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Axiomatizing core extensions

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  • Camelia Bejan
  • Juan Gómez

Abstract

We give an axiomatization of the aspiration core on the domain of all TU-games using a relaxed feasibility condition, non-emptiness, individual rationality, and generalized versions of the reduced game property (consistency) and superadditivity. Our axioms also characterize the C-core (Guesnerie and Oddou, Econ Lett 3(4):301–306, 1979 ; Sun et al. J Math Econ 44(7–8):853–860, 2008 ) and the core on appropriate subdomains. The main result of the paper generalizes Peleg’s (J Math Econ 14(2):203–214, 1985 ) core axiomatization to the entire family of TU-games. Copyright Springer-Verlag 2012

Suggested Citation

  • Camelia Bejan & Juan Gómez, 2012. "Axiomatizing core extensions," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(4), pages 885-898, November.
    • Handle: RePEc:spr:jogath:v:41:y:2012:i:4:p:885-898
    DOI: 10.1007/s00182-011-0316-4
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    References listed on IDEAS

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    8. Peter Sudhölter & Yan-An Hwang, 2001. "Axiomatizations of the core on the universal domain and other natural domains," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(4), pages 597-623.
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    Cited by:

    1. Camelia Bejan & Juan Camilo Gómez & Anne van den Nouweland, 2022. "On the importance of reduced games in axiomatizing core extensions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(3), pages 637-668, October.
    2. Gonzalez, Stéphane & Grabisch, Michel, 2016. "Multicoalitional solutions," Journal of Mathematical Economics, Elsevier, vol. 64(C), pages 1-10.
    3. R. Arribillaga, 2015. "Convergence of the approximate cores to the aspiration core in partitioning games," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 521-534, July.
    4. Stéphane Gonzalez & Aymeric Lardon, 2018. "Optimal deterrence of cooperation," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(1), pages 207-227, March.
    5. Stéphane Gonzalez & Michel Grabisch, 2015. "Autonomous coalitions," Annals of Operations Research, Springer, vol. 235(1), pages 301-317, December.
    6. Camelia Bejan & Juan Camilo Gómez, 2017. "Employment lotteries, endogenous firm formation and the aspiration core," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(2), pages 215-226, October.
    7. repec:hal:pseose:halshs-00881108 is not listed on IDEAS
    8. Bejan, Camelia & Gómez, Juan Camilo & van den Nouweland, Anne, 2021. "Feasibility-free axiomatization of the core and its non-empty extension," Economics Letters, Elsevier, vol. 201(C).
    9. Fatma Aslan & Papatya Duman & Walter Trockel, 2020. "Non-cohesive TU-games: Efficiency and Duality," Working Papers CIE 138, Paderborn University, CIE Center for International Economics.
    10. Aslan, Fatma & Duman, Papatya & Trockel, Walter, 2019. "Duality for General TU-games Redefined," Center for Mathematical Economics Working Papers 620, Center for Mathematical Economics, Bielefeld University.
    11. Fatma Aslan & Papatya Duman & Walter Trockel, 2020. "Non-cohesive TU-games: Duality and P-core," Working Papers CIE 136, Paderborn University, CIE Center for International Economics.
    12. repec:hal:pseose:halshs-01235632 is not listed on IDEAS

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    More about this item

    Keywords

    Core extensions; Axiomatization; Aspiration core; C-core; Consistency; C71;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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