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On the accessibility of the core

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  • Yang, Yi-You

Abstract

We define a new notion of dominance, sequential z-dominance, and show that for any TU game with a nonempty core, every process of successive blocks must terminate in the core if the notion of sequential z-dominance is employed. Moreover, this result leads to an upper bound for the number of blocks needed to reach the core, which is lower than the one given in Kóczy (2006).

Suggested Citation

  • Yang, Yi-You, 2010. "On the accessibility of the core," Games and Economic Behavior, Elsevier, vol. 69(1), pages 194-199, May.
  • Handle: RePEc:eee:gamebe:v:69:y:2010:i:1:p:194-199
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    References listed on IDEAS

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    1. Sengupta, Abhijit & Sengupta, Kunal, 1996. "A Property of the Core," Games and Economic Behavior, Elsevier, vol. 12(2), pages 266-273, February.
    2. Koczy, Laszlo A. & Lauwers, Luc, 2007. "The minimal dominant set is a non-empty core-extension," Games and Economic Behavior, Elsevier, vol. 61(2), pages 277-298, November.
    3. Koczy, Laszlo A., 2006. "The core can be accessed with a bounded number of blocks," Journal of Mathematical Economics, Elsevier, vol. 43(1), pages 56-64, December.
    4. Koczy, Laszlo A. & Lauwers, Luc, 2004. "The coalition structure core is accessible," Games and Economic Behavior, Elsevier, vol. 48(1), pages 86-93, July.
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    Citations

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    Cited by:

    1. Yang, Yi-You, 2012. "On the accessibility of core-extensions," Games and Economic Behavior, Elsevier, vol. 74(2), pages 687-698.
    2. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2010. "On the number of blocks required to access the core," MPRA Paper 26578, University Library of Munich, Germany.
    3. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2013. "An optimal bound to access the core in TU-games," Games and Economic Behavior, Elsevier, vol. 80(C), pages 1-9.
    4. Péter Szikora, 2013. "Introduction into the literature of cooperative game theory with special emphasis on dynamic games and the core," Proceedings- 11th International Conference on Mangement, Enterprise and Benchmarking (MEB 2013), Óbuda University, Keleti Faculty of Business and Management.
    5. Szikora Péter, 2011. "Tanítás értelmezhetõ-e, mint egy kooperatív dinamikus játék?," Proceedings- 9th International Conference on Mangement, Enterprise and Benchmarking (MEB 2011), Óbuda University, Keleti Faculty of Business and Management.
    6. Gedai, Endre & Kóczy, László Á. & Zombori, Zita, 2012. "Cluster games: A novel, game theory-based approach to better understand incentives and stability in clusters," MPRA Paper 65095, University Library of Munich, Germany.
    7. Sylvain Béal & Eric Rémila & Philippe Solal, 2013. "Accessibility and stability of the coalition structure core," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 78(2), pages 187-202, October.
    8. Yang, Yi-You, 2011. "Accessible outcomes versus absorbing outcomes," Mathematical Social Sciences, Elsevier, vol. 62(1), pages 65-70, July.
    9. repec:spr:compst:v:78:y:2013:i:2:p:187-202 is not listed on IDEAS
    10. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2011. "On the number of blocks required to access the coalition structure core," MPRA Paper 29755, University Library of Munich, Germany.
    11. Péter Szikora, 2012. "Dynamic cooperative models of coalition formation and the core," Proceedings- 10th International Conference on Mangement, Enterprise and Benchmarking (MEB 2012), Óbuda University, Keleti Faculty of Business and Management.
    12. Bolle Friedel & Otto Philipp E., 2016. "Matching as a Stochastic Process," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 236(3), pages 323-348, May.

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