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An optimal bound to access the core in TU-games

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  • Béal, Sylvain
  • Rémila, Eric
  • Solal, Philippe

Abstract

For any transferable utility game in coalitional form with a nonempty core, we show that that the number of blocks required to switch from an imputation out of the core to an imputation in the core is at most n-1, where n is the number of players. This bound exploits the geometry of the core and is optimal. It considerably improves the upper bounds found so far by Koczy (2006), Yang (2010, 2011) and a previous result by ourselves (2012) in which the bound was n(n-1)/2.

Suggested Citation

  • Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2012. "An optimal bound to access the core in TU-games," MPRA Paper 38972, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:38972
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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. John C. Harsanyi, 1974. "An Equilibrium-Point Interpretation of Stable Sets and a Proposed Alternative Definition," Management Science, INFORMS, vol. 20(11), pages 1472-1495, July.
    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. Yang, Yi-You, 2010. "On the accessibility of the core," Games and Economic Behavior, Elsevier, vol. 69(1), pages 194-199, May.
    5. 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.
    6. Yang, Yi-You, 2011. "Accessible outcomes versus absorbing outcomes," Mathematical Social Sciences, Elsevier, vol. 62(1), pages 65-70, July.
    7. Kamal Jain & Rakesh Vohra, 2010. "Extendability and von Neuman–Morgenstern stability of the core," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(4), pages 691-697, October.
    8. Ichiishi, Tatsuro, 1981. "Super-modularity: Applications to convex games and to the greedy algorithm for LP," Journal of Economic Theory, Elsevier, vol. 25(2), pages 283-286, October.
    9. Ray, Debraj, 1989. "Credible Coalitions and the Core," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(2), pages 185-187.
    10. Shellshear, Evan & Sudhölter, Peter, 2009. "On core stability, vital coalitions, and extendability," Games and Economic Behavior, Elsevier, vol. 67(2), pages 633-644, November.
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    Citations

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    Cited by:

    1. 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.
    2. repec:spr:compst:v:78:y:2013:i:2:p:187-202 is not listed on IDEAS
    3. 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.

    More about this item

    Keywords

    Core ; Block ; Weak dominance relation ; Strong dominance relation ; Davis-Maschler reduced games;

    JEL classification:

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

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