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Weighted nucleoli and dually essential coalitions

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  • Solymosi, Tamás

Abstract

We consider linearly weighted versions of the least core and the (pre)nucleolus and investigate the reduction possibilities in their computation. We slightly extend some well-known related results and establish their counterparts by using the dual game. Our main results imply, for example, that if the core of the game is not empty, all dually inessential coalitions (which can be weakly minorized by a partition in the dual game) can be ignored when we compute the per-capita least core and the per-capita (pre)nucleolus from the dual game. This could lead to the design of polynomial time algorithms for the per-capita (and other monotone nondecreasingly weighted versions of the) least core and the (pre)nucleolus in specific classes of balanced games with polynomial many dually esential coalitions.

Suggested Citation

  • Solymosi, Tamás, 2016. "Weighted nucleoli and dually essential coalitions," Corvinus Economics Working Papers (CEWP) 2016/12, Corvinus University of Budapest.
    • Handle: RePEc:cvh:coecwp:2016/12
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    References listed on IDEAS

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    1. Kleppe, J., 2010. "Modelling interactive behaviour, and solution concepts," Other publications TiSEM b9b96884-5761-48f0-9ee4-4, Tilburg University, School of Economics and Management.
    2. Jos A. M. Potters & Stef H. Tijs, 1992. "The Nucleolus of a Matrix Game and Other Nucleoli," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 164-174, February.
    3. Potters, J.A.M. & Tijs, S.H., 1992. "The nucleolus of a matrix game and other nucleoli," Other publications TiSEM ae3402e7-bd19-494b-b0a1-f, Tilburg University, School of Economics and Management.
    4. Nimrod Megiddo, 1978. "Computational Complexity of the Game Theory Approach to Cost Allocation for a Tree," Mathematics of Operations Research, INFORMS, vol. 3(3), pages 189-196, August.
    5. Oishi, Takayuki & Nakayama, Mikio & Hokari, Toru & Funaki, Yukihiko, 2016. "Duality and anti-duality in TU games applied to solutions, axioms, and axiomatizations," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 44-53.
    6. Mirjam Groote Schaarsberg & Peter Borm & Herbert Hamers & Hans Reijnierse, 2013. "Game theoretic analysis of maximum cooperative purchasing situations," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(8), pages 607-624, December.
    7. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Maschler, M & Potters, J A M & Tijs, S H, 1992. "The General Nucleolus and the Reduced Game Property," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(1), pages 85-106.
    9. Nguyen, Tri-Dung & Thomas, Lyn, 2016. "Finding the nucleoli of large cooperative games," European Journal of Operational Research, Elsevier, vol. 248(3), pages 1078-1092.
    10. Solymosi, Tamas & Raghavan, Tirukkannamangai E S, 1994. "An Algorithm for Finding the Nucleolus of Asignment Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(2), pages 119-143.
    11. Derks, Jean & Peters, Hans, 1998. "Orderings, excess functions, and the nucleolus," Mathematical Social Sciences, Elsevier, vol. 36(2), pages 175-182, September.
    12. Rodica Brânzei & Tamás Solymosi & Stef Tijs, 2005. "Strongly essential coalitions and the nucleolus of peer group games," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(3), pages 447-460, September.
    13. John Kleppe & Hans Reijnierse & Peter Sudhölter, 2016. "Axiomatizations of symmetrically weighted solutions," Annals of Operations Research, Springer, vol. 243(1), pages 37-53, August.
    14. René Brink & Ilya Katsev & Gerard Laan, 2011. "A polynomial time algorithm for computing the nucleolus for a class of disjunctive games with a permission structure," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(3), pages 591-616, August.
    15. M. Maschler & B. Peleg & L. S. Shapley, 1979. "Geometric Properties of the Kernel, Nucleolus, and Related Solution Concepts," Mathematics of Operations Research, INFORMS, vol. 4(4), pages 303-338, November.
    16. Takayuki Oishi & Mikio Nakayama, 2009. "Anti‐Dual Of Economic Coalitional Tu Games," The Japanese Economic Review, Japanese Economic Association, vol. 60(4), pages 560-566, December.
    17. Maschler, M. & Potters, J.A.M. & Tijs, S.H., 1992. "The general nucleolus and the reduced game property," Other publications TiSEM ab187dab-1b5b-40c3-a673-8, Tilburg University, School of Economics and Management.
    18. Mitsuo Suzuki & Mikio Nakayama, 1976. "The Cost Assignment of the Cooperative Water Resource Development: A Game Theoretical Approach," Management Science, INFORMS, vol. 22(10), pages 1081-1086, June.
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    More about this item

    Keywords

    per-capita (pre)nucleolus; least core; computation;
    All these keywords.

    JEL classification:

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

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