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The positive prekernel of a cooperative game


  • Peleg, Bezalel

    (Center for Mathematical Economics, Bielefeld University)

  • Sudhölter, Peter

    (Center for Mathematical Economics, Bielefeld University)


The positive prekernel, a solution of cooperative transferable utility games, is introduced. We show that this solution inherits many properties of the prekernel and of the core, which are both sub-solutions. It coincides with its individually rational variant, the positive kernel, when applied to any zero-monotonic game. The positive (pre)kernel is a sub-solution of the reactive (pre)bargaining set. We prove that the positive prekernel on the set of games with players belonging to a universe of at least three possible members can be axiomatized by non-emptiness, anonymity, reasonableness, the weak reduced game property, the converse reduced game property, and a weak version of unanimity for two-person games.
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Suggested Citation

  • Peleg, Bezalel & Sudhölter, Peter, 2017. "The positive prekernel of a cooperative game," Center for Mathematical Economics Working Papers 292, Center for Mathematical Economics, Bielefeld University.
  • Handle: RePEc:bie:wpaper:292

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    References listed on IDEAS

    1. Ruud de Mooij & A. Bovenberg, 1998. "Environmental Taxes, International Capital Mobility and Inefficient Tax Systems: Tax Burden vs. Tax Shifting," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 5(1), pages 7-39, February.
    2. Creedy, John & McDonald, Ian M, 1991. "Models of Trade Union Behaviour: A Synthesis," The Economic Record, The Economic Society of Australia, vol. 67(199), pages 346-359, December.
    3. Bovenberg, A. Lans & van der Ploeg, Frederick, 1996. "Optimal taxation, public goods and environmental policy with involuntary unemployment," Journal of Public Economics, Elsevier, vol. 62(1-2), pages 59-83, October.
    4. Bayindir-Upmann, Thorsten & Raith, Matthias G., 2003. "Should high-tax countries pursue revenue-neutral ecological tax reforms?," European Economic Review, Elsevier, vol. 47(1), pages 41-60, February.
    5. Schneider, Kerstin, 1997. " Involuntary Unemployment and Environmental Policy: The Double Dividend Hypothesis," Scandinavian Journal of Economics, Wiley Blackwell, vol. 99(1), pages 45-49, March.
    6. McDonald, Ian M & Solow, Robert M, 1981. "Wage Bargaining and Employment," American Economic Review, American Economic Association, vol. 71(5), pages 896-908, December.
    7. Koskela, Erkki & Schob, Ronnie, 1999. "Alleviating unemployment:: The case for green tax reforms," European Economic Review, Elsevier, vol. 43(9), pages 1723-1746, October.
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    Cited by:

    1. Sudhoelter,P. & Potters,J.A.M., 1999. "The semireactive bargaining set of a cooperative game," Center for Mathematical Economics Working Papers 313, Center for Mathematical Economics, Bielefeld University.
    2. 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.
    3. 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.
    4. Francesc Llerena & Carles Rafels, 2007. "Convex decomposition of games and axiomatizations of the core and the D-core," International Journal of Game Theory, Springer;Game Theory Society, vol. 35(4), pages 603-615, April.

    More about this item


    Betriebssystem; Spieltheorie;

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics


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