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New axiomatizations of the Owen value

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  • Xun-Feng Hu

    (Guangzhou University)

Abstract

In this paper, we propose three new axiomatizations of the Owen value, similar as the axiomatizations of the Shapley value of Chun (Int J Game Theory 20(2):183–190, 1991), van den Brink (Int J Game Theory 30(3):309–319, 2002), and Manuel et al. (Math Methods Oper Res 77:1–14, 2013), respectively. Firstly, we show that the additivity and null player property in Owen’s (in: Henn and Moeschlin (eds) Mathematical economics and game theory, Springer-Verlog, Berlin, 1977) axiomatization can be weakened into coalitional strategic equivalence. And then, we prove that the coalitional symmetry (respectively symmetry within union) and additivity in Owen’s (in: Henn and Moeschlin (eds) Mathematical economics and game theory, Springer-Verlog, Berlin, 1977) axiomatization can be weakened into a variation of fairness, named as coalitional fairness (respectively fairness within union). Finally, we show that the two fairness axioms in our second axiomatization can be weakened into two axioms, involving a special relation between players, named as indifference. Besides characterizing the Owen value, we also illustrate that our results can be extended to the Winter value, being a common single-valued solution for cooperative games with a level structure.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:93:y:2021:i:3:d:10.1007_s00186-021-00743-z
    DOI: 10.1007/s00186-021-00743-z
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    15. Xun-Feng Hu, 2020. "The weighted Shapley-egalitarian value for cooperative games with a coalition structure," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 193-212, April.
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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. Xinjuan Chen & Minghua Zhan & Zhihui Zhao, 2024. "A characterization of the Owen value via sign symmetries," Theory and Decision, Springer, vol. 97(3), pages 553-561, November.
    3. 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.
    4. André Casajus & Rodrigue Tido Takeng, 2022. "Second-order productivity, second-order payoffs, and the Owen value," Post-Print hal-03798448, HAL.
    5. Zijun Li & Fanyong Meng, 2023. "The potential and consistency of the Owen value for fuzzy cooperative games with a coalition structure," Fuzzy Optimization and Decision Making, Springer, vol. 22(3), pages 387-414, September.

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    More about this item

    Keywords

    Cooperative game; Coalition structure; Owen value; Shapley value; Winter value; Level structure;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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