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Owen coalitional value without additivity axiom

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  • Anna Khmelnitskaya
  • Elena Yanovskaya

Abstract

We show that the Owen value for TU games with coalition structure can be characterized without the additivity axiom similarly as it was done by Young for the Shapley value for general TU games. Our axiomatization via four axioms of efficiency, marginality, symmetry across coalitions, and symmetry within coalitions is obtained from the original Owen’s one by the replacement of additivity and null-player via marginality. We show that the alike axiomatization for the generalization of the Owen value suggested by Winter for games with level structure is valid as well. Copyright Springer-Verlag 2007

Suggested Citation

  • Anna Khmelnitskaya & Elena Yanovskaya, 2007. "Owen coalitional value without additivity axiom," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(2), pages 255-261, October.
    • Handle: RePEc:spr:mathme:v:66:y:2007:i:2:p:255-261
    DOI: 10.1007/s00186-006-0119-8
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    References listed on IDEAS

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    1. 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.
    2. Anna B. Khmelnitskaya, 2003. "Shapley value for constant-sum games," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(2), pages 223-227, December.
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    Cited by:

    1. Sylvain Béal & Marc Deschamps & Mostapha Diss & Rodrigue Tido Takeng, 2024. "Cooperative games with diversity constraints," Working Papers hal-04447373, HAL.
    2. Riccardo Ferretti & Giovanni Gallo & Andrea Landi & Valeria Venturelli, 2018. "Market-Book Ratios of European Banks: What Does Explain the Structural Fall?," Centro Studi di Banca e Finanza (CEFIN) (Center for Studies in Banking and Finance) 18011, Universita di Modena e Reggio Emilia, Dipartimento di Economia "Marco Biagi".
    3. Meng, Fanyong & Chen, Xiaohong & Zhang, Qiang, 2015. "A coalitional value for games on convex geometries with a coalition structure," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 605-614.
    4. Pulido, Manuel A. & Sánchez-Soriano, Joaquín, 2009. "On the core, the Weber set and convexity in games with a priori unions," European Journal of Operational Research, Elsevier, vol. 193(2), pages 468-475, March.
    5. Knezevic, David & Krüger, Niclas & Nordström, Martin, 2019. "A Guarantee – Does the Obligee Agree? A Risk Premium Decomposition of Sub-Sovereign Bond Spreads," Working Papers 2019:12, Örebro University, School of Business.
    6. C. Manuel & E. González-Arangüena & R. Brink, 2013. "Players indifferent to cooperate and characterizations of the Shapley value," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(1), pages 1-14, February.
    7. André Casajus & Rodrigue Tido Takeng, 2023. "Second-order productivity, second-order payoffs, and the Owen value," Annals of Operations Research, Springer, vol. 320(1), pages 1-13, January.
    8. Riccardo Ferretti & Giovanni Gallo & Andrea Landi & Valeria Venturelli, 2018. "Market-Book Ratios of European Banks: What Does Explain the Structural Fall?," Centro Studi di Banca e Finanza (CEFIN) (Center for Studies in Banking and Finance) 0065, Universita di Modena e Reggio Emilia, Dipartimento di Economia "Marco Biagi".
    9. Guangming Wang & Zeguang Cui & Erfang Shan, 2022. "An Axiomatization of the Value α for Games Restricted by Augmenting Systems," Mathematics, MDPI, vol. 10(15), pages 1-9, August.
    10. Michael Jones & Jennifer Wilson, 2013. "Two-step coalition values for multichoice games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(1), pages 65-99, February.
    11. Besner, Manfred, 2017. "Weighted Shapley levels values," MPRA Paper 82978, University Library of Munich, Germany.
    12. André Casajus, 2010. "Another characterization of the Owen value without the additivity axiom," Theory and Decision, Springer, vol. 69(4), pages 523-536, October.
    13. Gómez-Rúa, María & Vidal-Puga, Juan, 2010. "The axiomatic approach to three values in games with coalition structure," European Journal of Operational Research, Elsevier, vol. 207(2), pages 795-806, December.
    14. J. C. Gonçalves-Dosantos & I. García-Jurado & J. Costa & J. M. Alonso-Meijide, 2022. "Necessary players and values," Annals of Operations Research, Springer, vol. 318(2), pages 935-961, November.
    15. André Casajus & Rodrigue Tido Takeng, 2022. "Second-order productivity, second-order payoffs, and the Owen value," Post-Print hal-03798448, HAL.
    16. Manfred Besner, 2022. "Harsanyi support levels solutions," Theory and Decision, Springer, vol. 93(1), pages 105-130, July.
    17. Besner, Manfred, 2018. "The weighted Shapley support levels values," MPRA Paper 87617, University Library of Munich, Germany.
    18. Erfang Shan, 2023. "Marginality and a Characterization of the Owen Graph value," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(2), pages 451-461, June.
    19. Xun-Feng Hu & Deng-Feng Li, 2021. "The Equal Surplus Division Value for Cooperative Games with a Level Structure," Group Decision and Negotiation, Springer, vol. 30(6), pages 1315-1341, December.
    20. Xun-Feng Hu, 2021. "New axiomatizations of the Owen value," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(3), pages 585-603, June.
    21. Silvia Lorenzo-Freire, 2017. "New characterizations of the Owen and Banzhaf–Owen values using the intracoalitional balanced contributions property," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(3), pages 579-600, October.
    22. Hüttner, Frank & Sunder, Marco, 2011. "Decomposing R2 with the Owen value," Working Papers 100, University of Leipzig, Faculty of Economics and Management Science.
    23. Besner, Manfred, 2023. "The per capita Shapley support levels value," MPRA Paper 116457, University Library of Munich, Germany.

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