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The Positive Prekernel Of A Cooperative Game

Author

Listed:
  • PETER SUDHÖLTER

    (Institute of Mathematical Economics, University of Bielefeld, P.O. Box 100131, D-33501 Bielefeld, Germany)

  • BEZALEL PELEG

    (Center for Rationality and Interactive Decision Theory, The Hebrew University of Jerusalem, Feldman Building, Givat-Ram, 91904 Jerusalem, Israel)

Abstract

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.

Suggested Citation

  • Peter Sudhölter & Bezalel Peleg, 2000. "The Positive Prekernel Of A Cooperative Game," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 2(04), pages 287-305.
    • Handle: RePEc:wsi:igtrxx:v:02:y:2000:i:04:n:s0219198900000196
    DOI: 10.1142/S0219198900000196
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    Cited by:

    1. Peter Sudhölter & Jos A. M. Potters, 2001. "The semireactive bargaining set of a cooperative game," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(1), pages 117-139.
    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.
    5. Michel Grabisch & Hervé Moulin & José Manuel Zarzuelo, 2024. "Professor Peter Sudhölter (1957–2024)," International Journal of Game Theory, Springer;Game Theory Society, vol. 53(2), pages 289-294, June.

    More about this item

    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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