuss another generalization of the Shapley value and provide a characterization.

Suggested Citation

  • 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.
  • Handle: RePEc:wsi:igtrxx:v:09:y:2007:i:02:n:s021919890700145x
    DOI: 10.1142/S021919890700145X

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    References listed on IDEAS

    1. Zhao, Jingang, 2001. "A characterization for the negative welfare effects of cost reduction in Cournot oligopoly," International Journal of Industrial Organization, Elsevier, vol. 19(3-4), pages 455-469, March.
    2. Reinhard Selten, 1973. "A Simple Model of Imperfect Competition, where 4 are Few and 6 are Many," Center for Mathematical Economics Working Papers 008, Center for Mathematical Economics, Bielefeld University.
    3. Bolger, E M, 1989. "A Set of Axioms for a Value for Partition Function Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(1), pages 37-44.
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    1. repec:wsi:igtrxx:v:09:y:2007:i:03:n:s0219198907001515 is not listed on IDEAS
    2. Joss Sanchez-Perez, 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 Technology, Institute of Organization and Management, vol. 2, pages 97-122.
    3. Grabisch, Michel & Funaki, Yukihiko, 2012. "A coalition formation value for games in partition function form," European Journal of Operational Research, Elsevier, vol. 221(1), pages 175-185.
    4. repec:eee:gamebe:v:108:y:2018:i:c:p:81-92 is not listed on IDEAS
    5. Macho-Stadler, Inés & Pérez-Castrillo, David & Wettstein, David, 2018. "Values for environments with externalities – The average approach," Games and Economic Behavior, Elsevier, vol. 108(C), pages 49-64.
    6. Ines Macho-Stadler & David Perez-Castrillo & David Wettstein, 2017. "Extensions Of The Shapley Value For Environments With Externalities," Working Papers 1716, Ben-Gurion University of the Negev, Department of Economics.
    7. Effrosyni Diamantoudi & Inés Macho-Stadler & David Pérez-Castrillo & Licun Xue, 2015. "Sharing the surplus in games with externalities within and across issues," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 60(2), pages 315-343, October.
    8. Yuan Ju & Peter Borm, 2006. "A Non-cooperative Approach to the Compensation Rules for Primeval Games," Keele Economics Research Papers KERP 2006/18, Centre for Economic Research, Keele University.
    9. Ju, Y., 2004. "The Consensus Value for Games in Partition Function Form," Discussion Paper 2004-60, Tilburg University, Center for Economic Research.
    10. Ju, Yuan & Borm, Peter, 2008. "Externalities and compensation: Primeval games and solutions," Journal of Mathematical Economics, Elsevier, vol. 44(3-4), pages 367-382, February.
    11. Sanchez-Perez, Joss, 2015. "A decomposition for the space of games with externalities," MPRA Paper 67932, University Library of Munich, Germany.
    12. Geoffroy de Clippel & Roberto Serrano, 2008. "Marginal Contributions and Externalities in the Value," Econometrica, Econometric Society, vol. 76(6), pages 1413-1436, November.
    13. M. Álvarez-Mozos & O. Tejada, 2015. "The Banzhaf value in the presence of externalities," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(4), pages 781-805, April.
    14. José María Alonso-Meijide & Mikel Alvarez-Mozos & María Gloria Fiestras-Janeiro & Andrés Jiménez-Losada, 2016. "Some structural properties of a lattice of embedded coalitions," UB Economics Working Papers 2016/349, Universitat de Barcelona, Facultat d'Economia i Empresa, UB Economics.
    15. Yuan Ju & David Wettstein, 2009. "Implementing cooperative solution concepts: a generalized bidding approach," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 39(2), pages 307-330, May.
    16. Toumasatos, Evangelos & Steinshamn, Stein Ivar, 2017. "Coalition Formation with Externalities: The Case of the Northeast Atlantic Mackerel Fishery in a Pre and Post Brexit Context," Discussion Papers 2017/11, Norwegian School of Economics, Department of Business and Management Science.
    17. Casajus, André, 2009. "Outside options, component efficiency, and stability," Games and Economic Behavior, Elsevier, vol. 65(1), pages 49-61, January.
    18. repec:wsi:igtrxx:v:08:y:2006:i:03:n:s0219198906000941 is not listed on IDEAS
    19. Pham Do, K.H. & Folmer, H., 2003. "International Fisheries Agreements : The Feasibility and Impacts of Partial Cooperation," Discussion Paper 2003-52, Tilburg University, Center for Economic Research.
    20. repec:eee:gamebe:v:108:y:2018:i:c:p:65-80 is not listed on IDEAS
    21. repec:spr:jogath:v:46:y:2017:i:1:d:10.1007_s00182-016-0530-1 is not listed on IDEAS
    22. Fukuda, E. & Tijs, S.H. & Brânzei, R. & Muto, S., 2002. "Compromising in Partition Function Form Games and Cooperation in Perfect Extensive Form," Discussion Paper 2002-117, Tilburg University, Center for Economic Research.
    23. Hafalir, Isa E., 2007. "Efficiency in coalition games with externalities," Games and Economic Behavior, Elsevier, vol. 61(2), pages 242-258, November.
    24. Maria Ekes, 2013. "Application of Generalized Owen Value for Voting Games in Partition Function Form," Collegium of Economic Analysis Annals, Warsaw School of Economics, Collegium of Economic Analysis, issue 32, pages 43-53.

    More about this item


    Partition function form game; Shapley value;

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics


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