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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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    File URL: http://hdl.handle.net/10.1007/s00182-011-0316-4
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    References listed on IDEAS

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    1. Sun, Ning & Trockel, Walter & Yang, Zaifu, 2008. "Competitive outcomes and endogenous coalition formation in an n-person game," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 853-860, July.
    2. Guesnerie, R. & Oddou, C., 1979. "On economic games which are not necessarily superadditive : Solution concepts and application to a local public good problem with few a agents," Economics Letters, Elsevier, vol. 3(4), pages 301-306.
    3. Serrano, Roberto & Volij, Oscar, 1998. "Axiomatizations of neoclassical concepts for economies," Journal of Mathematical Economics, Elsevier, vol. 30(1), pages 87-108, August.
    4. Tadenuma, K, 1992. "Reduced Games, Consistency, and the Core," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(4), pages 325-334.
    5. Hart, Sergiu, 1985. "An Axiomatization of Harsanyi's Nontransferable Utility Solution," Econometrica, Econometric Society, vol. 53(6), pages 1295-1313, November.
    6. Peleg, B, 1986. "On the Reduced Game Property and Its Converse," International Journal of Game Theory, Springer;Game Theory Society, vol. 15(3), pages 187-200.
    7. Aumann, Robert J, 1985. "An Axiomatization of the Non-transferable Utility Value," Econometrica, Econometric Society, vol. 53(3), pages 599-612, May.
    8. Peleg, Bezalel, 1985. "An axiomatization of the core of cooperative games without side payments," Journal of Mathematical Economics, Elsevier, vol. 14(2), pages 203-214, April.
    9. Guni Orshan & Peter Sudhölter, 2010. "The positive core of a cooperative game," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 113-136, March.
    10. 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.
    11. Keiding, Hans, 1986. "An axiomatization of the core of a cooperative game," Economics Letters, Elsevier, vol. 20(2), pages 111-115.
    12. Hokari, Toru & Kibris, Ozgur, 2003. "Consistency, converse consistency, and aspirations in TU-games," Mathematical Social Sciences, Elsevier, vol. 45(3), pages 313-331, July.
    13. Voorneveld, Mark & van den Nouweland, Anne, 1998. "A new axiomatization of the core of games with transferable utility," Economics Letters, Elsevier, vol. 60(2), pages 151-155, August.
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    Citations

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    Cited by:

    1. 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.
    2. Stéphane Gonzalez & Michel Grabisch, 2015. "Autonomous coalitions," Annals of Operations Research, Springer, vol. 235(1), pages 301-317, December.
    3. Stéphane Gonzalez & Aymeric Lardon, 2016. "Optimal Deterrence of Cooperation," GREDEG Working Papers 2016-22, Groupe de REcherche en Droit, Economie, Gestion (GREDEG CNRS), University of Nice Sophia Antipolis, revised Jun 2017.
    4. Gonzalez, Stéphane & Grabisch, Michel, 2016. "Multicoalitional solutions," Journal of Mathematical Economics, Elsevier, vol. 64(C), pages 1-10.
    5. repec:spr:etbull:v:5:y:2017:i:2:d:10.1007_s40505-017-0115-6 is not listed on IDEAS
    6. Stéphane Gonzalez & Michel Grabisch, 2015. "Autonomous coalitions," Annals of Operations Research, Springer, vol. 235(1), pages 301-317, December.
    7. Gonzalez, Stéphane & Grabisch, Michel, 2016. "Multicoalitional solutions," Journal of Mathematical Economics, Elsevier, vol. 64(C), pages 1-10.
    8. R. Pablo Arribillaga, 2016. "Axiomatizing core extensions on NTU games," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(3), pages 585-600, August.

    More about this item

    Keywords

    Core extensions; Axiomatization; Aspiration core; C-core; Consistency; C71;

    JEL classification:

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

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