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The semireactive bargaining set of a cooperative game

Author

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  • Peter Sudhölter
  • Jos A. M. Potters

Abstract

The semireactive bargaining set, a solution for cooperative games, is introduced. This solution is in general a subsolution of the bargaining set and a supersolution of the reactive bargaining set. However, on various classes of transferable utility games the semireactive and the reactive bargaining set coincide. The semireactive prebargaining set on TU games can be axiomatized by one-person rationality, the reduced game property, a weak version of the converse reduced game property with respect to subgrand coalitions, and subgrand stability. Furthermore, it is shown that there is a suitable weakening of subgrand stability, which allows to characterize the prebargaining set. Replacing the reduced game by the imputation saving reduced game and employing individual rationality as an additional axiom yields characterizations of both, the bargaining set and the semireactive bargaining set.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jogath:v:30:y:2001:i:1:p:117-139
    Note: Received September 2000/Revised version June 2001
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    Citations

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    Cited by:

    1. Tamás Solymosi, 2008. "Bargaining sets and the core in partitioning games," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 16(4), pages 425-440, December.
    2. Meinhardt, Holger Ingmar, 2025. "Polynomial-Time Algorithms for Computing the Nucleolus: An Assessment," MPRA Paper 126932, University Library of Munich, Germany.
    3. 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.
    4. Daniel Granot, 2010. "The reactive bargaining set for cooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 163-170, March.
    5. 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.
    6. Josep M. Izquierdo & Carles Rafels, 2010. "On the coincidence between the Shimomuras bargaining sets and the core," Working Papers in Economics 241, Universitat de Barcelona. Espai de Recerca en Economia.
    7. Josep M Izquierdo & Carles Rafels, 2012. "On the coincidence of the core and the bargaining sets," Economics Bulletin, AccessEcon, vol. 32(3), pages 2035-2043.
    8. Marilda Sotomayor & David Pérez-Castrillo, 2025. "The Tradewise-Function Form for Transferable Utility Games," Working Papers 1481, Barcelona School of Economics.
    9. Morelli, Massimo & Montero, Maria, 2003. "The demand bargaining set: general characterization and application to majority games," Games and Economic Behavior, Elsevier, vol. 42(1), pages 137-155, January.

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