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Axiomatizations of the core on the universal domain and other natural domains


  • Peter Sudhölter

    () (Institute of Mathematical Economics, University of Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany)

  • Yan-An Hwang

    (National Dong Hua University, Hualien, Taiwan)


We prove that the core on the set of all transferable utility games with players contained in a universe of at least five members can be axiomatized by the zero inessential game property, covariance under strategic equivalence, anonymity, boundedness, the weak reduced game property, the converse reduced game property, and the reconfirmation property. These properties also characterize the core on certain subsets of games, e.g., on the set of totally balanced games, on the set of balanced games, and on the set of superadditive games. Suitable extensions of these properties yield an axiomatization of the core on sets of nontransferable utility games.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:jogath:v:29:y:2001:i:4:p:597-623 Note: Received September 1999/Final version December 2000

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    References listed on IDEAS

    1. Atila Abdulkadiroğlu & Parag A. Pathak & Alvin E. Roth, 2005. "The New York City High School Match," American Economic Review, American Economic Association, vol. 95(2), pages 364-367, May.
    2. Atila Abdulkadiroglu & Parag A. Pathak & Alvin E. Roth & Tayfun Sönmez, 2006. "Changing the Boston School Choice Mechanism," Boston College Working Papers in Economics 639, Boston College Department of Economics.
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    Cited by:

    1. Guni Orshan & Peter Sudhölter, 2012. "Nonsymmetric variants of the prekernel and the prenucleolus," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(4), pages 809-828, November.
    2. Llerena, Francesc, 2007. "An axiomatization of the core of games with restricted cooperation," Economics Letters, Elsevier, vol. 95(1), pages 80-84, April.
    3. Grabisch, Michel & Sudhölter, Peter, 2014. "On the restricted cores and the bounded core of games on distributive lattices," European Journal of Operational Research, Elsevier, vol. 235(3), pages 709-717.
    4. Albizuri, M. Josune & Sudhölter, Peter, 2014. "On the Core of Games with Communication Structures," Discussion Papers of Business and Economics 6/2014, University of Southern Denmark, Department of Business and Economics.
    5. Yan-An Hwang & Yu-Hsien Liao, 2011. "The multi-core, balancedness and axiomatizations for multi-choice games," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(4), pages 677-689, November.
    6. 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.
    7. Ling-Yun Chung & Yu-Hsien Liao & Wen-Ying Hsieh & Tsu-Yin Chen & Chen-Kun Lin, 2016. "Alternative Reductions and Axiomatizations of the Unit-Level-Core," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(06), pages 1-15, December.
    8. Yan-An Hwang, 2006. "Two characterizations of the consistent egalitarian solution and of the core on NTU games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(3), pages 557-568, December.
    9. Camelia Bejan & Juan Gómez, 2012. "Axiomatizing core extensions," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(4), pages 885-898, November.
    10. repec:hal:cesptp:hal-00759893 is not listed on IDEAS
    11. Yan-An Hwang, 2013. "On the core: complement-reduced game and max-reduced game," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(2), pages 339-355, May.
    12. Gooni Orshan & Peter Sudholter, 2001. "Reconfirming the Prenucleolus," Discussion Paper Series dp267, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    13. repec:hal:cesptp:halshs-00950109 is not listed on IDEAS
    14. M. Albizuri & Peter Sudhölter, 2016. "Characterizations of the core of TU and NTU games with communication structures," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(2), pages 451-475, February.
    15. Michel Grabisch & Peter Sudhölter, 2012. "The bounded core for games with precedence constraints," Annals of Operations Research, Springer, vol. 201(1), pages 251-264, December.
    16. Sudhölter, Peter & Zarzuelo, José M., 2015. "On highway problems," Discussion Papers of Business and Economics 13/2015, University of Southern Denmark, Department of Business and Economics.
    17. Yu-Hsien Liao, 2012. "Converse consistent enlargements of the unit-level-core of the multi-choice games," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 20(4), pages 743-753, December.
    18. 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.
    19. Ling-Yun Chung & Yu-Hsien Liao, 2014. "A Consistent Allocation Rule: Non-emptiness, Reductions, Domination and Axiomatization," Review of Economics & Finance, Better Advances Press, Canada, vol. 4, pages 61-74, November.
    20. Yan-An Hwang & Yu-Hsien Liao, 2010. "The unit-level-core for multi-choice games: the replicated core for TU games," Journal of Global Optimization, Springer, vol. 47(2), pages 161-171, June.
    21. repec:spr:compst:v:64:y:2006:i:3:p:557-568 is not listed on IDEAS
    22. repec:spr:mathme:v:85:y:2017:i:3:d:10.1007_s00186-017-0575-3 is not listed on IDEAS
    23. Ata Atay & Francesc Llerena & Marina Núñez, 2016. "Generalized three-sided assignment markets: core consistency and competitive prices," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 572-593, October.
    24. repec:hal:journl:halshs-00673909 is not listed on IDEAS
    25. Sudhölter, Peter & Zarzuelo, José M., 2017. "Characterizations of highway toll pricing methods," European Journal of Operational Research, Elsevier, vol. 260(1), pages 161-170.

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    TU game · core · kernel; NTU game.;


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